Teamwork Approach to Hearing Aids Innovations

**Chapter 8**

**Abstract**

Variation of Sensitivity of a MEMS

Capacitive Accelerometer Based

The present research seeks to improve a highly sensitive MEMS capacitive accelerometer as a probable completely implantable hearing aid microphone. The research analyses the effect of different suspension system topologies on accelerometer efficiency. The topology of folded beam suspension is considered to be the most suitable for the proposed system. The design factors such as weight, height and resonant frequency are considered to make the accelerometer an effective

accelerometer occupies 1mm2 of sensing area and achieves a nominal capacitance of

**Keywords:** Microelectromechanical system (MEMS), totally implantable hearing aid (TIHA), capacitive accelerometer, mechanical amplification, microlever,

The universe is perceived by means of the five senses. By conjunction these five senses determine the nature of our world experience. If some meaning is lacking it removes a whole aspect of life. Similarly, the quality of life experience for people with hearing loss is significantly diminished. An individual with a completely functioning sense of hearing can hardly understand the suffering of those living with the hearing impairment. WHO reports that 15 percent of the world's adults, or approximately 766 million people, are experiencing the substantial loss of audience [1]. In India this figure is alarmingly more than 63 million, according to Varshney [2]. In most cases of hearing loss, traditional hearing aids may offer effective rehabilitation, but the societal stigma linked with wearing external hearing aids prohibits several patients from even talking about such devices. Consequently, semiimplantable middle ear and cochlear prosthetic devices are increasingly approved. Over the years, curiosity in middle ear implants has grown significantly to facilitate patients with traditional hearing aids who do not get sufficient assistance [3].

biomedical system which can be completely implanted with COMSOL MULTIPHYSICS 4.2 the optimized system is simulated and validated. The

5.30 pF and an optimized capacitive sensitivity of 6.89fF.

Microphone with Suspension

*Apoorva Dwivedi, Prateek Asthana, Gargi Khanna*

System Topology

*and Tarun Chaudhary*

sound pressure level (SPL)

**1. Introduction**

**111**

#### **Chapter 8**

## Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with Suspension System Topology

*Apoorva Dwivedi, Prateek Asthana, Gargi Khanna and Tarun Chaudhary*

#### **Abstract**

The present research seeks to improve a highly sensitive MEMS capacitive accelerometer as a probable completely implantable hearing aid microphone. The research analyses the effect of different suspension system topologies on accelerometer efficiency. The topology of folded beam suspension is considered to be the most suitable for the proposed system. The design factors such as weight, height and resonant frequency are considered to make the accelerometer an effective biomedical system which can be completely implanted with COMSOL MULTIPHYSICS 4.2 the optimized system is simulated and validated. The accelerometer occupies 1mm2 of sensing area and achieves a nominal capacitance of 5.30 pF and an optimized capacitive sensitivity of 6.89fF.

**Keywords:** Microelectromechanical system (MEMS), totally implantable hearing aid (TIHA), capacitive accelerometer, mechanical amplification, microlever, sound pressure level (SPL)

#### **1. Introduction**

The universe is perceived by means of the five senses. By conjunction these five senses determine the nature of our world experience. If some meaning is lacking it removes a whole aspect of life. Similarly, the quality of life experience for people with hearing loss is significantly diminished. An individual with a completely functioning sense of hearing can hardly understand the suffering of those living with the hearing impairment. WHO reports that 15 percent of the world's adults, or approximately 766 million people, are experiencing the substantial loss of audience [1]. In India this figure is alarmingly more than 63 million, according to Varshney [2]. In most cases of hearing loss, traditional hearing aids may offer effective rehabilitation, but the societal stigma linked with wearing external hearing aids prohibits several patients from even talking about such devices. Consequently, semiimplantable middle ear and cochlear prosthetic devices are increasingly approved. Over the years, curiosity in middle ear implants has grown significantly to facilitate patients with traditional hearing aids who do not get sufficient assistance [3].

Electromagnetics-based middle ear implants [4, 5] and Piezoelectric [6, 7] have been developed for hearing loss gain. Such techniques, however, do not offer protection from damage to cochlear hair cells in hearing loss. While current cochlear implants that are partially implantable treat injured hair cells in the cochlea through direct stimulation of the auditory nerve, they remain dependent on external microphone, speech processor, and radiofrequency (RF) coils [8]. The everpresent need for invisibility has fuelled the creation of a completely implantable hearing aid to free the patient from the extreme loss of hearing without any social stigma.

section addresses the sensor's operating theory and assessing the stiffness constant as a suspension mechanism for various springs. The fourth section explains the outcomes of the modelling and simulation followed by a conclusion in Section 5.

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with…*

Various forms of TIHAs have been documented in the literature, such as Totally Implantable Communication Assistance (TICA) [13], Totally Implantable Cochlear Implant (TICI/TIKI) [14], Carina [15, 16], and Esteem [15–17]. Carina and TIKI, implanted in the temporal bone under the skin, experience severe body noise amplification during mastication, sound attenuation and head contact distortion due to the skin's sound-filtering effect. TICA and Esteem, when implanted in the ear canal or ossicular chain, solved those issues. Yet they are susceptible to the feedback problem between the embedded microphone and the sound source. The literature recorded MEMS capacitive sensor based microphones [18–20]. They are put straight on the umbo. Regrettably, this approach can induce a significant damping effect on the frequency response of the ossicular middle ear chain at frequencies above 1 kHz due to the loading of sensor weight on the umbo [18–20]. Yip et al. [21] have suggested a piezoelectric sensor as a microphone of the FIHA. The umbo is placed at one end of the microphone, and the middle- wall is connected at the other end. The microphone, however, suffers from the problem of feedback, because it resembles Esteem. Woo et al. [22] introduces a trans- microphone. It consists of a ventilation tube mounted in the eardrum along with a connected acoustic duct with an electret microphone at the end extending into the middle-ear cavity. The method presented potential benefits, such as comparatively quick surgery, exceptional sound collection and protection from any outside impact. The possible disadvantages, however, contain the tube dropping into the ear canal or middle ear cavity, the fluid entering the tube, and the sensitivity loss, and the cerumen covering the microphone, and inhibiting sound collection. Koch et al. [23] presents a piezoelectric transducer which is implanted into the incudostapedial joint gap. While it provides advantages such as relatively easy installation and revocable surgery, the

**2. Development of totally implantable hearing aids**

*DOI: http://dx.doi.org/10.5772/intechopen.97185*

transducer suffers from low frequency (<1 KHz) output degradation.

Young et al.'s proposed model is the mass loading effect.

**113**

From the literature review it was observed that the system proposed by Young et al. [20] using the capacitive sensing scheme used provides many advantages over the other types: fairly simple mechanical structure compared to other types; henceforth easy manufacturing, excellent linearity, good noise efficiency, a reduced amount of power consumption and very small temperature-induced drift. Together with the mechanical elements, the capacitance sensing signal conditioning circuit can also be monolithically mounted on the same substratum. The only downside of

The present paper proposes changes to Young's approach by using different topologies of the suspension system taking into account their effect on device sensitivity. The impact of loading can be evaded by maintaining the sensor's total packed mass below 20 mg. In addition, the overall prototype microsystem will show a packed dimension of less than 3.5 mm for implantation on the umbo without impacting other structures inside the middle ear cavity. The tip of the umbo usually has a scale between 1.5 mm and 2 mm. The accelerometer is therefore built within a compact 1 mm/1 mm band. Absolute umbo acceleration along the primary axis is around 1 g [18–20]. As per audiologists, the loudness of regular human communication is about 60 dB SPL (sound pressure level), and the typical voice speech is in the frequency range from 500 Hz to 8000 Hz. The accelerometer is worked within the normal range of speech conversation frequency, in which the response is flat.

Although current partially implantable cochlear implants are being increaasingly used, their usage of an external microphone, speech processor and radio frequency (RF) coils has still not addressed the issue of social stigma and embarrassment. The need to provide the users freedom from the psychological discomfort, physical inconvenience and offer improved performance has accelerated the exploration and growth of fully implantable hearing aids (FIHAs). The FIHAs, with all the elements implanted internally and using the natural sound conduction of the body, eliminate many of the issues like sound filtering, improved sound amplification, problem of feedback, ringing issues and social prejudice faced in conventional hearing aids.

The MEMS capacitive accelerometer described in the paper is designed to be placed on umbo to act as a middle ear microphone as shown in **Figure 1**. Optimizing the geometry of the device has already increased the performance of the accelerometer [9–12]. This article studies the effect of various suspension system (spring) topologies on the sensitivity of the accelerometer and then proposes the most suitable suspension system for enhanced performance. The optimized model satisfies the requisite design requirements regarding the fully implantable microphone's surgical placement.

The article consists of 5 parts. The first segment discusses the implementation of hearing aids based on MEMS which are entirely implantable. The second segment describes the development of hearing aids which are entirely implantable. The third

**Figure 1.** *Proposed fully implantable microphone in middle ear.*

section addresses the sensor's operating theory and assessing the stiffness constant as a suspension mechanism for various springs. The fourth section explains the outcomes of the modelling and simulation followed by a conclusion in Section 5.

### **2. Development of totally implantable hearing aids**

Various forms of TIHAs have been documented in the literature, such as Totally Implantable Communication Assistance (TICA) [13], Totally Implantable Cochlear Implant (TICI/TIKI) [14], Carina [15, 16], and Esteem [15–17]. Carina and TIKI, implanted in the temporal bone under the skin, experience severe body noise amplification during mastication, sound attenuation and head contact distortion due to the skin's sound-filtering effect. TICA and Esteem, when implanted in the ear canal or ossicular chain, solved those issues. Yet they are susceptible to the feedback problem between the embedded microphone and the sound source. The literature recorded MEMS capacitive sensor based microphones [18–20]. They are put straight on the umbo. Regrettably, this approach can induce a significant damping effect on the frequency response of the ossicular middle ear chain at frequencies above 1 kHz due to the loading of sensor weight on the umbo [18–20]. Yip et al. [21] have suggested a piezoelectric sensor as a microphone of the FIHA. The umbo is placed at one end of the microphone, and the middle- wall is connected at the other end. The microphone, however, suffers from the problem of feedback, because it resembles Esteem. Woo et al. [22] introduces a trans- microphone. It consists of a ventilation tube mounted in the eardrum along with a connected acoustic duct with an electret microphone at the end extending into the middle-ear cavity. The method presented potential benefits, such as comparatively quick surgery, exceptional sound collection and protection from any outside impact. The possible disadvantages, however, contain the tube dropping into the ear canal or middle ear cavity, the fluid entering the tube, and the sensitivity loss, and the cerumen covering the microphone, and inhibiting sound collection. Koch et al. [23] presents a piezoelectric transducer which is implanted into the incudostapedial joint gap. While it provides advantages such as relatively easy installation and revocable surgery, the transducer suffers from low frequency (<1 KHz) output degradation.

From the literature review it was observed that the system proposed by Young et al. [20] using the capacitive sensing scheme used provides many advantages over the other types: fairly simple mechanical structure compared to other types; henceforth easy manufacturing, excellent linearity, good noise efficiency, a reduced amount of power consumption and very small temperature-induced drift. Together with the mechanical elements, the capacitance sensing signal conditioning circuit can also be monolithically mounted on the same substratum. The only downside of Young et al.'s proposed model is the mass loading effect.

The present paper proposes changes to Young's approach by using different topologies of the suspension system taking into account their effect on device sensitivity. The impact of loading can be evaded by maintaining the sensor's total packed mass below 20 mg. In addition, the overall prototype microsystem will show a packed dimension of less than 3.5 mm for implantation on the umbo without impacting other structures inside the middle ear cavity. The tip of the umbo usually has a scale between 1.5 mm and 2 mm. The accelerometer is therefore built within a compact 1 mm/1 mm band. Absolute umbo acceleration along the primary axis is around 1 g [18–20]. As per audiologists, the loudness of regular human communication is about 60 dB SPL (sound pressure level), and the typical voice speech is in the frequency range from 500 Hz to 8000 Hz. The accelerometer is worked within the normal range of speech conversation frequency, in which the response is flat.

Electromagnetics-based middle ear implants [4, 5] and Piezoelectric [6, 7] have been developed for hearing loss gain. Such techniques, however, do not offer protection from damage to cochlear hair cells in hearing loss. While current

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

stigma.

**Figure 1.**

**112**

*Proposed fully implantable microphone in middle ear.*

phone's surgical placement.

cochlear implants that are partially implantable treat injured hair cells in the cochlea through direct stimulation of the auditory nerve, they remain dependent on external microphone, speech processor, and radiofrequency (RF) coils [8]. The everpresent need for invisibility has fuelled the creation of a completely implantable hearing aid to free the patient from the extreme loss of hearing without any social

Although current partially implantable cochlear implants are being increaasingly used, their usage of an external microphone, speech processor and radio frequency (RF) coils has still not addressed the issue of social stigma and embarrassment. The need to provide the users freedom from the psychological discomfort, physical inconvenience and offer improved performance has accelerated the exploration and growth of fully implantable hearing aids (FIHAs). The FIHAs, with all the elements implanted internally and using the natural sound conduction of the body, eliminate many of the issues like sound filtering, improved sound amplification, problem of feedback, ringing issues and social prejudice faced in conventional hearing aids. The MEMS capacitive accelerometer described in the paper is designed to be placed on umbo to act as a middle ear microphone as shown in **Figure 1**. Optimizing the geometry of the device has already increased the performance of the accelerometer [9–12]. This article studies the effect of various suspension system (spring) topologies on the sensitivity of the accelerometer and then proposes the most suitable suspension system for enhanced performance. The optimized model satisfies the requisite design requirements regarding the fully implantable micro-

The article consists of 5 parts. The first segment discusses the implementation of hearing aids based on MEMS which are entirely implantable. The second segment describes the development of hearing aids which are entirely implantable. The third Consequently, the accelerometer's resonant frequency is chosen to be higher than the standard frequency range for human conversation. Yet the resonant frequency can not be too high; then the displacement of the confirmed mass decreases. The accelerometer was therefore designed to set the resonant frequency at about 10,000 Hz.

#### **3. Working principle of the device**

#### **3.1 Structural design**

The comb drive capacitive accelerometer used in this work includes four folded beams as a suspension device and a handheld finger seismic mass as shown in **Figure 2**. A comb drive structure consists of a set of pairs of capacitive fingers instead of one capacitive plate. Another set is fixed, and the other set remains movable. Further the two anchors are set also. The four folded beams bind each of the anchors to the movable central seismic mass. Let's say; x1 is the distances between the set finger and the movable finger on the left and x2 on the right.

On the umbo is set the capacitive accelerometer. The eardrum vibrates in response to incoming sound causing the umbo to vibrate along with it. The pressure coming in exerts a force on the sensor. The seismic mass with the moving fingers shifts in the direction of body force under the impact of this force, which changes the power between the moving and the fixed finger. The capacitance shift is calculated using a low noise electronic interface circuitry.

The input umbo acceleration *a,* causes a body force *Fext* to act on the accelerometer with effective mass *Me.*

$$F\_{\text{ext}} = \mathbf{M}\_{\text{c}} \mathbf{a} \tag{1}$$

Δ*x <sup>a</sup>* <sup>¼</sup> *Me ke*

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with…*

Δ*x <sup>a</sup>* <sup>¼</sup> <sup>1</sup> *ω*2 0

where ω<sup>0</sup> is the resonant angular frequency.

*DOI: http://dx.doi.org/10.5772/intechopen.97185*

frequency at 10000 Hz.

*3.2.1 Folded beam*

**Figure 3.**

**115**

*A folded beam structure.*

**3.2 Stiffness constant evaluation**

The resonant frequency of the sensor is given as *<sup>f</sup>* <sup>0</sup> <sup>¼</sup> <sup>1</sup>

eter geometry which affects the sensitivity of the device.

was resolved into three constituents organized in a row.

constant (*k1/4)* of one such folded beam is given in Eq. (6) as.

1 *k*1*=*<sup>4</sup> ¼ 1 *kc*<sup>1</sup> þ 1 *kc*<sup>2</sup> þ 1 *kc*<sup>3</sup>

*ω*<sup>0</sup> ¼

That also reflects the sensitivity of the unit to mechanical/displacement. The Eq. (3) shows that the device's displacement sensitivity has a direct relation to the seismic mass and an inverse relationship to the accelerometer's stiffness constant. Hence, the device's displacement sensitivity can be amplified by increasing the seismic mass and reducing the system's stiffness constant. The displacement sensitivity is inversely proportional to the square of the resonant angular frequency.

> <sup>¼</sup> *Me ke*

> > ffiffiffiffiffiffi *ke Me*

> > > 2*π*

ffiffiffiffi *ke Me* q .

s

The values of mass and stiffness constant are determined to keep the resonant

The seismic mass can be suspended using various topology suspension systems (springs) based on 1) geometry: standard folded and round folded; 2) beam orientation: standard folded and inverted folded, and 3) series combination of springs. Each of these different types of suspension systems produces a specific accelerom-

**Figure 3** indicates a folded beam-structure. The structure of the folded beam

The accelerometer is composed of four folded beams as springs. The stiffness

(3)

(4)

(5)

(6)

The acceleration applied displaces the seismic mass by a distance of *Δx* from its mean spot. The force needed to displace the seismic mass is given.

$$F\_{spring} = k\_{\varepsilon} \Delta x \tag{2}$$

where *ke* is the effective spring constant. In the equilibrium condition when Fext = Fspring, we get.

**Figure 2.** *Prototype of the capacitive accelerometer.*

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with… DOI: http://dx.doi.org/10.5772/intechopen.97185*

$$\frac{\Delta\infty}{a} = \frac{M\_{\epsilon}}{k\_{\epsilon}}\tag{3}$$

That also reflects the sensitivity of the unit to mechanical/displacement. The Eq. (3) shows that the device's displacement sensitivity has a direct relation to the seismic mass and an inverse relationship to the accelerometer's stiffness constant. Hence, the device's displacement sensitivity can be amplified by increasing the seismic mass and reducing the system's stiffness constant. The displacement sensitivity is inversely proportional to the square of the resonant angular frequency.

$$\frac{\Delta\mathbf{x}}{a} = \frac{1}{\alpha\_0^2} = \frac{M\_\epsilon}{k\_\epsilon} \tag{4}$$

$$
\rho\_0 = \sqrt{\frac{k\_\epsilon}{M\_\epsilon}}\tag{5}
$$

where ω<sup>0</sup> is the resonant angular frequency.

The resonant frequency of the sensor is given as *<sup>f</sup>* <sup>0</sup> <sup>¼</sup> <sup>1</sup> 2*π* ffiffiffiffi *ke Me* q .

The values of mass and stiffness constant are determined to keep the resonant frequency at 10000 Hz.

#### **3.2 Stiffness constant evaluation**

The seismic mass can be suspended using various topology suspension systems (springs) based on 1) geometry: standard folded and round folded; 2) beam orientation: standard folded and inverted folded, and 3) series combination of springs. Each of these different types of suspension systems produces a specific accelerometer geometry which affects the sensitivity of the device.

#### *3.2.1 Folded beam*

Consequently, the accelerometer's resonant frequency is chosen to be higher than the standard frequency range for human conversation. Yet the resonant frequency can not be too high; then the displacement of the confirmed mass decreases. The accelerometer was therefore designed to set the resonant frequency at about

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

The comb drive capacitive accelerometer used in this work includes four folded

The input umbo acceleration *a,* causes a body force *Fext* to act on the accelerom-

The acceleration applied displaces the seismic mass by a distance of *Δx* from its

where *ke* is the effective spring constant. In the equilibrium condition when

mean spot. The force needed to displace the seismic mass is given.

*Fext* ¼ *Mea* (1)

*Fspring* ¼ *ke*Δ*x* (2)

beams as a suspension device and a handheld finger seismic mass as shown in **Figure 2**. A comb drive structure consists of a set of pairs of capacitive fingers instead of one capacitive plate. Another set is fixed, and the other set remains movable. Further the two anchors are set also. The four folded beams bind each of the anchors to the movable central seismic mass. Let's say; x1 is the distances between the set finger and the movable finger on the left and x2 on the right. On the umbo is set the capacitive accelerometer. The eardrum vibrates in response to incoming sound causing the umbo to vibrate along with it. The pressure coming in exerts a force on the sensor. The seismic mass with the moving fingers shifts in the direction of body force under the impact of this force, which changes the power between the moving and the fixed finger. The capacitance shift is calcu-

10,000 Hz.

**3.1 Structural design**

eter with effective mass *Me.*

Fext = Fspring, we get.

**Figure 2.**

**114**

*Prototype of the capacitive accelerometer.*

**3. Working principle of the device**

lated using a low noise electronic interface circuitry.

**Figure 3** indicates a folded beam-structure. The structure of the folded beam was resolved into three constituents organized in a row.

The accelerometer is composed of four folded beams as springs. The stiffness constant (*k1/4)* of one such folded beam is given in Eq. (6) as.

$$\mathbf{x}\_{k\_1} = \begin{array}{c} \mathbf{1}\_{k\_1} = \frac{1}{k\_{c1}} + \frac{1}{k\_{c2}} + \frac{1}{k\_{c3}} \\ \mathbf{1}\_{k\_2} \\ \mathbf{1}\_{k\_3} \\ \mathbf{1}\_{k\_4} \\ \mathbf{1}\_{k\_5} \\ \vdots \\ \mathbf{1}\_{k\_{c1}} \end{array} \tag{6}$$

**Figure 3.** *A folded beam structure.*

where *kc1*, *kc2*, and *kc3* are the stiffness constants [23] for the constituent 1 (C1), constituent 2 (C2) and constituent 3 (C3) respectively given as.

$$\frac{1}{k\_{c1}} = \frac{L\_s^{\,^3}}{12EI\_s} + \frac{6(1+\mu)L\_s}{5W\_s} \tag{7}$$

*3.2.3 Round folded beam*

1 *ke* ¼ 1 *Et*

**Figure 5.**

**Table 1.**

**117**

*A round folded beam structure.*

identical to the regular folded beam.

*DOI: http://dx.doi.org/10.5772/intechopen.97185*

*Ls* 3 2*Ws* 3 þ

*3.2.4 Series combination of springs*

1 *kc*<sup>2</sup> <sup>¼</sup> <sup>24</sup>*r*<sup>3</sup> *Ws* 3 *π* <sup>16</sup> � <sup>1</sup> *π* þ

The total stiffness constant is thus obtained by Eq. (14).

3 1ð Þ þ *μ* 5*Ws*

combinations from the sequence are shown in **Figure 6**.

A circular folded beam is made of round edges rather than rectangular edges as seen in **Figure 5**. For constituent 1 and constituent 3 the stiffness constants are

� �

!

From Eq. (4) it is detected that the displacement of the seismic mass increases with decreasing stiffness. Thus, a sequence of combinations of springs may be used to improve evidence mass displacement. Since the area of the proposed system is limited, however, the addition of a series of combinations of springs leads to a reduction in the width of the seismic mass resulting in a decrease in the seismic mass and thus a decrease in the displacement as shown in **Table 1**. Therefore a compromise is needed when choosing the combination of the pair. Some of the

The stiffness constants and seismic mass width for different arrangements of springs are given by **Table 1**. *Wpm* denotes the width of the seismic mass, *Wa* is the

**Number of springs in series The width of the proof mass (m) Stiffness constant**

 *Wpm* <sup>¼</sup> <sup>1000</sup> � <sup>10</sup>�<sup>6</sup> � <sup>2</sup>ð Þ *Wa* <sup>þ</sup> <sup>2</sup>*Ws* <sup>þ</sup> *Db ke Wpm* <sup>¼</sup> <sup>1000</sup> � <sup>10</sup>�<sup>6</sup> � <sup>4</sup>ð*Wa* <sup>þ</sup> <sup>2</sup>*Ws* <sup>þ</sup> *Db*Þ � <sup>2</sup>*Db ke/2 Wpm* <sup>¼</sup> <sup>1000</sup> � <sup>10</sup>�<sup>6</sup> � <sup>6</sup>ð*Wa* <sup>þ</sup> <sup>2</sup>*Ws* <sup>þ</sup> *Db*Þ � <sup>4</sup>*Db ke/3 Wpm* <sup>¼</sup> <sup>1000</sup> � <sup>10</sup>�<sup>6</sup> � <sup>8</sup>ð*Wa* <sup>þ</sup> <sup>2</sup>*Ws* <sup>þ</sup> *Db*Þ � <sup>6</sup>*Db ke/4 Wpm* <sup>¼</sup> <sup>1000</sup> � <sup>10</sup>�<sup>6</sup> � <sup>10</sup>ð*Wa* <sup>þ</sup> <sup>2</sup>*Ws* <sup>þ</sup> *Db*Þ � <sup>8</sup>*Db ke/5*

*Proof mass widths and stiffness constants for a different combination of springs.*

1 24*π* þ 3*πL*<sup>2</sup> *sr* 4*W*<sup>3</sup> *s*

> 1 24*π*

þ 3*πL*<sup>2</sup> *sr* 4*W*<sup>3</sup> *s*

� �

(13)

(14)

The stiffness constant for the constituent 2 is evaluated by [25] as.

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with…*

þ 24*r*<sup>3</sup> *Ws* 3 *π* <sup>16</sup> � <sup>1</sup> *π* þ

As C1 and C2 constituents are of same dimensions, the stiffness constant of both these components are equal as given below.

$$\frac{1}{k\_{c3}} = \frac{1}{k\_{c1}}\tag{8}$$

$$\frac{1}{k\_{c2}} = \frac{L\_{c2}}{EA\_{c2}} - \frac{L\_{s}L\_{c2}^{2}}{4EI\_{c2}}\tag{9}$$

where *E* is the modulus of elasticity of the material, *Ls* is the length of the spring beam, *Lc2* is the length of the transverse bar, *Wc2* is the width of the bar, *Ws* is the width of the spring beam, *<sup>I</sup>* <sup>¼</sup> *tWs* 3 <sup>12</sup> is the moment of inertia of component 1, *Ic*<sup>2</sup> ¼ *tWc*<sup>2</sup> 3 <sup>12</sup> is the moment of inertia of component 2, *Ac*<sup>2</sup> ¼ *tWc*<sup>2</sup> is the area of cross-section of component 2. *Wc2* is the same as *Ws*.

As the four springs have the same geometry and are made of same material, the effective stiffness constant *ke* [24] is evaluated by Eqs. (10) and (11) as.

$$\frac{1}{k\_{\epsilon}} = \frac{1}{4k\_{1/4}}\tag{10}$$

$$\frac{1}{k\_{\varepsilon}} = \frac{1}{Et} \left( \frac{L\_{\star}^{\circ}}{2W\_{\circ}^{\circ}} + \frac{\mathfrak{Z}(1+\mu)}{5W\_{\circ}} + \frac{L\_{\circ 2}}{4W\_{\circ 2}} - \frac{\mathfrak{Z}L\_{\circ}L\_{\circ 2}^{2}}{4W\_{\circ 2}^{3}} \right) \tag{11}$$

#### *3.2.2 Inverted folded beam*

The inverted folded beam, as seen in **Figure 4**, differs from folded beam only in terms of suspension orientation. The constant of stiffness is measured the same way as for the regular folded beam. In this case, it will require two supplementary support constituents identical to component 2 to connect the beam to the seismic mass and anchor. Adding both of these constituents gives us the constant stiffness as.

$$\frac{1}{k\_{\varepsilon}} = \frac{1}{Et} \left( \frac{L\_{\varepsilon}^{\frac{3}{3}}}{2W\_{\varepsilon}^{\frac{3}{3}}} + \frac{3(1+\mu)}{5W\_{\varepsilon}} + \frac{3L\_{\varepsilon 2}}{4W\_{\varepsilon 2}} - \frac{9L\_{\varepsilon}L\_{\varepsilon 2}^2}{4W\_{\varepsilon 2}^3} \right) \tag{12}$$

**Figure 4.** *An inverted folded beam as a suspension system in an accelerometer.*

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with… DOI: http://dx.doi.org/10.5772/intechopen.97185*

#### *3.2.3 Round folded beam*

where *kc1*, *kc2*, and *kc3* are the stiffness constants [23] for the constituent 1 (C1),

As C1 and C2 constituents are of same dimensions, the stiffness constant of both

¼ 1 *kc*<sup>1</sup>

where *E* is the modulus of elasticity of the material, *Ls* is the length of the spring beam, *Lc2* is the length of the transverse bar, *Wc2* is the width of the bar, *Ws* is the

<sup>12</sup> is the moment of inertia of component 2, *Ac*<sup>2</sup> ¼ *tWc*<sup>2</sup> is the area of cross-section

As the four springs have the same geometry and are made of same material, the

<sup>¼</sup> <sup>1</sup> 4*k*1*=*<sup>4</sup>

The inverted folded beam, as seen in **Figure 4**, differs from folded beam only in terms of suspension orientation. The constant of stiffness is measured the same way as for the regular folded beam. In this case, it will require two supplementary support constituents identical to component 2 to connect the beam to the seismic mass and anchor. Adding both of these constituents gives us the constant stiffness as.

> 3 1ð Þ þ *μ* 5*Ws*

þ 3*Lc*<sup>2</sup> 4*Wc*<sup>2</sup>

!

þ *Lc*<sup>2</sup> 4*Wc*<sup>2</sup>

!

3 1ð Þ þ *μ* 5*Ws*

� *LsL*<sup>2</sup> *c*2 4*EIc*<sup>2</sup>

<sup>12</sup> is the moment of inertia of component 1, *Ic*<sup>2</sup> ¼

� <sup>3</sup>*LsL*<sup>2</sup> *c*2 4*W*<sup>3</sup> *c*2

� <sup>9</sup>*LsL*<sup>2</sup>

*c*2 4*W*<sup>3</sup> *c*2

6 1ð Þ þ *μ Ls* 5*Ws*

(7)

(8)

(9)

(10)

(11)

(12)

constituent 2 (C2) and constituent 3 (C3) respectively given as.

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

1 *kc*<sup>1</sup>

these components are equal as given below.

width of the spring beam, *<sup>I</sup>* <sup>¼</sup> *tWs*

of component 2. *Wc2* is the same as *Ws*.

1 *ke* ¼ 1 *Et*

1 *ke* ¼ 1 *Et*

*3.2.2 Inverted folded beam*

*tWc*<sup>2</sup> 3

**Figure 4.**

**116**

<sup>¼</sup> *Ls* 3 12*EIs* þ

> 1 *kc*<sup>3</sup>

<sup>¼</sup> *Lc*<sup>2</sup> *EAc*<sup>2</sup>

1 *kc*<sup>2</sup>

3

effective stiffness constant *ke* [24] is evaluated by Eqs. (10) and (11) as.

*Ls* 3 2*Ws* <sup>3</sup> þ

*Ls* 3 2*Ws* <sup>3</sup> þ

*An inverted folded beam as a suspension system in an accelerometer.*

1 *ke*

A circular folded beam is made of round edges rather than rectangular edges as seen in **Figure 5**. For constituent 1 and constituent 3 the stiffness constants are identical to the regular folded beam.

The stiffness constant for the constituent 2 is evaluated by [25] as.

$$\frac{1}{k\_{c2}} = \frac{24r^3}{W\_s^{\,3}} \left( \frac{\pi}{16} - \frac{1}{\pi} + \frac{1}{24\pi} \right) + \frac{3\pi L\_s^2 r}{4W\_s^3} \tag{13}$$

The total stiffness constant is thus obtained by Eq. (14).

$$\frac{1}{k\_{\varepsilon}} = \frac{1}{Et} \left( \frac{L\_{\circ}^{\circ}}{2W\_{\circ}^{\circ}} + \frac{3(1+\mu)}{5W\_{\circ}} + \frac{24r^{3}}{W\_{\circ}^{\circ}} \left( \frac{\pi}{16} - \frac{1}{\pi} + \frac{1}{24\pi} \right) + \frac{3\pi L\_{\circ}^{2}r}{4W\_{\circ}^{3}} \right) \tag{14}$$

#### *3.2.4 Series combination of springs*

From Eq. (4) it is detected that the displacement of the seismic mass increases with decreasing stiffness. Thus, a sequence of combinations of springs may be used to improve evidence mass displacement. Since the area of the proposed system is limited, however, the addition of a series of combinations of springs leads to a reduction in the width of the seismic mass resulting in a decrease in the seismic mass and thus a decrease in the displacement as shown in **Table 1**. Therefore a compromise is needed when choosing the combination of the pair. Some of the combinations from the sequence are shown in **Figure 6**.

The stiffness constants and seismic mass width for different arrangements of springs are given by **Table 1**. *Wpm* denotes the width of the seismic mass, *Wa* is the

**Figure 5.** *A round folded beam structure.*


**Table 1.** *Proof mass widths and stiffness constants for a different combination of springs.*

#### *Hearing Loss - From Multidisciplinary Teamwork to Public Health*

width of the anchor, *Ws* is the width of the spring beam, and *Db* is the gap spacing

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with…*

the Rayleigh principle [24] as shown in Eqs. (15)-(17).

Effective mass due to the transverse bar is.

Effective mass due to the beam is.

*DOI: http://dx.doi.org/10.5772/intechopen.97185*

The effective mass of the folded suspension beam has been calculated by using

*Mb*,*<sup>e</sup>* <sup>¼</sup> <sup>13</sup>*ρWstLs*

The accelerometer's effective mass consists mainly of the evidence mass and smaller spring beam contributions. Consider the folded beam segment shown in

*Mpm* ¼ *tρ LpmWpm* þ 2*N fL fW <sup>f</sup>*

where *Lf* is the length of the finger, *Lpm* is the length of the seismic mass, and *Wpm* is the width of the seismic mass. The number of sensing fingers *Nf* on each side of the seismic mass is restricted by the width of the central seismic mass. Depending

*<sup>=</sup>* <sup>2</sup>*<sup>W</sup> <sup>f</sup>* <sup>þ</sup> *<sup>x</sup>*<sup>1</sup> <sup>þ</sup> *<sup>x</sup>*<sup>2</sup>

The seismic mass for other spring combinations can be determined along similar

The sum of the capacitance from each side depends on the finger width *Wf*, finger overlap length *Lf0*, dielectric constant *K*, relative permittivity *ϵ0*, device layer thickness *t*, the number of sensing fingers *Nf* and the air gap between adjacent

where C0 is the capacitance between the fixed and movable fingers as depicted by Eq. (21) and Cpm is the capacitance between the movable fingers and the seismic

*Mt*,*<sup>e</sup>* <sup>¼</sup> <sup>1</sup> 3

Four folded beams exist, with each beam having two lateral parts. Consequently, the whole of eight sections add to the effective mass represented in Eq. (17) by the first term. Each folded beam has a transverse section. So, as seen in the second term in Eq. (17), the mass due to the transverse section is multiplied by four times. The seismic mass contains the mass on either side of the seismic mass due to the rectangular disk, and the mass due to the comb fingers.

**Figure 4**. Therefore the total effective accelerometer mass is.

on the various constraints, they can be calculated as.

*N <sup>f</sup>* ¼ *Wpm* � 2*p <sup>f</sup>*

<sup>35</sup> (15)

*ρWc*2*tLc*<sup>2</sup> (16)

*Me* ¼ 8*Mb*,*<sup>e</sup>* þ 4*Mt*,*<sup>e</sup>* þ *Mpm* (17)

(18)

*Ct*<sup>0</sup> <sup>¼</sup> *<sup>C</sup>*<sup>0</sup> <sup>þ</sup> *Cpm* (20)

(19)

within the spring beam.

The test of proof is.

**3.3 Capacitance evaluation**

fingers. It can be expressed by.

mass body as shown by Eq. (22) in **Figure 7**.

lines.

**119**

**Figure 6.** *Different series combination of springs (a) two springs, (b) three springs, (c) four springs and (d) five springs in series respectively.*

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with… DOI: http://dx.doi.org/10.5772/intechopen.97185*

width of the anchor, *Ws* is the width of the spring beam, and *Db* is the gap spacing within the spring beam.

The effective mass of the folded suspension beam has been calculated by using the Rayleigh principle [24] as shown in Eqs. (15)-(17).

Effective mass due to the beam is.

$$M\_{b, \epsilon} = \frac{\mathbf{1} \mathbf{3} \rho W\_s t L\_s}{\mathbf{3} \mathbf{5}} \tag{15}$$

Effective mass due to the transverse bar is.

$$M\_{t, \varepsilon} = \frac{1}{3} \rho W\_{\varepsilon 2} t L\_{\varepsilon 2} \tag{16}$$

The accelerometer's effective mass consists mainly of the evidence mass and smaller spring beam contributions. Consider the folded beam segment shown in **Figure 4**. Therefore the total effective accelerometer mass is.

$$M\_{\varepsilon} = 8M\_{b,\varepsilon} + 4M\_{l,\varepsilon} + M\_{pm} \tag{17}$$

Four folded beams exist, with each beam having two lateral parts. Consequently, the whole of eight sections add to the effective mass represented in Eq. (17) by the first term. Each folded beam has a transverse section. So, as seen in the second term in Eq. (17), the mass due to the transverse section is multiplied by four times. The seismic mass contains the mass on either side of the seismic mass due to the rectangular disk, and the mass due to the comb fingers. The test of proof is.

$$\mathbf{M}\_{pm} = \mathbf{t}\rho \left(\mathbf{L}\_{pm}\mathbf{W}\_{pm} + 2\mathbf{N}\_{f}\mathbf{L}\_{f}\mathbf{W}\_{f}\right) \tag{18}$$

where *Lf* is the length of the finger, *Lpm* is the length of the seismic mass, and *Wpm* is the width of the seismic mass. The number of sensing fingers *Nf* on each side of the seismic mass is restricted by the width of the central seismic mass. Depending on the various constraints, they can be calculated as.

$$N\_f = \left(W\_{pm} - 2p\_f\right) / \left(2W\_f + \varkappa\_1 + \varkappa\_2\right) \tag{19}$$

The seismic mass for other spring combinations can be determined along similar lines.

#### **3.3 Capacitance evaluation**

The sum of the capacitance from each side depends on the finger width *Wf*, finger overlap length *Lf0*, dielectric constant *K*, relative permittivity *ϵ0*, device layer thickness *t*, the number of sensing fingers *Nf* and the air gap between adjacent fingers. It can be expressed by.

$$\mathbf{C}\_{t0} = \left(\mathbf{C}\_0 + \mathbf{C}\_{pm}\right) \tag{20}$$

where C0 is the capacitance between the fixed and movable fingers as depicted by Eq. (21) and Cpm is the capacitance between the movable fingers and the seismic mass body as shown by Eq. (22) in **Figure 7**.

**Figure 6.**

**118**

*series respectively.*

*Different series combination of springs (a) two springs, (b) three springs, (c) four springs and (d) five springs in*

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

**Figure 7.** *Different dimensions used in capacitance formulation.*

$$\mathbf{C}\_{0} = \left(\frac{K\varepsilon\_{0}L\_{f0}t}{\mathbf{x}\_{1}} + \frac{K\varepsilon\_{0}L\_{f0}t}{\mathbf{x}\_{2}}\right) \times 2\mathbf{N}\_{f} \tag{21}$$

$$\mathbf{C}\_{pm} = \frac{\varepsilon\_0 t \mathbf{W}\_f \left(2\mathbf{N}\_f + \mathbf{1}\right)}{L\_f - L\_{f0}} \tag{22}$$

• The average sensor width must be in 1 mm.

*DOI: http://dx.doi.org/10.5772/intechopen.97185*

• Sensor resonant frequency shall be 10,000 Hz.

• The sensor must have a total mass of less than 20 mg.

**4.1 Sensitivity variation with different spring topologies**

application.

**Table 2.**

**121**

combinations as shown in **Table 4**.

*Optimized accelerometer dimensions for the proposed device.*

The optimized parameters of the geometry, as shown in **Table 2** [9]. The number of sensing fingers is found to be 174 on each side of the central seismic mass. The spring measurements and the seismic mass are calculated to hold the resonant frequency at about 10,000 Hz. Silicon density is 2330Kg/m3, and its elasticity modulus is 131Gpa. Silicon practically does not exhibit mechanical hysteresis. It therefore constitutes an ideal candidate material for sensors and actuators.

Microsystems built and manufactured with silicon provide greater versatility than

microsystem consisting of accelerometer and electronics interface circuitry needs to be housed in a biocompatible packaging. Recent advancements show that with minor surface modifications using laser nano texturing could increase the biocompatibility of silicon. Also, silicon compounds like silicon carbide is a promising biocompatible material. The Air is selected as dielectric medium as it offers negligible damping. The aspect ratio which is used is 12.5. Aspect ratio is the structure thickness ratio, and the finger spacing distance. Energy harvesting methodologies may be utilised to provide the power requirements for the proposed device [26–29].

Study of the device's output was carried out with different topologies for the spring. Parameters such as the resonant frequency, displacement sensitivity, capacitive sensitivity, seismic mass, and stiffness constants for the same spring beam length of 72 μm are evaluated in **Table 3**. If the number of springs in series rises, the device's displacement and capacitive sensitivity rise as a result of a steady drop in stiffness. The seismic mass and resonant frequency are finding a decrease though. The resonant frequency for our microphone needs to be outside of the usual 8000 Hz hearing range. Although the sensitivity of the device is improved, the combinations of more than one spring can not be approved for the proposed

Another alternative is to keep identical resonant frequencies for different

**Geometry Parameter Value (μm)** Length of sense finger 100 The width of sense finger 1 Gap spacing (x1, x2) 1, 2 The thickness of the device 12.5 Length of spring beam 72 Length of the proof mass 740 The width of the proof mass 884 Width of spring 2

with other substrate materials. In the proposed research work the entire

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with…*

The variation in sensing capacitance value under displacement *Δx* of the seismic mass is given by.

$$
\Delta \mathbf{C} = \left( \frac{K \varepsilon\_0 L\_{f0} t}{\varkappa\_1} \frac{\Delta \mathbf{x}}{\varkappa\_1} - \frac{K \varepsilon\_0 L\_{f0} t}{\varkappa\_2} \frac{\Delta \mathbf{x}}{\varkappa\_2} \right) \times \mathbf{2} N\_f \tag{23}
$$

Capacitive Sensitivity is given as change in capacitance with respect to applied acceleration *ΔC/a* (fF/g).

#### **4. Results and discussions**

The device's capacitive sensitivity depends on various geometrical parameters which conflict with each other. Simultaneous optimisation of all design parameters is essential for a highly sensitive device. An optimal problem with the accelerometer-based hearing aid that optimizes both of these variables was formulated mathematically, and simulative analysis was performed using COMSOL. As stated in the authors 'previous work [9], the various geometry parameters have been optimised. The system parameters also need to meet the constraints that need to be taken into account when designing the middle ear implantable microphone. The design constraints are:

• The average sensor length must be within 1 mm.

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with… DOI: http://dx.doi.org/10.5772/intechopen.97185*


The optimized parameters of the geometry, as shown in **Table 2** [9]. The number of sensing fingers is found to be 174 on each side of the central seismic mass. The spring measurements and the seismic mass are calculated to hold the resonant frequency at about 10,000 Hz. Silicon density is 2330Kg/m3, and its elasticity modulus is 131Gpa. Silicon practically does not exhibit mechanical hysteresis. It therefore constitutes an ideal candidate material for sensors and actuators. Microsystems built and manufactured with silicon provide greater versatility than with other substrate materials. In the proposed research work the entire microsystem consisting of accelerometer and electronics interface circuitry needs to be housed in a biocompatible packaging. Recent advancements show that with minor surface modifications using laser nano texturing could increase the biocompatibility of silicon. Also, silicon compounds like silicon carbide is a promising biocompatible material. The Air is selected as dielectric medium as it offers negligible damping. The aspect ratio which is used is 12.5. Aspect ratio is the structure thickness ratio, and the finger spacing distance. Energy harvesting methodologies may be utilised to provide the power requirements for the proposed device [26–29].

#### **4.1 Sensitivity variation with different spring topologies**

Study of the device's output was carried out with different topologies for the spring. Parameters such as the resonant frequency, displacement sensitivity, capacitive sensitivity, seismic mass, and stiffness constants for the same spring beam length of 72 μm are evaluated in **Table 3**. If the number of springs in series rises, the device's displacement and capacitive sensitivity rise as a result of a steady drop in stiffness. The seismic mass and resonant frequency are finding a decrease though. The resonant frequency for our microphone needs to be outside of the usual 8000 Hz hearing range. Although the sensitivity of the device is improved, the combinations of more than one spring can not be approved for the proposed application.

Another alternative is to keep identical resonant frequencies for different combinations as shown in **Table 4**.


#### **Table 2.**

*Optimized accelerometer dimensions for the proposed device.*

*<sup>C</sup>*<sup>0</sup> <sup>¼</sup> *<sup>K</sup>ε*0*<sup>L</sup> <sup>f</sup>*0*<sup>t</sup> x*1

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

*Different dimensions used in capacitance formulation.*

<sup>Δ</sup>*<sup>C</sup>* <sup>¼</sup> *<sup>K</sup>ε*0*<sup>L</sup> <sup>f</sup>*0*<sup>t</sup> x*1

• The average sensor length must be within 1 mm.

mass is given by.

**Figure 7.**

acceleration *ΔC/a* (fF/g).

**4. Results and discussions**

The design constraints are:

**120**

þ

*Cpm* <sup>¼</sup> *<sup>ε</sup>*0*tW <sup>f</sup>* <sup>2</sup>*<sup>N</sup> <sup>f</sup>* <sup>þ</sup> <sup>1</sup> *L <sup>f</sup>* � *L <sup>f</sup>*<sup>0</sup>

> Δ*x x*1

Capacitive Sensitivity is given as change in capacitance with respect to applied

The device's capacitive sensitivity depends on various geometrical parameters which conflict with each other. Simultaneous optimisation of all design parameters

accelerometer-based hearing aid that optimizes both of these variables was formulated mathematically, and simulative analysis was performed using COMSOL. As stated in the authors 'previous work [9], the various geometry parameters have been optimised. The system parameters also need to meet the constraints that need to be taken into account when designing the middle ear implantable microphone.

is essential for a highly sensitive device. An optimal problem with the

The variation in sensing capacitance value under displacement *Δx* of the seismic

� *<sup>K</sup>ε*0*<sup>L</sup> <sup>f</sup>*0*<sup>t</sup> x*2

Δ*x x*2

*Kε*0*L <sup>f</sup>*0*t x*2

� 2*N <sup>f</sup>* (21)

� 2*N <sup>f</sup>* (23)

(22)

#### *Hearing Loss - From Multidisciplinary Teamwork to Public Health*


#### **Table 3.**

*The parameters associated with the different series combination of springs for a similar length.*


than the folded beam's. Therefore the option of round folded beam provides no

*Comparison of performance of standard folded beam and round folded beam for same resonant frequency.*

*Comparison of performance of standard folded beam and round folded beam for the same length.*

**Displacement Sensitivity (nm/g)**

The parameters relating to the configuration of the accelerometer are shown in **Table 8**. The table contrasts the outcomes of the experiment and of simulation. The percentage difference between the analytical and simulation results is less than 10 percent, as is evident from the table. Therefore the findings of the modeling and

**Figure 8** provides the simulation environment for the proposed accelerometer. The First Resonant Frequency is at 10,209 Hz as shown in **Figure 9**. The average stress caused at 100 dB SPL and 10,000 Hz is 0.25 GPa, as shown in **Figure 10**. The average stress is slightly lower than silicon yield power (7 GPa). The yield strength of a material represents the highest stress that can produce without causing plastic deformation in a material. A material exhibits a defined permanent deformation at the stress. Yield strength is very critical in engineering structural design, as it must withstand the force sustained during use when constructing a part, and the part must not permanently deform. Hence the yield strength in any structure must sufficiently exceed the maximum stress produced. The yield strength of silicon (7GPa) in the proposed model is considerably higher than the average stress developed in the structure. COMSOL MULTIPHYSICS simulates the concept with optimized parameters, and validates the effects of the simulations and

**Parameter Analytical Value Simulation Value Error (%)** Resonant Frequency (Hz) 10018 10209 1.87 Nominal Capacitance (pF) 5.17 5.30 2.45 Displacment Sensitivity (nm/g) 2.47 2.65 6.79 Capacitive Sensitivity (fF/g) 6.41 6.89 6.97

major benefit over the folded beam.

**Geometry of folded beam**

Standard folded beam

Round folded beam

**The geometry of the spring beam**

Standard folded beam

Round folded beam

**Table 6.**

**Table 7.**

**Resonant frequency (Hz)**

*DOI: http://dx.doi.org/10.5772/intechopen.97185*

**Resonant frequency (Hz)**

**Displacement Sensitivity (nm/g)**

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with…*

**Capacitive Sensitivity (fF/g)**

10016 2.4771 6.4631 72 20.079 79.519

8848 3.1736 8.2893 72 20.079 62.066

**Capacitive Sensitivity (fF/g)**

10016 2.4771 6.4631 72 20.079 79.519

10019 2.4756 6.4589 66 20.078 79.564

**Length of beam (μm)**

**Length of the beam (μm)**

**Proof mass (ng)**

> **Proof mass (ng)**

**Spring constant (Nm/s)**

**Spring constant (Nm/s)**

simulation show strong agreement.

*Comparison of the analytical and simulation results.*

simulation.

**Table 8.**

**123**

#### **Table 4.**

*The parameters associated with the different series combination of springs for similar resonant frequency.*


#### **Table 5.**

*Comparison of performance of the device with standard folded and inverted folded beam.*

It is observed that the displacement and capacitive response are almost identical for different combinations. The length of spring beam needs to be changed to keep the resonant frequencies identical for different combinations. A decline in the seismic mass is noticed with increased number of springs in the arrangement. However, as shown in **Table 4**, no significant change in sensitivity is obtained and the arrangement is of no useful consequence. **Table 5** provides a comparison of regular folded beam sensitivities with inverted folded beam. The regular folded beam provides greater flexibility for the same length of the spring beam (72 μm) than the inverted folded beam.

The output for the spring beam length (72 μm) of folded beam and round folded beam is compared in **Table 6**. The round folded beam has an impressive sensitivity of 8.29 fF/g, an improvement over the regular folded beam. Nonetheless, this substantial improvement comes at the expense of the reduced 8849 Hz resonant frequency (very close to the standard 8000 Hz hearing range). The topology is therefore not suitable for the proposed study.

In **Table 7**, the output of round folded beam was also assessed for similar resonant frequency of 10019 Hz. The strength in this situation is significantly less *Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with… DOI: http://dx.doi.org/10.5772/intechopen.97185*


**Table 6.**

*Comparison of performance of standard folded beam and round folded beam for the same length.*


**Table 7.**

*Comparison of performance of standard folded beam and round folded beam for same resonant frequency.*

than the folded beam's. Therefore the option of round folded beam provides no major benefit over the folded beam.

The parameters relating to the configuration of the accelerometer are shown in **Table 8**. The table contrasts the outcomes of the experiment and of simulation. The percentage difference between the analytical and simulation results is less than 10 percent, as is evident from the table. Therefore the findings of the modeling and simulation show strong agreement.

**Figure 8** provides the simulation environment for the proposed accelerometer. The First Resonant Frequency is at 10,209 Hz as shown in **Figure 9**. The average stress caused at 100 dB SPL and 10,000 Hz is 0.25 GPa, as shown in **Figure 10**. The average stress is slightly lower than silicon yield power (7 GPa). The yield strength of a material represents the highest stress that can produce without causing plastic deformation in a material. A material exhibits a defined permanent deformation at the stress. Yield strength is very critical in engineering structural design, as it must withstand the force sustained during use when constructing a part, and the part must not permanently deform. Hence the yield strength in any structure must sufficiently exceed the maximum stress produced. The yield strength of silicon (7GPa) in the proposed model is considerably higher than the average stress developed in the structure. COMSOL MULTIPHYSICS simulates the concept with optimized parameters, and validates the effects of the simulations and simulation.


#### **Table 8.**

*Comparison of the analytical and simulation results.*

It is observed that the displacement and capacitive response are almost identical for different combinations. The length of spring beam needs to be changed to keep the resonant frequencies identical for different combinations. A decline in the seismic mass is noticed with increased number of springs in the arrangement. However, as shown in **Table 4**, no significant change in sensitivity is obtained and the arrangement is of no useful consequence. **Table 5** provides a comparison of regular folded beam sensitivities with inverted folded beam. The regular folded beam provides greater flexibility for the same length of the spring beam (72 μm)

The output for the spring beam length (72 μm) of folded beam and round folded beam is compared in **Table 6**. The round folded beam has an impressive sensitivity of 8.29 fF/g, an improvement over the regular folded beam. Nonetheless, this substantial improvement comes at the expense of the reduced 8849 Hz resonant frequency (very close to the standard 8000 Hz hearing range). The topology is

In **Table 7**, the output of round folded beam was also assessed for similar resonant frequency of 10019 Hz. The strength in this situation is significantly less

than the inverted folded beam.

**No of springs in combination**

**Table 3.**

**Table 4.**

**Table 5.**

**122**

**The orientation of the spring beam**

Inverted folded beam

**No of turns in spring**

**Resonant frequency**

> **Resonant frequency (Hz)**

**Resonant frequency (Hz)**

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

**Displacement Sensitivity (nm/g)**

*The parameters associated with the different series combination of springs for a similar length.*

**Capacitive Sensitivity (fF/g)**

 10016 2.4771 6.4631 20.079 72 79.519 10019 2.4753 6.4581 17.404 60 68.967 10033 2.4688 6.4408 14.731 56 58.536 10030 2.4699 6.4437 12.058 54 47.894 10021 2.4746 6.456 9.386 55 37.209

*The parameters associated with the different series combination of springs for similar resonant frequency.*

Folded beam 10016 2.4771 6.4631 72 20.079 79.519

**Capacitive Sensitivity (fF/g)**

10224 2.377 6.2011 72 20.079 82.867

**Displacement (nm/g)**

*Comparison of performance of the device with standard folded and inverted folded beam.*

**Proof mass (ng)**

**Length of the beam (μm)**

**Length of spring (μm)**

> **Proof mass (ng)**

**Displacement Sensitivity (nm/g)**

 10016 2.4771 6.4631 20.079 79.519 7606.5 4.2947 11.236 17.406 39.76 6750 5.453 14.292 14.734 26.506 6461.4 7.1856 15.611 12.061 19.88 6550.3 5.7914 15.186 9.3889 15.904

**Capacitive Sensitivity (fF/g)**

**Proof mass (ng)**

**Stiffness constant (Nm/s)**

> **Spring Constant**

**Spring constant (Nm/s)**

therefore not suitable for the proposed study.

#### **Figure 8.** *The simulation setup in COMSOL MULTIPHYSICS.*

**Figure 10.**

**Table 9.**

**Figure 11.**

**125**

*The frequency response of the optimized model.*

*Maximum stress induced in the optimized model.*

*DOI: http://dx.doi.org/10.5772/intechopen.97185*

*Comparison of proposed model with the model of Young et al.*

**Parameter Proposed Model Young et al. [20] Improvement (%)** Resonant Frequency (Hz) 10209 10000 2.04 Nominal Capacitance (pF) 5.30 2.40 54.7 Displacment Sensitivity (nm/g) 2.65 2.50 5.66 Capacitive Sensitivity (fF/g) 6.89 5.00 27.43

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with…*

**Figure 9.** *The first resonant mode of the optimized model.*

The proposed accelerometer is compared to previous MEMS capacitive sensors developed by Young et al. [20]. The new design shows an increase in capacitive sensitivity of 27.43 per cent over Young's research as shown in **Table 9**.

**Figure 11** shows the proposed accelerometer frequency response conforming to input umbo accelerations of 0.1 g, 0.5 g, and 1.0 g. The device's frequency response is almost flat from 500 Hz to 8000 Hz (the standard conversation range) with a peak at around 10,000 Hz that reflects the accelerometer's first resonant frequency (10,000 Hz). The flat frequency response shall indicate the accelerometer's operating range.

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with… DOI: http://dx.doi.org/10.5772/intechopen.97185*

**Figure 10.** *Maximum stress induced in the optimized model.*


#### **Table 9.**

*Comparison of proposed model with the model of Young et al.*

**Figure 11.** *The frequency response of the optimized model.*

The proposed accelerometer is compared to previous MEMS capacitive sensors developed by Young et al. [20]. The new design shows an increase in capacitive sensitivity of 27.43 per cent over Young's research as shown in

(10,000 Hz). The flat frequency response shall indicate the accelerometer's

**Figure 11** shows the proposed accelerometer frequency response conforming to input umbo accelerations of 0.1 g, 0.5 g, and 1.0 g. The device's frequency response is almost flat from 500 Hz to 8000 Hz (the standard conversation range) with a peak at around 10,000 Hz that reflects the accelerometer's first resonant frequency

**Table 9**.

**124**

**Figure 9.**

*The first resonant mode of the optimized model.*

**Figure 8.**

*The simulation setup in COMSOL MULTIPHYSICS.*

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

operating range.

### **5. Conclusion**

The research paper proposes an improved MEMS capacitive accelerometer to be used as a microphone for the completely implantable hearing. The effect of different types of suspension systems on accelerometer performance is being studied, and the folded beam spring topology is considered to be the most suitable for the proposed application. The analytical model was developed and validated with simulation results from COMSOL MULTIPHYSICS. The accelerometer occupies a small sensing region of 1mm<sup>2</sup> , an overall packed weight of less than 20 mg and a resonant frequency of almost 10,000 Hz. The accelerometer is designed so it can be inserted surgically and functions well within the standard conversational range of speech. Optimized efficiency of 5.30 pF, displacement sensitivity of 2.65 nm/ g and capacitive sensitivity of 6.89fF/g is achieved with an improvement in sensitivity of 27.43 per cent. The proposed design can therefore be suggested for possible application in totally implantable hearing devices.

**References**

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Sep; 13(3):206-14.

[1] Wang D. Deep learning reinvents the hearing aid. IEEE spectrum. 2017 Feb

*DOI: http://dx.doi.org/10.5772/intechopen.97185*

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with…*

hearing application. Biomedical Engineering/Biomedizinische Technik.

[10] Dwivedi A, Khanna G. Numerical simulation and modelling of a novel MEMS capacitive accelerometer based microphone for fully implantable hearing aid. Microsystem Technologies.

2018 Nov 27; 63(6):699-708.

2019 Feb;25(2):399-411.

(ahead-of-print).

Singapore.

(2):114-9.

[11] Dwivedi A, Khanna G. A microelectromechanical system (MEMS) capacitive accelerometerbased microphone with enhanced sensitivity for fully implantable hearing

aid: a novel analytical approach. Biomedical Engineering/

Biomedizinische Technik. 2020 Jul 3;1

[12] Dwivedi A, Asthana P, Khanna G. Effect of Micro Lever Width on the Mechanical Sensitivity of a MEMS Capacitive Accelerometer. InAdvances in VLSI, Communication, and Signal Processing 2020 (pp. 525-532). Springer,

[13] Zenner HP, Leysieffer H. Total implantation of the implex TICA hearing amplifier implant for highfrequency sensorineural hearing loss: the tübingen university experience. Otolaryngologic Clinics of North America. 2001 Apr 1; 34(2):417-46.

[14] Briggs RJ, Eder HC, Seligman PM,

[15] Bruschini LU, Forli FR, Santoro A, Bruschini PA, Berrettini ST. Fully implantable Otologics MET Carina™

sensorineural hearing loss. Preliminary surgical and clinical results. Acta

Cowan RS, Plant KL, Dalton J, Money DK, Patrick JF. Initial clinical experience with a totally implantable cochlear implant research device. Otology & Neurotology. 2008 Feb 1; 29

device for the treatment of

[2] Varshney S. Deafness in India. Indian

[3] Haynes DS, Young JA, Wanna GB,

overview. Trends in amplification. 2009

[4] Kim MK, Yoon YH, Park IY, Cho JH. Design of differential electromagnetic transducer for implantable middle ear hearing device using finite element method. Sensors and Actuators A: Physical. 2006 Aug 14; 130:234-40.

[5] Häusler R, Stieger C, Bernhard H, Kompis M. A novel implantable hearing system with direct acoustic cochlear

[6] Zenner HP, Baumann JW, Reischl G, Plinkert P, Zimmermann R, Mauz PS, Limberger A, Maassen MM. Patient selection for incus body coupling of a totally implantable middle ear implant. Acta oto-laryngologica. 2003 Jun 1; 123

[7] Urquiza R, López J, Gonzalez-Herrera A, Povedano V, Ciges M. Tympanic-ossicular prostheses and MEMS technology: whats and whys. Acta oto-laryngologica. 2009 Jan 1; 129

[8] Zeng FG, Rebscher S, Harrison W, Sun X, Feng H. Cochlear implants: system design, integration, and

evaluation. IEEE reviews in biomedical engineering. 2008 Nov 5; 1:115-42.

[9] Dwivedi A, Khanna G. Sensitivity enhancement of a folded beam MEMS capacitive accelerometer-based microphone for fully implantable

stimulation. Audiology and Neurotology. 2008; 13(4):247-56.

(6):683-96.

(4):411-5.

**127**

Journal of Otology. 2016; 22: 73.

Glasscock III ME. Middle ear implantable hearing devices: an

#### **Author details**

Apoorva Dwivedi<sup>1</sup> \*, Prateek Asthana<sup>2</sup> , Gargi Khanna<sup>1</sup> and Tarun Chaudhary<sup>3</sup>

1 Electronics and Communication Engineering Department, NIT Hamirpur, Hamirpur, Himachal Pradesh, India

2 Bharat Institute of Engineering and Technology, Hyderabad, India

3 Electronics and Communicaion Engineering Department, NIT Jalandhar, Jalandhar, Punjab, India

\*Address all correspondence to: apoorva.dwivedi07@gmail.com

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Variation of Sensitivity of a MEMS Capacitive Accelerometer Based Microphone with… DOI: http://dx.doi.org/10.5772/intechopen.97185*

#### **References**

**5. Conclusion**

sensing region of 1mm<sup>2</sup>

**Author details**

Apoorva Dwivedi<sup>1</sup>

Jalandhar, Punjab, India

**126**

Hamirpur, Himachal Pradesh, India

provided the original work is properly cited.

\*, Prateek Asthana<sup>2</sup>

1 Electronics and Communication Engineering Department, NIT Hamirpur,

3 Electronics and Communicaion Engineering Department, NIT Jalandhar,

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

2 Bharat Institute of Engineering and Technology, Hyderabad, India

\*Address all correspondence to: apoorva.dwivedi07@gmail.com

totally implantable hearing devices.

The research paper proposes an improved MEMS capacitive accelerometer to be used as a microphone for the completely implantable hearing. The effect of different types of suspension systems on accelerometer performance is being studied, and the folded beam spring topology is considered to be the most suitable for the proposed application. The analytical model was developed and validated with simulation results from COMSOL MULTIPHYSICS. The accelerometer occupies a small

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

frequency of almost 10,000 Hz. The accelerometer is designed so it can be inserted surgically and functions well within the standard conversational range of speech. Optimized efficiency of 5.30 pF, displacement sensitivity of 2.65 nm/ g and capacitive sensitivity of 6.89fF/g is achieved with an improvement in sensitivity of 27.43 per cent. The proposed design can therefore be suggested for possible application in

, an overall packed weight of less than 20 mg and a resonant

, Gargi Khanna<sup>1</sup> and Tarun Chaudhary<sup>3</sup>

[1] Wang D. Deep learning reinvents the hearing aid. IEEE spectrum. 2017 Feb 28; 54(3):32-7.

[2] Varshney S. Deafness in India. Indian Journal of Otology. 2016; 22: 73.

[3] Haynes DS, Young JA, Wanna GB, Glasscock III ME. Middle ear implantable hearing devices: an overview. Trends in amplification. 2009 Sep; 13(3):206-14.

[4] Kim MK, Yoon YH, Park IY, Cho JH. Design of differential electromagnetic transducer for implantable middle ear hearing device using finite element method. Sensors and Actuators A: Physical. 2006 Aug 14; 130:234-40.

[5] Häusler R, Stieger C, Bernhard H, Kompis M. A novel implantable hearing system with direct acoustic cochlear stimulation. Audiology and Neurotology. 2008; 13(4):247-56.

[6] Zenner HP, Baumann JW, Reischl G, Plinkert P, Zimmermann R, Mauz PS, Limberger A, Maassen MM. Patient selection for incus body coupling of a totally implantable middle ear implant. Acta oto-laryngologica. 2003 Jun 1; 123 (6):683-96.

[7] Urquiza R, López J, Gonzalez-Herrera A, Povedano V, Ciges M. Tympanic-ossicular prostheses and MEMS technology: whats and whys. Acta oto-laryngologica. 2009 Jan 1; 129 (4):411-5.

[8] Zeng FG, Rebscher S, Harrison W, Sun X, Feng H. Cochlear implants: system design, integration, and evaluation. IEEE reviews in biomedical engineering. 2008 Nov 5; 1:115-42.

[9] Dwivedi A, Khanna G. Sensitivity enhancement of a folded beam MEMS capacitive accelerometer-based microphone for fully implantable

hearing application. Biomedical Engineering/Biomedizinische Technik. 2018 Nov 27; 63(6):699-708.

[10] Dwivedi A, Khanna G. Numerical simulation and modelling of a novel MEMS capacitive accelerometer based microphone for fully implantable hearing aid. Microsystem Technologies. 2019 Feb;25(2):399-411.

[11] Dwivedi A, Khanna G. A microelectromechanical system (MEMS) capacitive accelerometerbased microphone with enhanced sensitivity for fully implantable hearing aid: a novel analytical approach. Biomedical Engineering/ Biomedizinische Technik. 2020 Jul 3;1 (ahead-of-print).

[12] Dwivedi A, Asthana P, Khanna G. Effect of Micro Lever Width on the Mechanical Sensitivity of a MEMS Capacitive Accelerometer. InAdvances in VLSI, Communication, and Signal Processing 2020 (pp. 525-532). Springer, Singapore.

[13] Zenner HP, Leysieffer H. Total implantation of the implex TICA hearing amplifier implant for highfrequency sensorineural hearing loss: the tübingen university experience. Otolaryngologic Clinics of North America. 2001 Apr 1; 34(2):417-46.

[14] Briggs RJ, Eder HC, Seligman PM, Cowan RS, Plant KL, Dalton J, Money DK, Patrick JF. Initial clinical experience with a totally implantable cochlear implant research device. Otology & Neurotology. 2008 Feb 1; 29 (2):114-9.

[15] Bruschini LU, Forli FR, Santoro A, Bruschini PA, Berrettini ST. Fully implantable Otologics MET Carina™ device for the treatment of sensorineural hearing loss. Preliminary surgical and clinical results. Acta

Otorhinolaryngologica Italica. 2009 Apr; 29(2):79.

[16] Pulcherio JO, Bittencourt AG, Burke PR, da Costa Monsanto R, De Brito R, Tsuji RK, Bento RF. Carina® and Esteem®: a systematic review of fully implantable hearing devices. PLoS One. 2014 Oct 17; 9(10):e110636.

[17] Kraus EM, Shohet JA, Catalano PJ. Envoy esteem totally implantable hearing system: phase 2 trial, 1-year hearing results. Otolaryngology–Head and Neck Surgery. 2011 Jul; 145(1): 100-9.

[18] Ko WH, Zhang R, Huang P, Guo J, Ye X, Young DJ, Megerian CA. Studies of MEMS acoustic sensors as implantable microphones for totally implantable hearing-aid systems. IEEE Transactions on Biomedical Circuits and Systems. 2009 Sep 25; 3(5):277-85.

[19] Zurcher MA, Semaan M, Megerian CA, Ko WH, Young DJ. A MEMS capacitive accelerometer design as middle ear microphone based on ossicular chain micromechanic characterization at umbo for fully implantable cochlear prosthesis. Sensors and Materials. 2010 Jan 1; 22(6):297-312.

[20] Young DJ, Zurcher MA, Semaan M, Megerian CA, Ko WH. MEMS capacitive accelerometer-based middle ear microphone. IEEE Transactions on Biomedical Engineering. 2012 Apr 20; 59(12):3283-92.

[21] Yip M, Jin R, Nakajima HH, Stankovic KM, Chandrakasan AP. A fully-implantable cochlear implant SoC with piezoelectric middle-ear sensor and arbitrary waveform neural stimulation. IEEE journal of solid-state circuits. 2014 Sep 25; 50(1):214-29.

[22] Woo ST, Shin DH, Lim HG, Seong KW, Gottlieb P, Puria S, Lee KY, Cho JH. A new trans-tympanic microphone approach for fully

implantable hearing devices. Sensors. 2015 Sep; 15(9):22798-810.

**Chapter 9**

Matching

*Reza Hashemian*

which uses the negative feedback technique.

**1. Introduction**

**129**

**Keywords:** Analog circuit design, audio amplifiers, feedback theory, fixator-norator pairs, frequency profiles, hearing aids, nullors

provide some advantages in some aspects over the digital technology.

Hearing aid market is definitely dominated by fully digital hearing aids. With many recent advancements in the industry the prices are also keep rising and getting almost unaffordable for some hearing- impaired patients. This chapter provides a simple and very cost effective method for the design and implementation of stand-alone analog amplifiers or pre-amplifiers for digital hearing aids. Although somewhat behind in the technology and the market, analog hearing aids can still

**Abstract**

Cost-Effective Design of

Amplifiers for Hearing Aides

This chapter starts reviewing Fixator-Norator Pairs (FNP) as an effective tool used to design analog amplifiers for a prescribed bandwidth and frequency profile. Among number of cases and applications, designing for hearing aides are particularly important, where the hearing frequency profiles, known as audiograms, are changing from person to person, and also for a person by the age. The design is mainly focused on front-end or stand-alone amplifiers. In case of a front-end the response from the amplifier can be digitized, properly controlled and adjusted to fit the digital application. Here is how the design proceed. For a given audiogram, an Audiogram Generator Circuit (AGC) is initially constructed. This AGC, usually a complete passive circuit, produces a frequency response that closely matches with the audiogram, obtained from a hearing impaired patient. The AGC is then embedded in an amplifier circuit where a fixator is placed at its output port, "forcing" the amplifier to generate the desired output frequency response profile. A flat band frequency response, for example, compensates the hearing losses and provides a uniform hearing to the patient in the entire audio bandwidth. The amplifier can be further enhanced to perform other requirements, for example, to cancel undesirable noises in certain frequencies or to magnify the voice in critical frequencies for clarity. Another alternative design methodology is also introduced in this chapter,

Using Nullors for Response

[23] Koch M, Eßinger TM, Stoppe T, Lasurashvili N, Bornitz M, Zahnert T. Fully implantable hearing aid in the incudostapedial joint gap. Hearing research. 2016 Oct 1; 340:169-78.

[24] Wai-Chi W, Azid AA, Majlis BY. Formulation of stiffness constant and effective mass for a folded beam. Archives of Mechanics. 2010 Apr 11; 62 (5):405-18.

[25] Wong WC, Azid IA, Majlis BY. Theoretical analysis of stiffness constant and effective mass for a round-folded beam in MEMS accelerometer. Strojniški vestnik-Journal of Mechanical Engineering. 2011 Jun 15; 57(6):517-25.

[26] Asthana P, Khanna G. Finiteelement modeling of piezoelectric energy harvesters using lead-based and lead-free materials for voltage generation. Journal of Asian Ceramic Societies. 2018 Oct 2; 6(4):394-400.

[27] Asthana P, Khanna G. A broadband piezoelectric energy harvester for IoT based applications. Microelectronics Journal. 2019 Nov 1; 93:104635.

[28] Asthana P, Dwivedi A, Khanna G. Finite Element Modeling of a Wideband Piezoelectric Energy Harvester for Ambient Vibration Extraction. InAdvances in VLSI, Communication, and Signal Processing 2020 (pp. 549-556). Springer, Singapore.

[29] Asthana P, Khanna G. Power amplification interface circuit for broadband piezoelectric energy harvester. Microelectronics Journal. 2020 Apr 1; 98:104734.

#### **Chapter 9**

Otorhinolaryngologica Italica. 2009

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

implantable hearing devices. Sensors.

[23] Koch M, Eßinger TM, Stoppe T, Lasurashvili N, Bornitz M, Zahnert T. Fully implantable hearing aid in the incudostapedial joint gap. Hearing research. 2016 Oct 1; 340:169-78.

[24] Wai-Chi W, Azid AA, Majlis BY. Formulation of stiffness constant and effective mass for a folded beam. Archives of Mechanics. 2010 Apr 11; 62

[25] Wong WC, Azid IA, Majlis BY. Theoretical analysis of stiffness constant and effective mass for a round-folded beam in MEMS accelerometer.

[26] Asthana P, Khanna G. Finiteelement modeling of piezoelectric energy harvesters using lead-based and

lead-free materials for voltage generation. Journal of Asian Ceramic Societies. 2018 Oct 2; 6(4):394-400.

Strojniški vestnik-Journal of Mechanical Engineering. 2011 Jun 15; 57(6):517-25.

[27] Asthana P, Khanna G. A broadband piezoelectric energy harvester for IoT based applications. Microelectronics Journal. 2019 Nov 1; 93:104635.

[28] Asthana P, Dwivedi A, Khanna G. Finite Element Modeling of a Wideband Piezoelectric Energy Harvester for Ambient Vibration Extraction.

InAdvances in VLSI, Communication,

(pp. 549-556). Springer, Singapore.

[29] Asthana P, Khanna G. Power amplification interface circuit for broadband piezoelectric energy harvester. Microelectronics Journal.

and Signal Processing 2020

2020 Apr 1; 98:104734.

2015 Sep; 15(9):22798-810.

(5):405-18.

[16] Pulcherio JO, Bittencourt AG, Burke PR, da Costa Monsanto R, De Brito R, Tsuji RK, Bento RF. Carina® and Esteem®: a systematic review of fully implantable hearing devices. PLoS One. 2014 Oct 17; 9(10):e110636.

[17] Kraus EM, Shohet JA, Catalano PJ. Envoy esteem totally implantable hearing system: phase 2 trial, 1-year hearing results. Otolaryngology–Head and Neck Surgery. 2011 Jul; 145(1):

[18] Ko WH, Zhang R, Huang P, Guo J, Ye X, Young DJ, Megerian CA. Studies

[20] Young DJ, Zurcher MA, Semaan M,

capacitive accelerometer-based middle ear microphone. IEEE Transactions on Biomedical Engineering. 2012 Apr 20;

Megerian CA, Ko WH. MEMS

[21] Yip M, Jin R, Nakajima HH, Stankovic KM, Chandrakasan AP. A fully-implantable cochlear implant SoC with piezoelectric middle-ear sensor and arbitrary waveform neural stimulation. IEEE journal of solid-state circuits. 2014

[22] Woo ST, Shin DH, Lim HG,

Cho JH. A new trans-tympanic microphone approach for fully

Seong KW, Gottlieb P, Puria S, Lee KY,

59(12):3283-92.

Sep 25; 50(1):214-29.

**128**

of MEMS acoustic sensors as implantable microphones for totally implantable hearing-aid systems. IEEE Transactions on Biomedical Circuits and Systems. 2009 Sep 25; 3(5):277-85.

[19] Zurcher MA, Semaan M, Megerian CA, Ko WH, Young DJ. A MEMS capacitive accelerometer design as middle ear microphone based on ossicular chain micromechanic characterization at umbo for fully implantable cochlear prosthesis. Sensors and Materials. 2010 Jan 1; 22(6):297-312.

Apr; 29(2):79.

100-9.

## Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching

*Reza Hashemian*

### **Abstract**

This chapter starts reviewing Fixator-Norator Pairs (FNP) as an effective tool used to design analog amplifiers for a prescribed bandwidth and frequency profile. Among number of cases and applications, designing for hearing aides are particularly important, where the hearing frequency profiles, known as audiograms, are changing from person to person, and also for a person by the age. The design is mainly focused on front-end or stand-alone amplifiers. In case of a front-end the response from the amplifier can be digitized, properly controlled and adjusted to fit the digital application. Here is how the design proceed. For a given audiogram, an Audiogram Generator Circuit (AGC) is initially constructed. This AGC, usually a complete passive circuit, produces a frequency response that closely matches with the audiogram, obtained from a hearing impaired patient. The AGC is then embedded in an amplifier circuit where a fixator is placed at its output port, "forcing" the amplifier to generate the desired output frequency response profile. A flat band frequency response, for example, compensates the hearing losses and provides a uniform hearing to the patient in the entire audio bandwidth. The amplifier can be further enhanced to perform other requirements, for example, to cancel undesirable noises in certain frequencies or to magnify the voice in critical frequencies for clarity. Another alternative design methodology is also introduced in this chapter, which uses the negative feedback technique.

**Keywords:** Analog circuit design, audio amplifiers, feedback theory, fixator-norator pairs, frequency profiles, hearing aids, nullors

#### **1. Introduction**

Hearing aid market is definitely dominated by fully digital hearing aids. With many recent advancements in the industry the prices are also keep rising and getting almost unaffordable for some hearing- impaired patients. This chapter provides a simple and very cost effective method for the design and implementation of stand-alone analog amplifiers or pre-amplifiers for digital hearing aids. Although somewhat behind in the technology and the market, analog hearing aids can still provide some advantages in some aspects over the digital technology.

The chapter is the extended version of [1], and the objective here is to design amplifiers that exhibit frequency responses that can vary and match with any specific frequency profile in demand. In this chapter, we are considering amplifiers that are applicable to hearing aid designs. There are several main criteria associated with this design as:

design of a two terminal component/circuit that needs to replace the pairing norator. This is, in fact, the key property of a fixator that we are able to use in this chapter to design amplifier circuits that exhibit some specified frequency profiles

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

**3. Frequency profiles matching in hearing aid applications**

Next, we are going to investigate how this property of a fixator works for us to

Consider designing an analog amplifier for a hearing aid application. Given a hearing profile (audiogram) of a hearing impaired patient, the question is how can we compensate for the hearing losses of the patient within the entire dynamic frequency range? We may go even further and design for a response that is beyond the mere compensation of the hearing losses, but enhancing or reducing the

response in certain frequency areas as needed. For example, if the individual works in a factory and he/she is exposed to certain excessive sounds (noises) within certain frequencies, the hearing device must be capable of acting as a noise cancelation device [4], helping to reduce the noise as it provides amplification in other

This last point might be of interest to those working in the occupational technology, construction workers, and those working long hours with heavy equipment and machinery. Other applications might be in public health services such as in nursing homes to enhance certain alarms like passing vehicles, and so on, for the elderly safety. What is interesting in our analog hearing aid is that, to add those extras, such as noise cancelations or sound enhancements to the system all we need to do is to redesign the passive portion of the system without touching the active

So, we can define two objectives here: 1) compensate for the hearing losses and make it uniform within the entire dynamic frequency range, and 2) add a certain selective frequency response profile on top of the flat normal hearing. In other words, given the audiogram of a hearing impaired patient and also a desire hearing frequency profile constructed for the patient's need, how can we design an amplifier

To put the problem into a mathematical perspective, suppose *H(s)* denotes the audiogram of a hearing impaired patient, *F(s)* is the final desirable voice spectrum that is tailored for the individual, and *T(s)* is the transfer function of the hearing

To simplify the problem, we split it into two cases, just described. First, we only assume a flat frequency response for the final hearing comprehension, i.e., *F(s) = 1* for the entire frequency bandwidth. In the second case, we try to enhance the response to follow a certain desirable frequency profile *F(s)*. We continue our design strategy for the first case here and will follow it for the second case in a later Section.

Suppose *H(s)* is the transfer function of an audiogram, being represented by:

*F s*ðÞ¼ *T s*ð Þ ∗ *H s*ð Þ (1)

*H s*ðÞ¼ *N s*ð Þ*=D s*ð Þ (2)

and bandwidths.

design hearing aid amplifiers.

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

areas of the bandwidth.

(amplifier) device.

that satisfies both?

**131**

amplifier that provides such a response. Then

**4. Design for flat frequency response**


#### **2. Fixator Norator pairs and their properties in design for frequency profiles**

Fixator-Noratpr Pairs and their properties in analog circuit designs are covered in [2]. A fixator, denoted by Fx(Vj, Ij) or Fx(Ij, Vj), symbolically shown in **Figure 1**, is a two terminal component with both its current Ij and voltage Vj specified. A nullator, denoted by Fx(0, 0), is a special case of a fixator where Vj and Ij are both zero. So by definition, a fixator can be assigned to a design constraint to keep it unchanged during the design process. Then a paring norator, with its V and I unspecified, can provide the conditions in the circuit to allow the fixator to hold onto the values. Hence, a fixator and its paring norator work together to satisfy the Kirchhoff Laws [3], and they must be mutually sensitive to each other. It is important to note that, because a fixator needs to keep its variables (I and V) as designated, its pairing norator must be ultra-sensitive to small variations in the fixator in order to keep the fixator values unchanged.

A major property of a fixator is its ability to stick to a design constraint, whether fixed or variable in time or frequency, based on a pre-specified setting. For example, a fixator can be assigned to a circuit port to keep its frequency response close to a given frequency profile. In return the pairing norator must be capable of providing the necessary condition in the circuit for the fixator to operate. In short, a fixator is used to keep a design constraint as specified, shifting the problem to the

**Figure 1.** *Fixators; (a) a voltage fixator; (b) a current fixator; (c) the symbol.*

#### *Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

design of a two terminal component/circuit that needs to replace the pairing norator. This is, in fact, the key property of a fixator that we are able to use in this chapter to design amplifier circuits that exhibit some specified frequency profiles and bandwidths.

Next, we are going to investigate how this property of a fixator works for us to design hearing aid amplifiers.

#### **3. Frequency profiles matching in hearing aid applications**

Consider designing an analog amplifier for a hearing aid application. Given a hearing profile (audiogram) of a hearing impaired patient, the question is how can we compensate for the hearing losses of the patient within the entire dynamic frequency range? We may go even further and design for a response that is beyond the mere compensation of the hearing losses, but enhancing or reducing the response in certain frequency areas as needed. For example, if the individual works in a factory and he/she is exposed to certain excessive sounds (noises) within certain frequencies, the hearing device must be capable of acting as a noise cancelation device [4], helping to reduce the noise as it provides amplification in other areas of the bandwidth.

This last point might be of interest to those working in the occupational technology, construction workers, and those working long hours with heavy equipment and machinery. Other applications might be in public health services such as in nursing homes to enhance certain alarms like passing vehicles, and so on, for the elderly safety. What is interesting in our analog hearing aid is that, to add those extras, such as noise cancelations or sound enhancements to the system all we need to do is to redesign the passive portion of the system without touching the active (amplifier) device.

So, we can define two objectives here: 1) compensate for the hearing losses and make it uniform within the entire dynamic frequency range, and 2) add a certain selective frequency response profile on top of the flat normal hearing. In other words, given the audiogram of a hearing impaired patient and also a desire hearing frequency profile constructed for the patient's need, how can we design an amplifier that satisfies both?

To put the problem into a mathematical perspective, suppose *H(s)* denotes the audiogram of a hearing impaired patient, *F(s)* is the final desirable voice spectrum that is tailored for the individual, and *T(s)* is the transfer function of the hearing amplifier that provides such a response. Then

$$F(\mathfrak{s}) = T(\mathfrak{s}) \* H(\mathfrak{s}) \tag{1}$$

To simplify the problem, we split it into two cases, just described. First, we only assume a flat frequency response for the final hearing comprehension, i.e., *F(s) = 1* for the entire frequency bandwidth. In the second case, we try to enhance the response to follow a certain desirable frequency profile *F(s)*. We continue our design strategy for the first case here and will follow it for the second case in a later Section.

#### **4. Design for flat frequency response**

Suppose *H(s)* is the transfer function of an audiogram, being represented by:

$$H(\mathfrak{s}) = N(\mathfrak{s})/D(\mathfrak{s})\tag{2}$$

The chapter is the extended version of [1], and the objective here is to design amplifiers that exhibit frequency responses that can vary and match with any specific frequency profile in demand. In this chapter, we are considering amplifiers that are applicable to hearing aid designs. There are several main criteria associated

• The design needs to be simple and highly modular. By this modularity, we mean to separate the active device, as an engine, from the rest of the circuit, as

• To be easily adaptable to variations, either for different hearing-impaired patients or the natural changes happening in the hearing situation of an

**2. Fixator Norator pairs and their properties in design for frequency**

Fixator-Noratpr Pairs and their properties in analog circuit designs are covered in [2]. A fixator, denoted by Fx(Vj, Ij) or Fx(Ij, Vj), symbolically shown in **Figure 1**, is a two terminal component with both its current Ij and voltage Vj specified. A nullator, denoted by Fx(0, 0), is a special case of a fixator where Vj and Ij are both zero. So by definition, a fixator can be assigned to a design constraint to keep it unchanged during the design process. Then a paring norator, with its V and I unspecified, can provide the conditions in the circuit to allow the fixator to hold onto the values. Hence, a fixator and its paring norator work together to satisfy the Kirchhoff Laws [3], and they must be mutually sensitive to each other. It is important to note that, because a fixator needs to keep its variables (I and V) as designated, its pairing norator must be ultra-sensitive to small variations in the fixator in

A major property of a fixator is its ability to stick to a design constraint, whether fixed or variable in time or frequency, based on a pre-specified setting. For example, a fixator can be assigned to a circuit port to keep its frequency response close to a given frequency profile. In return the pairing norator must be capable of providing the necessary condition in the circuit for the fixator to operate. In short, a fixator is used to keep a design constraint as specified, shifting the problem to the

with this design as:

**profiles**

**Figure 1.**

**130**

the controllers.

individual over time.

• Low cost and affordable with high quality.

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

order to keep the fixator values unchanged.

*Fixators; (a) a voltage fixator; (b) a current fixator; (c) the symbol.*

Then by referring to Eq. (1) and assuming *F(s) = 1,* the amplifier response,*T(s)*, becomes

$$T(\mathfrak{s}) = H(\mathfrak{s})^{-1} = D(\mathfrak{s})/N(\mathfrak{s})\tag{3}$$

So, the objective here is to design an amplifier that has a frequency response profile which is the inverse of an audiogram of our choice. In addition, this amplifier must be modular and adaptable to the changes that might happen to the hearing profile (audiogram). This change might be either due to the aging, or the amplifier may be used for another audiogram (patient) all together.

There are two known methods we can use for this functional inversion. One method is to apply the FNP technique as we introduced before, and the other method is to uses the negative feedback procedure [5], which is well known in control theory. We will introduce both methodologies in this chapter, although our preference and emphasis will be more on the former technique, as it is shown to be more reliable and accurate.

#### **5. FNP implementation of analog hearing aid amplifiers**

This implementation uses an FNP as a design tool. However, the FNP is later replaced with a high gain operational amplifier when the amplifier is constructed. Before we go into the details, here is the Problem Statement.

*Problem statement* – Given an audiogram of a hearing-impaired patient, design a front-end or stand-alone analog amplifier that is fully adaptable and has a wide voice dynamic range covering the audio range from 250 Hz to 8 KHz, as specified in the audiogram [1].

*Design procedure* – The design proposed is modular with two parts: a) a controlling circuit, generating the hearing loss frequency profile as the output, and b) an amplifier acting as an engine module for the system. The control unit must be closely equivalent to the patient's audiogram, and any performance variations, such as tuning and modifications, are done on this module, which is usually a passive circuit. Therefore, the design of hearing aid is mainly concentrated on the design of the passive control unit, leaving the amplifier undisturbed during the application. This means, once the amplifier (engine) is designed it is left unaltered, and all other variations and adaptations are done on the controlling module. This is one of the main criteria of the system, where the variations and control is concentrated on the passive unit, which is more stable and design friendly.

practical design technique is to estimate the locations of the poles and zeros for a given audiogram first, and then construct a AGC that closely displays those poles and zeros, and hence, nearly mimics the audiogram [7]. An alternative design method is also presented in [8]. Here, in this chapter, we follow an ad hoc technique where we first try to assemble an RC ladder circuit to produce an AGC with the frequency profile close to the audiogram. We then modify the circuit and add more ladder stages if necessary to get it right and accurate enough. We can always leave

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

Another issue to pay attention to here is the phase angle. The experiment show that we need to be concern about the phase delay in an AGC as well. Because of the reactive elements (C and L) in the circuit, phase delay is generated, which causes time delay in the signal processing. In case this time delay is uniformly distributed throughout the frequency spectrum, i.e., the phase in linear vs. the frequency, then the group delay will be constant and the uniform delay only causes a constant delay between the actual voice (signal) and what is received and comprehended through the hearing aid. However, in case the time delay is dependent on the frequency of the signal, and the time delay variation is large then it may cause poor fidelity and distortion in the comprehended voice. So, for a reliable design we need to pay attention to both magnitude and the phase of the signal getting out of an AGC.

some room for on (application) site tuning, of course.

*Audiogram of the left ear of a patient with hearing impairment.*

**Figure 2.**

**133**

Let us begin our design procedure from the transfer function *T(s)*, given in Eq. (3). **Figure 2** shows an audiogram taken from the left ear of a hearing impaired patient. Notice that the hearing loss is quite large, and it is more than 60dB at high pitch voices. So, to compensate for this loss we need to use an amplifier with high gain, getting to 60 dB or higher at high frequencies. A typical amplifier suitable for this design can consist of one or two stage of Op-Amps with wide enough bandwidth. Next, we proceed with the design of the control module.

*Control Unit* - Our next stage of the design is to construct the controlling module for a flat comprehended hearing profile (*F(s) = 1*). The module must be so designed that it generates an output frequency profile duplicated from the selected audiogram, or simply have a transfer function close to H(s). Apparently, because of the losses in the magnitude of the response, the controlling circuit, called *Audiogram Generator Circuit (AGC),* can be totally passive RC (or RLC) circuit.

There are different methods available to construct such an AGC, and because it is a passive circuit its design and synthesis can be quite straight forward [6]. A more *Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

#### **Figure 2.**

Then by referring to Eq. (1) and assuming *F(s) = 1,* the amplifier response,*T(s)*,

So, the objective here is to design an amplifier that has a frequency response profile which is the inverse of an audiogram of our choice. In addition, this amplifier must be modular and adaptable to the changes that might happen to the hearing profile (audiogram). This change might be either due to the aging, or the amplifier

There are two known methods we can use for this functional inversion. One method is to apply the FNP technique as we introduced before, and the other method is to uses the negative feedback procedure [5], which is well known in control theory. We will introduce both methodologies in this chapter, although our preference and emphasis will be more on the former technique, as it is shown to be

This implementation uses an FNP as a design tool. However, the FNP is later replaced with a high gain operational amplifier when the amplifier is constructed.

*Problem statement* – Given an audiogram of a hearing-impaired patient, design a front-end or stand-alone analog amplifier that is fully adaptable and has a wide voice dynamic range covering the audio range from 250 Hz to 8 KHz, as specified in

*Design procedure* – The design proposed is modular with two parts: a) a controlling circuit, generating the hearing loss frequency profile as the output, and b) an amplifier acting as an engine module for the system. The control unit must be closely equivalent to the patient's audiogram, and any performance variations, such as tuning and modifications, are done on this module, which is usually a passive circuit. Therefore, the design of hearing aid is mainly concentrated on the design of the passive control unit, leaving the amplifier undisturbed during the application. This means, once the amplifier (engine) is designed it is left unaltered, and all other variations and adaptations are done on the controlling module. This is one of the main criteria of the system, where the variations and control is concentrated on the

Let us begin our design procedure from the transfer function *T(s)*, given in Eq. (3). **Figure 2** shows an audiogram taken from the left ear of a hearing impaired patient. Notice that the hearing loss is quite large, and it is more than 60dB at high pitch voices. So, to compensate for this loss we need to use an amplifier with high gain, getting to 60 dB or higher at high frequencies. A typical amplifier suitable for this design can consist of one or two stage of Op-Amps with wide enough band-

*Control Unit* - Our next stage of the design is to construct the controlling module for a flat comprehended hearing profile (*F(s) = 1*). The module must be so designed that it generates an output frequency profile duplicated from the selected audiogram, or simply have a transfer function close to H(s). Apparently, because of the losses in the magnitude of the response, the controlling circuit, called *Audiogram*

There are different methods available to construct such an AGC, and because it is a passive circuit its design and synthesis can be quite straight forward [6]. A more

may be used for another audiogram (patient) all together.

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

**5. FNP implementation of analog hearing aid amplifiers**

Before we go into the details, here is the Problem Statement.

passive unit, which is more stable and design friendly.

width. Next, we proceed with the design of the control module.

*Generator Circuit (AGC),* can be totally passive RC (or RLC) circuit.

*T s*ðÞ¼ *H s*ð Þ�<sup>1</sup> <sup>¼</sup> *D s*ð Þ*=N s*ð Þ (3)

becomes

more reliable and accurate.

the audiogram [1].

**132**

practical design technique is to estimate the locations of the poles and zeros for a given audiogram first, and then construct a AGC that closely displays those poles and zeros, and hence, nearly mimics the audiogram [7]. An alternative design method is also presented in [8]. Here, in this chapter, we follow an ad hoc technique where we first try to assemble an RC ladder circuit to produce an AGC with the frequency profile close to the audiogram. We then modify the circuit and add more ladder stages if necessary to get it right and accurate enough. We can always leave some room for on (application) site tuning, of course.

Another issue to pay attention to here is the phase angle. The experiment show that we need to be concern about the phase delay in an AGC as well. Because of the reactive elements (C and L) in the circuit, phase delay is generated, which causes time delay in the signal processing. In case this time delay is uniformly distributed throughout the frequency spectrum, i.e., the phase in linear vs. the frequency, then the group delay will be constant and the uniform delay only causes a constant delay between the actual voice (signal) and what is received and comprehended through the hearing aid. However, in case the time delay is dependent on the frequency of the signal, and the time delay variation is large then it may cause poor fidelity and distortion in the comprehended voice. So, for a reliable design we need to pay attention to both magnitude and the phase of the signal getting out of an AGC.

Presently, we consider two AGC circuits given in **Figure 3(a)** and **(b)**, and their symbolic representation in **Figure 3(c)**. **Figure 4** shows the magnitude frequency responses of both AGCs in comparison with the actual audiogram. To further compare the two circuits, both the magnitude and the phase Bode plots are shown in **Figure 5(a)** and **(b)**. In comparing their responses, we realize that the *RC1* module, also structurally more involved, is showing more accurate results than the *RC2* module. Notice the followings points in the response of the *RC1* module: 1) its magnitude is closer to that of the audiogram, and 2) its phase delay is almost linear, providing a nearly constant group delay. So, we have two choices to select one. Either select the *RC1* module (**Figure 3(a)**) for less distortion and better comprehended voice, or alternatively chose the *RC1* module for its simplicity.

However, we may still need to observe the roots (poles and zeros) of the modules, in case we may want to modify the responds for a better fit. To clearly identify the roots, we use a technique initially introduced in [9]. This technique converts the real axis roots (poles and zeros) of an RC circuit to roots on the imaginary axis where the sweeping excitation signal encounter with the roots and so generates

#### **Figure 3.**

*(a) And (b) two AGCs matching with the audiogram given in Figure 1; (c) the AGC block diagram.*

peaks and notches. To implement this technique for our case we first need to create two LC circuits, *LC1* and *LC2* for *RC1* and *RC2*, respectively. To create *LC1* and *LC2*

*(a) And (b) the frequency response of the two AGC corcuits; (c) the frequency response of the corresponding LC*

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

we need to go through the following steps:

**Figure 5.**

*circuits.*

**135**

**Figure 4.** *Comparing the frequency responses from the two AGC candidates, RC1, and RC2 with the audiogram.*

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

**Figure 5.**

Presently, we consider two AGC circuits given in **Figure 3(a)** and **(b)**, and their symbolic representation in **Figure 3(c)**. **Figure 4** shows the magnitude frequency responses of both AGCs in comparison with the actual audiogram. To further compare the two circuits, both the magnitude and the phase Bode plots are shown in **Figure 5(a)** and **(b)**. In comparing their responses, we realize that the *RC1* module, also structurally more involved, is showing more accurate results than the *RC2* module. Notice the followings points in the response of the *RC1* module: 1) its magnitude is closer to that of the audiogram, and 2) its phase delay is almost linear, providing a nearly constant group delay. So, we have two choices to select one. Either select the *RC1* module (**Figure 3(a)**) for less distortion and better comprehended voice, or alternatively chose the *RC1* module for its simplicity.

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

However, we may still need to observe the roots (poles and zeros) of the modules, in case we may want to modify the responds for a better fit. To clearly identify the roots, we use a technique initially introduced in [9]. This technique converts the real axis roots (poles and zeros) of an RC circuit to roots on the imaginary axis where the sweeping excitation signal encounter with the roots and so generates

*(a) And (b) two AGCs matching with the audiogram given in Figure 1; (c) the AGC block diagram.*

*Comparing the frequency responses from the two AGC candidates, RC1, and RC2 with the audiogram.*

**Figure 3.**

**Figure 4.**

**134**

*(a) And (b) the frequency response of the two AGC corcuits; (c) the frequency response of the corresponding LC circuits.*

peaks and notches. To implement this technique for our case we first need to create two LC circuits, *LC1* and *LC2* for *RC1* and *RC2*, respectively. To create *LC1* and *LC2* we need to go through the following steps:


Here is how it works.

*Corresponding LC circuits* – As fully explained in [9], it is simply proven that, if *LCi* is the corresponding LC circuit of an RC circuit, *RCi*, then for any real axis root ωRC in *RCi* there exist a pair of conjugate roots �*ωLC* on the *jω* axis for *LC*<sup>i</sup> so that they are related through the relationship ωRC = ωLC 2 , or in the log format the scaling factor is specified by

$$\log\left(o\_{L\mathcal{C}}\right) = \log\left(o\_{\mathcal{RC}}\right)/2\tag{4}$$

fixator *Fo(1.0, 0)* is providing the desired output as we stated, and a pairing norator

*(a) And (b) symbolic design of a hearing aid amplifier using an FNP; (c) a simplified equivalent circuit for test*

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

What we need to do next is to see how we can replace the norator with a real sub-circuit, which turns out to be an amplifier, and then try to design it. **Figure 7(a)** shows a reconstruction of the complete hearing aid system presented in **Figure 6 (c)**, except the impaired hearing block is removed. To complete this design all we need to do is to design the norator amplifier. As mentioned earlier, because of the high losses that we experience at high frequencies the amplifier must provide a gain of 60 dB or more to compensate for the impairment. In this study, we selected an amplifier that uses a TI - LM318 Op-Amp with a bandwidth of 15 MHz. This Op-Amp can provide a gain of 66 dB (2000 V/V) at 8 KHz, which is well above the required value for this case study. **Table 1** provides the Electrical Characteristics of

**Figure 7(b)** shows the amplifier constructed using LM318 Op-Amp along with its symbolic representation. With the rated gain-bandwidth product given, this Op-Amp is a very well fit to our design, although its power (0.5 W) is on the high side.

discussed here). **Figure 7(c)** is the response from the amplifier. As we can expect, this is exactly the opposite of the AGC, *RC2* frequency characteristic, shown in

There are certainly other choices of Op-Amps that can replace LM318 (not

*Vn(*�*,* �*)* is instead added to the input port to allow this to happen. Again, the difference here is that we are now looking for a constant amplitude output from the AGC and not the input. Next we may ask, what type of the input signal the norator must provide to the AGC (replaced for the impaired hearing) so that the output is well achieved, i.e., the comprehended voice is uniformly constant? For the solution, we refer to **Figure 6(c)**. As we can see here, the norator is replaced with an Op-Amp, and as a feedback. It provides the necessary signal to the AGC for a constant amplitude output. So, if we now assume that the AGC represents the impaired hearing situation then the output of the impaired hearing is also flat as we desired, actually representing the improved hearing status of the

individual.

**Figure 6.**

*purposes.*

the TI - LM318 Op-Amp.

**Figure 5(a)**.

**137**

The advantage of getting the poles and zeros through the corresponding LC circuit is that, we can access the actual and accurate locations of the roots in terms of peaks and notches that ultimately guide us into a better design of the AGC. This means, we can study the location of the real axis roots of an AGC, make appropriate changes to the locations of the roots so that the frequency response of the AGC gets close enough to the actual audiogram (**Figure 1**). **Figure 5(c)** shows two such plots for the corresponding LC circuits *LC1* and *LC2*. By observing the plots, we can extract several conclusions essential to the design. For instance, to produce a nearly constant group delay we need to create a balance between the poles and zeros of the circuit, as poles produce more lags and zeros generate more leads in the phase angle. Referring to our case of the AGCs, Bode plots in **Figure 5(c)**, we notice five poles and one zero for *LC1* transfer function that are well distributed within the bandwidth region. This, as shown in **Figure 5(b)**, produces a close to linear phase shift spanning about 200 degrees. Whereas for *LC2* the phase shift is far from linear distribution. So, the better choice for this design is clearly *RC1*, although the circuit is more involved with more components. However, for the reason that is mentioned in Example 1, we choose *RC2* as the selected AGC for our design. This concludes our control unit (AGC) design.

*Amplifier*: Now that we have done with the AGC design, our next task is to design the amplifier and the system all together. In this design we must come up with constructing the transfer function,*T(s)*, given in Eq.(3). As we notice, the roots of *T(s)* are the same as those of the AGC (*H(s)*) but the opposite, i.e., the poles of *H(s)* become the zeros of *T(s)* and vice versa. A new and rather simple method to realize *T(s)* is to use an FNP as a tool and later replace it with real components [2]. For this implementation we start with the circuit in **Figure 6**, showing an AGC circuit with an audio input signal connection that has a unit amplitude for the entire frequency bandwidth. As expected, this input signal generates an output close to the designated audiogram. Now, we may change the problem statement and ask the following question. What do we need to connect at the input port of the AGC in order to get an output signal with unit amplitude within the audio bandwidth (250 Hz to 8 KHz)? To answer this question we refer to **Figure 6(b)**, where a

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

#### **Figure 6.**

1.Change all resistors (*R*) in the RC circuit into inductors (*L*) with the same

2.The controlled sources and the controlling variables (I and V) must be of the same kind. So, for example, a voltage controlled current source VCCS must be changed to either a current controlled current source (CCCS) or to a voltage

3. Simulate the LC circuit and generate the Bode plots, and then rescale the

*Corresponding LC circuits* – As fully explained in [9], it is simply proven that, if *LCi* is the corresponding LC circuit of an RC circuit, *RCi*, then for any real axis root ωRC in *RCi* there exist a pair of conjugate roots �*ωLC* on the *jω* axis for *LC*<sup>i</sup> so that

The advantage of getting the poles and zeros through the corresponding LC circuit is that, we can access the actual and accurate locations of the roots in terms of peaks and notches that ultimately guide us into a better design of the AGC. This means, we can study the location of the real axis roots of an AGC, make appropriate changes to the locations of the roots so that the frequency response of the AGC gets close enough to the actual audiogram (**Figure 1**). **Figure 5(c)** shows two such plots for the corresponding LC circuits *LC1* and *LC2*. By observing the plots, we can extract several conclusions essential to the design. For instance, to produce a nearly constant group delay we need to create a balance between the poles and zeros of the circuit, as poles produce more lags and zeros generate more leads in the phase angle. Referring to our case of the AGCs, Bode plots in **Figure 5(c)**, we notice five poles and one zero for *LC1* transfer function that are well distributed within the bandwidth region. This, as shown in **Figure 5(b)**, produces a close to linear phase shift spanning about 200 degrees. Whereas for *LC2* the phase shift is far from linear distribution. So, the better choice for this design is clearly *RC1*, although the circuit is more involved with more components. However, for the reason that is mentioned in Example 1, we choose *RC2* as the selected AGC for our design. This concludes our

*Amplifier*: Now that we have done with the AGC design, our next task is to design the amplifier and the system all together. In this design we must come up with constructing the transfer function,*T(s)*, given in Eq.(3). As we notice, the roots of *T(s)* are the same as those of the AGC (*H(s)*) but the opposite, i.e., the poles of *H(s)* become the zeros of *T(s)* and vice versa. A new and rather simple method to realize *T(s)* is to use an FNP as a tool and later replace it with real components [2]. For this implementation we start with the circuit in **Figure 6**, showing an AGC circuit with an audio input signal connection that has a unit amplitude for the entire frequency bandwidth. As expected, this input signal generates an output close to the designated audiogram. Now, we may change the problem statement and ask the following question. What do we need to connect at the input port of the AGC in order to get an output signal with unit amplitude within the audio bandwidth (250 Hz to 8 KHz)? To answer this question we refer to **Figure 6(b)**, where a

2

log ð Þ¼ *ωLC* log ð Þ *ωRC =*2 (4)

, or in the log format the scaling

values.

frequency axis.

factor is specified by

control unit (AGC) design.

**136**

Here is how it works.

controlled voltage source (VCVS).

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

they are related through the relationship ωRC = ωLC

*(a) And (b) symbolic design of a hearing aid amplifier using an FNP; (c) a simplified equivalent circuit for test purposes.*

fixator *Fo(1.0, 0)* is providing the desired output as we stated, and a pairing norator *Vn(*�*,* �*)* is instead added to the input port to allow this to happen. Again, the difference here is that we are now looking for a constant amplitude output from the AGC and not the input. Next we may ask, what type of the input signal the norator must provide to the AGC (replaced for the impaired hearing) so that the output is well achieved, i.e., the comprehended voice is uniformly constant? For the solution, we refer to **Figure 6(c)**. As we can see here, the norator is replaced with an Op-Amp, and as a feedback. It provides the necessary signal to the AGC for a constant amplitude output. So, if we now assume that the AGC represents the impaired hearing situation then the output of the impaired hearing is also flat as we desired, actually representing the improved hearing status of the individual.

What we need to do next is to see how we can replace the norator with a real sub-circuit, which turns out to be an amplifier, and then try to design it. **Figure 7(a)** shows a reconstruction of the complete hearing aid system presented in **Figure 6 (c)**, except the impaired hearing block is removed. To complete this design all we need to do is to design the norator amplifier. As mentioned earlier, because of the high losses that we experience at high frequencies the amplifier must provide a gain of 60 dB or more to compensate for the impairment. In this study, we selected an amplifier that uses a TI - LM318 Op-Amp with a bandwidth of 15 MHz. This Op-Amp can provide a gain of 66 dB (2000 V/V) at 8 KHz, which is well above the required value for this case study. **Table 1** provides the Electrical Characteristics of the TI - LM318 Op-Amp.

**Figure 7(b)** shows the amplifier constructed using LM318 Op-Amp along with its symbolic representation. With the rated gain-bandwidth product given, this Op-Amp is a very well fit to our design, although its power (0.5 W) is on the high side. There are certainly other choices of Op-Amps that can replace LM318 (not discussed here). **Figure 7(c)** is the response from the amplifier. As we can expect, this is exactly the opposite of the AGC, *RC2* frequency characteristic, shown in **Figure 5(a)**.

**Figure 7.** *(a) Hearing aid amplifier; (b) the construction of the amplifier using high gain Op-amp: (c) the amplifier frequency response.*

We are now going through an examples to see how the technique practically works.

**Example 1** – For this example we again take the case of the hearing-impaired patient with the audiogram given in **Figure 2**. We then construct the audio amplifier given in **Figure 7(a)** and **(b)**. However, there are some design considerations that needs to be addressed here. Our main challenge is to produce enough gain at higher frequencies (8 KHz) where the hearing loss is the most. By using TI - LM318 Op-Amp we get a small signal bandwidth of 15 MHz, which means, at 8 KHz frequency we can barely get 2000 V/V or 66 dB gain. Hence, this explains one of the reasons for selecting *RC2* instead of *RC1* for this design, which is to settle with lower gain requirement.

For testing purposes, we attach another AGC (audiogram) to the output port of the amplifier, resembling the hearing situation of the person with hearing impaired. **Figure 8** shows the combination of three parts: the input signal representing the voice received, the audio amplifier for voice processing, and the AGC model representing the hearing-impaired of the patient. As shown, the audio amplifier (hearing aid) receives the voice, amplifies it, and sends it to the patient's ear. The entire circuit is simulated and the results are plotted in **Figure 9(a)** and **(b)**, for magnitude and phase, respectively. In **Figure 9** we observe the frequency response of the amplifier that is exactly opposite of the frequency profile of the audiogram, represented by the AGC. The final result is a hearing profile which is flat for the entire frequency range.

Before constructing the system for laboratory testing, the circuit is simulated using WinSpice, and the following is the main portion of the code used for the simulation.

**Electrical Characteristics (1)**

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

Input Offset Voltage TA = 25°C 2 4 4 10 mV Input Offset Current TA = 25°C 6 50 30 200 nA Input Bias Current TA = 25°C 120 250 150 500 nA Input Resistance TA = 25°C 1 3 0.5 3 MΩ Supply Current TA = 25°C 5 8 5 10 mA

Small Signal Bandwidth TA = 25°C, VS = 15 V 15 15 MHz Input Offset Voltage 6 15 mV Input Offset Current 100 300 nA *(1)These specifications apply for 5 V* <sup>≤</sup> *VS* <sup>≤</sup> *20 V and 55°C* <sup>≤</sup> *TA* <sup>≤</sup> *+125°C (Im118-n), 25°C* <sup>≤</sup> *TA* <sup>≤</sup> *+85°C (LM218-N), and 0 °C* <sup>≤</sup> *TA* <sup>≤</sup> *+70°C (LM318-N). Also, power supplies must be bypassed with 0.1 <sup>μ</sup>F disc capacitors. (2)Slew rate is tested with VS <sup>=</sup>15 V. The Im118-n is in a unity-gain non-inverting configuration. VIN is stepped from 7.5 V to +7.5 V and vice versa. The slew rates between 5.0 V and + 5.0 V and vice versa are tested and specified to exceed 50 V/μs.*

**LM218-N**

TA = 25°C, VS = 15 V 50 200 25 200 V/mV

**Min Typ Max Min Typ Max**

50 70 50 70 V/μs

**LM318-N Units**

**Parameter Conditions LM118-N/**

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

VOUT = 10 V, RL ≥ 2 kΩ

AV = 1(2)

Slew Rate TA = 25°C, VS = 15 V,

*Electrical characteristics of the TI - LM318 Op-amp used.*

.control. destroy all.

set units = degrees. ac dec 1000 250 8 k.

*A testing bench; testing the hearing aid amplifier.*

Large Signal Voltage

Gain

**Table 1.**

op

**139**

**Figure 8.**


*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

*(1)These specifications apply for 5 V* <sup>≤</sup> *VS* <sup>≤</sup> *20 V and 55°C* <sup>≤</sup> *TA* <sup>≤</sup> *+125°C (Im118-n), 25°C* <sup>≤</sup> *TA* <sup>≤</sup> *+85°C (LM218-N), and 0 °C* <sup>≤</sup> *TA* <sup>≤</sup> *+70°C (LM318-N). Also, power supplies must be bypassed with 0.1 <sup>μ</sup>F disc capacitors. (2)Slew rate is tested with VS <sup>=</sup>15 V. The Im118-n is in a unity-gain non-inverting configuration. VIN is stepped from 7.5 V to +7.5 V and vice versa. The slew rates between 5.0 V and + 5.0 V and vice versa are tested and specified to exceed 50 V/μs.*

#### **Table 1.**

We are now going through an examples to see how the technique practically

*(a) Hearing aid amplifier; (b) the construction of the amplifier using high gain Op-amp: (c) the amplifier*

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

**Example 1** – For this example we again take the case of the hearing-impaired patient with the audiogram given in **Figure 2**. We then construct the audio amplifier given in **Figure 7(a)** and **(b)**. However, there are some design considerations that needs to be addressed here. Our main challenge is to produce enough gain at higher frequencies (8 KHz) where the hearing loss is the most. By using TI - LM318 Op-Amp we get a small signal bandwidth of 15 MHz, which means, at 8 KHz frequency we can barely get 2000 V/V or 66 dB gain. Hence, this explains one of the reasons for selecting *RC2* instead of *RC1* for this design, which is to settle with lower

For testing purposes, we attach another AGC (audiogram) to the output port of the amplifier, resembling the hearing situation of the person with hearing impaired. **Figure 8** shows the combination of three parts: the input signal representing the voice received, the audio amplifier for voice processing, and the AGC model representing the hearing-impaired of the patient. As shown, the audio amplifier (hearing aid) receives the voice, amplifies it, and sends it to the patient's ear. The entire circuit is simulated and the results are plotted in **Figure 9(a)** and **(b)**, for magnitude and phase, respectively. In **Figure 9** we observe the frequency response of the amplifier that is exactly opposite of the frequency profile of the audiogram, represented by the AGC. The final result is a hearing profile which is flat for the

works.

**Figure 7.**

*frequency response.*

gain requirement.

entire frequency range.

**138**

*Electrical characteristics of the TI - LM318 Op-amp used.*

#### **Figure 8.**

*A testing bench; testing the hearing aid amplifier.*

Before constructing the system for laboratory testing, the circuit is simulated using WinSpice, and the following is the main portion of the code used for the simulation.

.control. destroy all. op set units = degrees. ac dec 1000 250 8 k. plot ph(v(5)) ph(v(16)) ph(v(9)). plot db(v(5)) db(v(16)) db(v(9)) .endc. \* Supplies and signal sources \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*. VCC 10 0 DC 5 VEE 0 20 DC 5 vi 1 0 DC 0 AC 90 m \* Combined Hearing Aid System \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*. rc c 1 50 x3 4 c 10 20 5 Amp2 x4 5 7 4 AGC3 x8 5 15 16 AGC3 r3 16 0 10Meg \* AGC, Defected hearing profile \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*. re e 1 50 x5 e 11 9 AGC 3 r6 9 0 10Meg \* Audiogram Generated Circuit \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* .subckt AGC3 1 2 3 r0 1 2 1 k c1 2 0 300n r1 2 3 2.5 k c2 3 0 400n .ends. \* Amplifier for high gain, Gain = 5 k V/V, 74 dB \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* .subckt Amp2 1 2 10 20 5 x1 1 2 10 20 3 Amp1 r1 0 4 1 k r2 4 5 100 k x2 3 4 10 20 5 LM318 .ends. \* Amplifier using LM318 Op-Amp, Gain = 50 V/V, 34 dB \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* .subckt Amp1 1 2 10 20 5 x1 3 4 10 20 5 LM318 r1 2 4 1 k r2 4 5 50 k r3 1 3 1 k r4 3 0 50 k c1 4 5 0.3p .ends. \* LM318 Op-Amp model parameters \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* .include op-models.txt .end.

Following the simulation, the hearing aid circuit is constructed and the tested in a laboratory setup. **Figure 10** shows the experimental bread board for testing purposes, and **Figures 11**–**13** are the test results at different frequencies.

**Figure 14**. We start constructing an AGC model for this case, which is much similar to the one we did for Example 1. The circuit is constructed from R and C components and is then simulated for its frequency responses. **Figure 15** shown the magnitude Bode plot of the AGC. In addition, the audiogram is also added to the figure for comparison. Our next step in the process is to construct the amplifier needed. Again, because of the modularity property the design procedure of the AGC is quite simple. All we need to do is to take the same amplifier constructed for Example 1 (**Figure 7(a)**) and replace its AGC, given at **Figure 3(b)**, with the new one created, for this example. For testing purposes, we again put all three units (the input signal representing the voice received, the audio amplifier with the new AGC, and a second AGC representing the hearing-impaired patient) together and simulate. The setup will be similar to the testing bench provided for Example 1 and shown in **Figure 10**. We then simulate the combined circuits again and plot the frequency responses. The responses from the amplifier and the one from the hearing profile, comprehended by the hearing-impaired patient, are given in **Figure 16**. Again, notice that the hearing has improved substantially by using the amplifier. As seen, the comprehended voice is quite flat just like the one we had in Example 1. Also

*Simulation results: (a) magnitude plots from the test bench in Figure 8, including the amplifier response,*

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

*audiogram, and the hearing profile by the hearing-impaired patient; (b) the phase responses.*

Further, in comparing plots in **Figure 16** with those in **Figure 9(a)**, we notice that the two amplifiers respond differently but the net results, i.e., the comprehended

notice that the ultimate phase angle has become flat, as well.

**Figure 9.**

**141**

The output responses of the amplifier are shown at 250 Hz, 1.0 KHz, and 4.0 KHz frequencies. Notice, that not only the magnitude changes and increases for higher frequencies, but phase delay also increases up to 82 degrees. Finally, **Table 2** shows the experimental results for the gain vs. frequencies for the amplifier.

**Example 2** – Now we are going to try a different audiogram in this example, one from a person with a rather mild hearing impairment. This audiogram is given in

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

#### **Figure 9.**

plot ph(v(5)) ph(v(16)) ph(v(9)). plot db(v(5)) db(v(16)) db(v(9))

VCC 10 0 DC 5 VEE 0 20 DC 5

x4 5 7 4 AGC3 x8 5 15 16 AGC3 r3 16 0 10Meg

x5 e 11 9 AGC 3 r6 9 0 10Meg

.subckt AGC3 1 2 3

rc c 1 50

re e 1 50

r0 1 2 1 k c1 2 0 300n r1 2 3 2.5 k c2 3 0 400n

r1 0 4 1 k r2 4 5 100 k

r1 2 4 1 k r2 4 5 50 k r3 1 3 1 k r4 3 0 50 k c1 4 5 0.3p

.include op-models.txt

.ends.

.ends.

.ends.

.end.

**140**

\* Supplies and signal sources \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*.

\* Combined Hearing Aid System \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*.

\* AGC, Defected hearing profile \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*.

\* Audiogram Generated Circuit \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*

.subckt Amp2 1 2 10 20 5 x1 1 2 10 20 3 Amp1

.subckt Amp1 1 2 10 20 5 x1 3 4 10 20 5 LM318

x2 3 4 10 20 5 LM318

\* Amplifier for high gain, Gain = 5 k V/V, 74 dB \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*

\* Amplifier using LM318 Op-Amp, Gain = 50 V/V, 34 dB \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*

\* LM318 Op-Amp model parameters \*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*

a laboratory setup. **Figure 10** shows the experimental bread board for testing purposes, and **Figures 11**–**13** are the test results at different frequencies.

Following the simulation, the hearing aid circuit is constructed and the tested in

The output responses of the amplifier are shown at 250 Hz, 1.0 KHz, and 4.0 KHz frequencies. Notice, that not only the magnitude changes and increases for higher frequencies, but phase delay also increases up to 82 degrees. Finally, **Table 2** shows the experimental results for the gain vs. frequencies for the amplifier.

**Example 2** – Now we are going to try a different audiogram in this example, one from a person with a rather mild hearing impairment. This audiogram is given in

vi 1 0 DC 0 AC 90 m

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

x3 4 c 10 20 5 Amp2

.endc.

*Simulation results: (a) magnitude plots from the test bench in Figure 8, including the amplifier response, audiogram, and the hearing profile by the hearing-impaired patient; (b) the phase responses.*

**Figure 14**. We start constructing an AGC model for this case, which is much similar to the one we did for Example 1. The circuit is constructed from R and C components and is then simulated for its frequency responses. **Figure 15** shown the magnitude Bode plot of the AGC. In addition, the audiogram is also added to the figure for comparison.

Our next step in the process is to construct the amplifier needed. Again, because of the modularity property the design procedure of the AGC is quite simple. All we need to do is to take the same amplifier constructed for Example 1 (**Figure 7(a)**) and replace its AGC, given at **Figure 3(b)**, with the new one created, for this example. For testing purposes, we again put all three units (the input signal representing the voice received, the audio amplifier with the new AGC, and a second AGC representing the hearing-impaired patient) together and simulate. The setup will be similar to the testing bench provided for Example 1 and shown in **Figure 10**. We then simulate the combined circuits again and plot the frequency responses. The responses from the amplifier and the one from the hearing profile, comprehended by the hearing-impaired patient, are given in **Figure 16**. Again, notice that the hearing has improved substantially by using the amplifier. As seen, the comprehended voice is quite flat just like the one we had in Example 1. Also notice that the ultimate phase angle has become flat, as well.

Further, in comparing plots in **Figure 16** with those in **Figure 9(a)**, we notice that the two amplifiers respond differently but the net results, i.e., the comprehended

totally remove the hearing deficiencies and provide a convenient hearing. The

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

*Input signal (lower) and the amplifier response (upper) for 1 KHz. Note the scale difference.*

*Input signal (lower) and the amplifier response (upper) for 4 KHz. Note the scale difference.*

**Frequency Hz 250 300 700 1 K 1.7 K 2 K 3 K 4 K** Gain Av V/V 3 4 13 20 39 65 98 200

1.Construct a passive AGC that represents the audiogram profile of a hearingimpaired patient as closely as possible, like the ones shown in **Figures 4** and **15**.

procedure is as follows:

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

**Figure 12.**

**Figure 13.**

**Table 2.**

**143**

*Audio amplifier experimental results.*

**Figure 10.** *A testing bench; experimenting the hearing aid amplifier.*

**Figure 11.**

*Input signal (lower) and the amplifier response (upper) for 250 Hz. Note the scale difference.*

voices are the same and completely flat. This shows the adaptability property of the amplifier. That is, as we discussed earlier, in shifting from one example (patient) to another all we need to do is to design a new AGC, while the amplifier unit remains unchanged, unless the ultimate gain of the amplifier in not sufficient to compensate for all the losses, recorded in the audiogram.

This brings us to the following algorithm for the construction of an adaptable amplifier for hearing aids.

#### **Algorithm 1.**

Given an audiogram similar to the one shown in **Figure 2** or **Figure 14**, we can construct an adaptable front-end or stand-alone analog amplifier that can be used to *Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

totally remove the hearing deficiencies and provide a convenient hearing. The procedure is as follows:

1.Construct a passive AGC that represents the audiogram profile of a hearingimpaired patient as closely as possible, like the ones shown in **Figures 4** and **15**.

#### **Figure 12.**

*Input signal (lower) and the amplifier response (upper) for 1 KHz. Note the scale difference.*

#### **Figure 13.**

voices are the same and completely flat. This shows the adaptability property of the amplifier. That is, as we discussed earlier, in shifting from one example (patient) to another all we need to do is to design a new AGC, while the amplifier unit remains unchanged, unless the ultimate gain of the amplifier in not sufficient to compensate

*Input signal (lower) and the amplifier response (upper) for 250 Hz. Note the scale difference.*

This brings us to the following algorithm for the construction of an adaptable

Given an audiogram similar to the one shown in **Figure 2** or **Figure 14**, we can construct an adaptable front-end or stand-alone analog amplifier that can be used to

for all the losses, recorded in the audiogram.

*A testing bench; experimenting the hearing aid amplifier.*

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

amplifier for hearing aids.

**Algorithm 1.**

**142**

**Figure 11.**

**Figure 10.**

*Input signal (lower) and the amplifier response (upper) for 4 KHz. Note the scale difference.*


#### **Table 2.**

*Audio amplifier experimental results.*

**Figure 14.** *Audiogram from a patient with mild hearing impairment.*

4. Simulate the entire system in a setup shown in **Figure 8**, for verification

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

*Magnitude and phase responses from the amplifier and the comprehended hearing profile.*

example, for factory workers for whom it may be needed to reduce certain machinery noises or enhance those related to the onsite conversation.

Up until now we have assumed that the comprehended voice by the patient needs to be flat, leading to the gain function of *F(s) = 1*. Now, we assume an arbitrary gain function *F(s)* recommended for the hearing-impaired patient, suit-

This is done by splitting the design procedure into two parts. In the first part we again assume a flat response with *F(s) = 1*, and in the second part we modify the amplifier so constructed to generate the frequency response *T(s)* for different *F(s)*. This modular design may also provide us with the options to switch between the

This concludes our design procedure for hearing aids with flat responses, where *F(s) = 1* in (1). What we need to do next is to extend the design to cover for the cases when *F(s)* is not necessarily flat due to some preferences in the hearing quality, for

purposes.

**Figure 16.**

**6. Design with extra gain added**

able for his/her application.

**145**

**Figure 15.**

*The comparison between the audiogram and the frequency response of the adopted AGC.*


*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

**Figure 16.** *Magnitude and phase responses from the amplifier and the comprehended hearing profile.*

4. Simulate the entire system in a setup shown in **Figure 8**, for verification purposes.

This concludes our design procedure for hearing aids with flat responses, where *F(s) = 1* in (1). What we need to do next is to extend the design to cover for the cases when *F(s)* is not necessarily flat due to some preferences in the hearing quality, for example, for factory workers for whom it may be needed to reduce certain machinery noises or enhance those related to the onsite conversation.

#### **6. Design with extra gain added**

Up until now we have assumed that the comprehended voice by the patient needs to be flat, leading to the gain function of *F(s) = 1*. Now, we assume an arbitrary gain function *F(s)* recommended for the hearing-impaired patient, suitable for his/her application.

This is done by splitting the design procedure into two parts. In the first part we again assume a flat response with *F(s) = 1*, and in the second part we modify the amplifier so constructed to generate the frequency response *T(s)* for different *F(s)*. This modular design may also provide us with the options to switch between the

2.Use the AGC and an amplifier with sufficient gain to construct an audio

3.The amplifier so constructed is adaptable, in a sense that for any other audiogram all we need to do is to replace the older AGC with a new one,

amplifier as discussed before and shown in **Figure 7(a)**.

*The comparison between the audiogram and the frequency response of the adopted AGC.*

constructed for a new patient.

*Audiogram from a patient with mild hearing impairment.*

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

**Figure 14.**

**Figure 15.**

**144**

two cases during the application. Knowing how to design for *F(s) = 1* by now, all we need to do here is to go for a desired arbitrary response, *F(s)* and add it to the system*.* Here is the problem statement.

*Problem statement* – Given an audiogram of a hearing-impaired patient, as shown in **Figures 2** or **14**, design a front-end or stand-alone amplifier that is fully adaptable and has a wide voice dynamic range covering from 250 Hz to 8 KHz, as specified in the audiogram. In addition, the amplifier is supposed to produce a comprehended voice frequency profile *F(s)* that is recommended for the patient.

*Design procedure* – To design such an amplifier we first follow the procedure explained in the previous section, i.e., design an amplifier *N* with the frequency response of *T s*ðÞ¼ *H s*ð Þ�<sup>1</sup> . As we discussed, this produces a flat response with *F(s) = 1*. We then follow the method explained in [8]. This method uses nullors to modify the amplifier circuit until it produces a transfer function*T s*ðÞ¼ *F s*ð Þ*=H s*ð Þ, where *F(s)* is the desired frequency response, which is produced by a *model circuit M*. Note that *M* does not need to be a physical circuit as long as it generates an output response *F(s)*.

So, the design starts by first assuming that we already have done the first part and constructed an amplifier *<sup>N</sup>* for *F(s) = 1,* which has *T s*ðÞ¼ *H s*ð Þ�<sup>1</sup> transfer function, as shown in **Figure 17(a)**. Next, let us assume we have been able to find a sub-circuit *P* (usually a feedback) so that by adding *P* to *N* the circuit can be realized to perform with a transfer function *T s*ðÞ¼ *F s*ð Þ*=H s*ð Þ, for an arbitrary *F(s)*.

4. Simulate the combined circuit. Evidently the frequency response of both circuits *M* and *N* must be identical, because of the parallel connections. So, *N* follows *M* in response. Because of the enforced response on the output of *N*, a virtual impedance function *Zp*ðÞ¼ *s Vp*ð Þ*s =Ip*ð Þ*s* is created for the norator *P* through the simulation. This means, if we replace the norator with a twoterminal circuit that has the impedance *Zp(s)*, then we get an independent response from *N* that is identical to that of *M*. Which means, *N* responds

*(a) Circuit* N *with a two-terminal* P *added; (b) realizing the two-terminal* P *by enforcing* N *to follow the*

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

5.Now we need to synthesize *P* such that its impedance characteristic is close enough to *Zp(s)*, for the specified bandwidth. Then we replace the norator *P* with the actual two-terminal *P* found. If *Zp(s)* is not realizable make proper

Note 3: The methodology works for nonlinear circuit as well, provided that the subcircuit *P* does not disturb the biasing situation of *N*. This is very important point, which means that circuit *N* must be protected by coupling/bypass capacitors, if necessary.

The following example clearly demonstrates the steps given in Algorithm 2. **Example 3** - **Figure 18** shows the same amplifier designed for Example 1 and illustrated in **Figure 8** for a flat comprehended voice bandwidth (*F(s) = 1*), except here a *model circuit M* is added to the configuration. The model circuit is connected to the amplifier in parallel and through a nullator at the output port. A paring norator *P* is also added to the AGC in the amplifier. The norator is in fact a "place holder" for an actual two terminal sub-circuit *P* that must be found to replace it. According to Algorithm 2, and for simulation purposes, we now need to replace the nullor with a high gain dependent source, and for this example we have selected a

The choice of CCVS is not unique, and in fact any of the four types of controlled sources can be selected, depending on the situation. For the present case, we first decide which variable (i or v) in the nullator is going to control the norator. We notice that the current in the nullator, although presently zero, is an effective

independently after being separated from *M*.

approximations/adjustments to fit.

**Figure 17.**

*desired response from* M*.*

CCVS, with the SPICE code given as:

**147**

va 2 12 DC 0 vb 11 13 DC 0 h1 13 0 va 1.0e6

In summary, for a given transfer function *T(s,)* we first design the circuit *N* for its *T s*ðÞ¼ *H s*ð Þ�<sup>1</sup> . We then add a sub-circuit *P* to *N* and modify *P* until we get *T s*ðÞ¼ *F s*ð Þ*=H s*ð Þ. So, our main objective here is to find the sub-circuit *P*. This is stated in a stepwise procedure, Algorithm 2.

#### **Algorithm 2**


Note 1: Practically, a norator can be a high gain controlled source or an Op Amp [2, 10].

*Note 2*: parallel connection of *N* and *M* in **Figure 17(b)** is only valid for voltage to voltage transfer functions. However, this is not the only option we have, and other configurations can also be adopted. For example, for a case of current sourcing the connections must be in series, as appropriate [8].

<sup>1</sup> Here we assume the connecting nodes of *P* to *N* are already specified. Going after the best location connecting *P* to *N* adds another dimension to the problem, which is outside of this chapter.

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

**Figure 17.**

two cases during the application. Knowing how to design for *F(s) = 1* by now, all we need to do here is to go for a desired arbitrary response, *F(s)* and add it to the

*Problem statement* – Given an audiogram of a hearing-impaired patient, as shown in **Figures 2** or **14**, design a front-end or stand-alone amplifier that is fully adaptable and has a wide voice dynamic range covering from 250 Hz to 8 KHz, as specified in the audiogram. In addition, the amplifier is supposed to produce a comprehended

. As we discussed, this produces a flat response with *F(s) = 1*.

*Design procedure* – To design such an amplifier we first follow the procedure explained in the previous section, i.e., design an amplifier *N* with the frequency

We then follow the method explained in [8]. This method uses nullors to modify the amplifier circuit until it produces a transfer function*T s*ðÞ¼ *F s*ð Þ*=H s*ð Þ, where *F(s)* is the desired frequency response, which is produced by a *model circuit M*. Note that *M* does not need to be a physical circuit as long as it generates an output response *F(s)*. So, the design starts by first assuming that we already have done the first part

and constructed an amplifier *<sup>N</sup>* for *F(s) = 1,* which has *T s*ðÞ¼ *H s*ð Þ�<sup>1</sup> transfer function, as shown in **Figure 17(a)**. Next, let us assume we have been able to find a sub-circuit *P* (usually a feedback) so that by adding *P* to *N* the circuit can be realized to perform with a transfer function *T s*ðÞ¼ *F s*ð Þ*=H s*ð Þ, for an arbitrary *F(s)*. In summary, for a given transfer function *T(s,)* we first design the circuit *N* for

*T s*ðÞ¼ *F s*ð Þ*=H s*ð Þ. So, our main objective here is to find the sub-circuit *P*. This is

1.Consider an amplifier *N* already designed for a flat hearing, with *F(s) = 1*. Next, try to find a model circuit *M* that produces a desirable frequency response *F(s)* that is realizable. If circuit *M* is not physically available, try to artificially synthesize *M*, possibly through a cascade decomposition method. *Note* that, because the model circuit *M* may only be needed for simulation purposes, the use of any ideal components, such as ideal controlled sources, in *M* is permissible,

2.Find a location in the circuit *N* such that adding a two terminal sub-circuit *P* to

3.Connect the two circuits *N* and *M* together in parallel, and keep the two output currents at zero by adding a nullator between the two outputs, as shown in **Figure 17(b)**. To match the nullator, add a norator *P* to the designated location

Note 1: Practically, a norator can be a high gain controlled source or an Op Amp

*Note 2*: parallel connection of *N* and *M* in **Figure 17(b)** is only valid for voltage to voltage transfer functions. However, this is not the only option we have, and other configurations can also be adopted. For example, for a case of current sourcing the

<sup>1</sup> Here we assume the connecting nodes of *P* to *N* are already specified. Going after the best location

connecting *P* to *N* adds another dimension to the problem, which is outside of this chapter.

.

*N* can bring a solution to the problem, as depicted in **Figure 17(a)**<sup>1</sup>

in *N*. This norator will be later replaced with a sub-circuit *P*.

. We then add a sub-circuit *P* to *N* and modify *P* until we get

voice frequency profile *F(s)* that is recommended for the patient.

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

system*.* Here is the problem statement.

stated in a stepwise procedure, Algorithm 2.

which makes it easier to generate.

connections must be in series, as appropriate [8].

response of *T s*ðÞ¼ *H s*ð Þ�<sup>1</sup>

its *T s*ðÞ¼ *H s*ð Þ�<sup>1</sup>

**Algorithm 2**

[2, 10].

**146**

*(a) Circuit* N *with a two-terminal* P *added; (b) realizing the two-terminal* P *by enforcing* N *to follow the desired response from* M*.*


Note 3: The methodology works for nonlinear circuit as well, provided that the subcircuit *P* does not disturb the biasing situation of *N*. This is very important point, which means that circuit *N* must be protected by coupling/bypass capacitors, if necessary.

The following example clearly demonstrates the steps given in Algorithm 2. **Example 3** - **Figure 18** shows the same amplifier designed for Example 1 and illustrated in **Figure 8** for a flat comprehended voice bandwidth (*F(s) = 1*), except here a *model circuit M* is added to the configuration. The model circuit is connected to the amplifier in parallel and through a nullator at the output port. A paring norator *P* is also added to the AGC in the amplifier. The norator is in fact a "place holder" for an actual two terminal sub-circuit *P* that must be found to replace it. According to Algorithm 2, and for simulation purposes, we now need to replace the nullor with a high gain dependent source, and for this example we have selected a CCVS, with the SPICE code given as:


The choice of CCVS is not unique, and in fact any of the four types of controlled sources can be selected, depending on the situation. For the present case, we first decide which variable (i or v) in the nullator is going to control the norator. We notice that the current in the nullator, although presently zero, is an effective

candidate to control the norator. So either CCVS or CCCS can be selected. For more practical reasons, here we chose CCVS that closely resembles an ordinary Op-Amp. The combined circuit also includes a patient's audiogram (AGC) representing his/her hearing situations. The entire circuit is then simulated and the results are

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

plot db(v(2)) db(v(7)), the magnitude responses, **Figure 19(a)** plot db(v(11)/I(vb)), the magnitude response of zp(s), **Figure 19(b)**

There are two response plots in **Figure 19**, one (*v(2)*) from the model circuit, and another one (*v(7)*) representing the original amplifier with the flat (*F(s) =* 1) response. In addition, **Figure 19(b)** shows the frequency response of the virtual impedance associated with the norator, i.e., *Vp(s)/ Ip(s)*. What we need to do now is to find a two terminal sub-circuit *P* with the impedance function *zp(s) = Vp(s)/ Ip(s)*

In search for a realizable sub-circuit *P* we first make the assumption that *P* must be a passive RC circuit. This is realistic because *P* is going to be part of the AGC, which is already designed with passive (R and C) components. In our search we simply notice that the norator characteristic curve (**Figure 19(b)**) appears to be a

*Testing the modified hearing aid amplifier for the final results pertain to a hearing-impaired patient.*

*Comparing the frequency response of the modified amplifier circuit with the original amplifier before being*

plotted in **Figure 19(a)**. The SPICE code for the plots are:

and then substitute it for the norator.

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

**Figure 20.**

**Figure 21.**

*modified.*

**149**

**Figure 19.**

*(a) Comparing the frequency response of the model circuit M with the amplifier before being modified; (b) the frequency plot representing the virtual impedance of the norator in Figure 18.*

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

candidate to control the norator. So either CCVS or CCCS can be selected. For more practical reasons, here we chose CCVS that closely resembles an ordinary Op-Amp.

The combined circuit also includes a patient's audiogram (AGC) representing his/her hearing situations. The entire circuit is then simulated and the results are plotted in **Figure 19(a)**. The SPICE code for the plots are:

plot db(v(2)) db(v(7)), the magnitude responses, **Figure 19(a)** plot db(v(11)/I(vb)), the magnitude response of zp(s), **Figure 19(b)**

There are two response plots in **Figure 19**, one (*v(2)*) from the model circuit, and another one (*v(7)*) representing the original amplifier with the flat (*F(s) =* 1) response. In addition, **Figure 19(b)** shows the frequency response of the virtual impedance associated with the norator, i.e., *Vp(s)/ Ip(s)*. What we need to do now is to find a two terminal sub-circuit *P* with the impedance function *zp(s) = Vp(s)/ Ip(s)* and then substitute it for the norator.

In search for a realizable sub-circuit *P* we first make the assumption that *P* must be a passive RC circuit. This is realistic because *P* is going to be part of the AGC, which is already designed with passive (R and C) components. In our search we simply notice that the norator characteristic curve (**Figure 19(b)**) appears to be a

**Figure 20.**

**Figure 18.**

**Figure 19.**

**148**

*Design procedure to modify the audio amplifier for a response given by the model circuit M (see Figure 17).*

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

*(a) Comparing the frequency response of the model circuit M with the amplifier before being modified; (b) the*

*frequency plot representing the virtual impedance of the norator in Figure 18.*

*Testing the modified hearing aid amplifier for the final results pertain to a hearing-impaired patient.*

**Figure 21.**

*Comparing the frequency response of the modified amplifier circuit with the original amplifier before being modified.*

low pass filter realizable by a parallel RC circuit. The plot approaches 56 dB (631) at low frequencies and it falls at higher frequencies with break point frequency at *fp = 118 Hz*. Next, to find the RC circuit, we first find *R1 = 631 Ω*, and then from *fp* we get the equivalent capacitor *C1 = (2π.fp.R1)*�*<sup>1</sup>* , or *C1 = 2.1 μF*. So, now the twoterminal norator *P* can be replaced with the components *R1* and *C1* in cascade, as shown in **Figure 20(a)**. The next step is to replace the older AGC in **Figure 18** with this modifies AGC, and then remove the model circuit all together.

Finally, **Figure 20(b)** shows a testing setup for the new hearing amplifier. After the simulation we plot the frequency response of the entire system as "Modified Amplifier", plotted in **Figure 21**. The Bode plot actually represents the voice heard and comprehended by the hearing-impaired patient. Also for comparison purposes, the result of a similar testing setup for the original amplifier with flat response (*F (s) = 1*) is also shown in **Figure 21**. A point to notice here is that, the new *R1C1* circuit although passive, it contributes to a higher gain in amplifier and helps for an enhanced hearing. However, the price we need to pay is to assume higher gain for the Op-Amp. For example, although a gain of 60 dB is sufficient for the hearing aid with a flat response, *F(s) =* 1, it is not enough for this kind of enhanced situation. With about 20 dB gain desired here, we need to add the same amount to the Op-Amp and make it for 80 dB gain. So, here we see that the gain of 66 dB we have adopted for the Op-Amp is not sufficient any more, or we may lose some gain and precision losses at high frequencies, as we notice it in **Figure 21**.

#### **7. Feedback implementation of analog hearing aids**

As mentioned before, there is an alternative implementation technique to design hearing-aid amplifiers. This technique uses the well-known negative feedback methodology, which consists of a high forward gain amplifier inverting a transfer function generated by a feedback circuit. Consider a high gain amplifier *A(s)* in the forward path of a feedback system, and an AGC, with the transfer function *H(s),* placed in the feedback. The system transfer function *T(s)* then becomes:

$$T(s) = \frac{A(s)}{1 + A(s)H(s)}\tag{5}$$

and for a special condition

$$A(\mathfrak{s})H(\mathfrak{s}) > \mathfrak{I} \tag{6}$$

$$T(\mathfrak{s}) \cong H(\mathfrak{s})^{-1} \tag{7}$$

performance. Notice that within the three plots (AGC, Hearing, and Amplifier) in each case the two AGCs are obviously the same, but the major difference is the following. In FNP implementation the frequency profile of the amplifiers is almost opposite of that of the AGC, whereas in the feedback case this is not true. In the

*Simulation results from the testing bench in Figure 22; (a) the amplifier response and hearing profile by the*

*hearing-impaired patient; (b) the frequency response of the AGC.*

**Figure 22.**

**Figure 23.**

**151**

*A test setup for the hearing aid amplifier using normal negative feedback.*

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

Eq. (7) is similar to Eq. (3) except for the constraint given in Eq. (6). This shows that the two methodologies, the feedback and the FNP, have elements in common, but different in implementation. We will discuss the major differences between the two later in this section However, let us analyze the feedback system first.

*Feedback Implementation* – **Figure 22** shows a feedback implementation of the hearing aid system testing setup. In the amplifier circuit part, the Op-Amp *A1* is constructed similar to what we did for FNP method in **Figure 7(b)**. For a better comparison between the feedback method and one using the FNP based design, we try to use identical components such as the AGC and the Op-Amp circuit. We then simulate the testing setup (**Figure 22**). The result of the simulation is shown in **Figure 23**. We can now compare these results with those obtained for the FNP case given in **Figure 9**. Although they look similar in general but they are different in

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

**Figure 22.** *A test setup for the hearing aid amplifier using normal negative feedback.*

#### **Figure 23.**

low pass filter realizable by a parallel RC circuit. The plot approaches 56 dB (631) at low frequencies and it falls at higher frequencies with break point frequency at *fp = 118 Hz*. Next, to find the RC circuit, we first find *R1 = 631 Ω*, and then from *fp* we

terminal norator *P* can be replaced with the components *R1* and *C1* in cascade, as shown in **Figure 20(a)**. The next step is to replace the older AGC in **Figure 18** with

Finally, **Figure 20(b)** shows a testing setup for the new hearing amplifier. After the simulation we plot the frequency response of the entire system as "Modified Amplifier", plotted in **Figure 21**. The Bode plot actually represents the voice heard and comprehended by the hearing-impaired patient. Also for comparison purposes, the result of a similar testing setup for the original amplifier with flat response (*F (s) = 1*) is also shown in **Figure 21**. A point to notice here is that, the new *R1C1* circuit although passive, it contributes to a higher gain in amplifier and helps for an enhanced hearing. However, the price we need to pay is to assume higher gain for the Op-Amp. For example, although a gain of 60 dB is sufficient for the hearing aid with a flat response, *F(s) =* 1, it is not enough for this kind of enhanced situation. With about 20 dB gain desired here, we need to add the same amount to the Op-Amp and make it for 80 dB gain. So, here we see that the gain of 66 dB we have adopted for the Op-Amp is not sufficient any more, or we may lose some gain and

As mentioned before, there is an alternative implementation technique to design

hearing-aid amplifiers. This technique uses the well-known negative feedback methodology, which consists of a high forward gain amplifier inverting a transfer function generated by a feedback circuit. Consider a high gain amplifier *A(s)* in the forward path of a feedback system, and an AGC, with the transfer function *H(s),*

*T s*ðÞ¼ *A s*ð Þ

Eq. (7) is similar to Eq. (3) except for the constraint given in Eq. (6). This shows that the two methodologies, the feedback and the FNP, have elements in common, but different in implementation. We will discuss the major differences between the

*Feedback Implementation* – **Figure 22** shows a feedback implementation of the hearing aid system testing setup. In the amplifier circuit part, the Op-Amp *A1* is constructed similar to what we did for FNP method in **Figure 7(b)**. For a better comparison between the feedback method and one using the FNP based design, we try to use identical components such as the AGC and the Op-Amp circuit. We then simulate the testing setup (**Figure 22**). The result of the simulation is shown in **Figure 23**. We can now compare these results with those obtained for the FNP case given in **Figure 9**. Although they look similar in general but they are different in

two later in this section However, let us analyze the feedback system first.

placed in the feedback. The system transfer function *T(s)* then becomes:

this modifies AGC, and then remove the model circuit all together.

precision losses at high frequencies, as we notice it in **Figure 21**.

**7. Feedback implementation of analog hearing aids**

and for a special condition

**150**

, or *C1 = 2.1 μF*. So, now the two-

<sup>1</sup> <sup>þ</sup> *A s*ð Þ*H s*ð Þ (5)

*A s*ð Þ*H s*ð Þ> >*1* (6) *T s*ðÞffi *H s*ð Þ�<sup>1</sup> (7)

get the equivalent capacitor *C1 = (2π.fp.R1)*�*<sup>1</sup>*

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

*Simulation results from the testing bench in Figure 22; (a) the amplifier response and hearing profile by the hearing-impaired patient; (b) the frequency response of the AGC.*

performance. Notice that within the three plots (AGC, Hearing, and Amplifier) in each case the two AGCs are obviously the same, but the major difference is the following. In FNP implementation the frequency profile of the amplifiers is almost opposite of that of the AGC, whereas in the feedback case this is not true. In the

However, in addition to its simplicity and cost effectiveness the analog hearing aid technique may still offer some advantages in certain areas. In particular, in comparing the two systems there are some operational factors to consider, and here are a couple of these factors. In digital technique, the incoming voice needs to go through ADC (analog-to-digital conversion), and after being processed the output signal reenters into an inverse process of DAC. This definitely adds to the *path delay* of the signal as well as reducing the *precision accuracy* of the signal due to the double data conversion. In case of analog methodology, however, we have neither of them. The signal stays analog all the way through, and the delay is just equal to the analog

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

A methodology is developed and explained in this chapter that uses nullors and FNPs to design amplifiers for certain frequency profiles. The method is applied for

The method works as follows: For a given hearing profile (audiogram), a circuit model, called Audiogram Generator Circuit (AGC), is initially constructed. This AGC has the same, or close to, frequency response of the audiogram. Now, because of typical losses in hearing, it is shown that this AGC is all passive for a hearingimpaired patient, and it can be made quite simple and modular. Next, an FNP is used to construct an adaptable amplifier inversely following the AGC frequency spectrum. This amplifier converts the frequency profile (transfer function) of the AGC such that the poles and zeros of the AGC are exchanged and become the zeros and poles of the amplifier circuit. So, when the amplifier is used as a hearing aid, the result will be a flat frequency response for the comprehended voice heard by the patient. A second design method is also introduced in the chapter, which use the negative feedback theory. Although not a powerful as the FNP method, the feed-

The FNP design is further extended to cover the cases in which extra gain, and in general some added frequency profile is needed. This feature may help to enhance signals in certain frequencies for clear understanding, or conversely, cancel some unwanted sounds and noises. Here, it is shown how the original amplifier can be modified by adding some sub-circuits to the original AGC without touching any other part in the amplifier (such as Op-Amp circuits). Three examples of actual

propagation delay of the signal through a limited number of devices.

designing audio amplifiers for front-end or stand-alone hearing aids.

back technique is modified for impedance matching.

cases of hearing-impaired patients are worked out.

**9. Conclusion**

**153**

**Figure 24.**

*Hearing aid amplifier using normal negative feedback. Another amplifier is added to prevent the AGC from being loaded.*

feedback we are losing the gain for high frequencies, and that is why we are not getting a flat response at the end, as we do in the FNP case (Hearing in **Figure 9**). The consequence is that we are loosing the voice quality at high frequencies.

This, as it turns out, is due to the lack of impedance matching in the feedback case. For a passive circuit like AGC, the 2R resistive loading creates a clear variation in the AGC response because of loading. However, this is not the case for FNP methodology. Let us look at **Figure 6(b)**. Because a fixator with zero current is connected to the output port the AGC is never loaded. So it stays unchanged no matter what happens to the rest of the circuit. Back to the feedback case, one way to correct the loading problem is to use a buffer stage at the output port of the AGC circuit. This is demonstrated in **Figure 24**, where an extra amplifier is added to the output of the AGC. This of course fulfills the impedance matching and prevents the AGC being loaded. Afterwards, if we simulate the circuit we see the improvement, and the response received is almost the same as given in **Figure 8** for FNP realization.

Finally, we need to mention another major difference between the feedback method and the FNP technique. Let us revisit Eq. (7) and compare it with Eq. (3). To have the two equations identical we need to have *A(s)H(s) > > 1*, as stated in Eq. (6). This is basically a serious constraint for designing hearing aids when the corresponding audiogram (AGC) displays a large loss in higher frequencies. To make it clear, let us assume that we get satisfied with 1% accuracy for the system when we use the feedback method. This means |*A(s)H(s)|* ≥ *100*, for all the bandwidth*.* This means we always need to have the gain of the amplifier 40 dB higher than the largest inverse loss in the feedback. For example, for an AGC with 60 dB loss at high frequency we need an amplifier gain of 100 dB, instead of 60 dB, to satisfy the job, and this makes the system harder to design. The good news, however, is that if we intend to use the setup shown in **Figure 24** for impedance matching purposes then we can split the high gain requirement between the two amplifiers in the feedback loop and make it more distributed amplifier, Of course there are still some consequences involved but we ignore them here for simplicity. In any case, this shows the superiority of the FNP method compared to the feedback theory.

This concludes our design alternative using negative feedback technique.

#### **8. Some basic comparisons with digital technology**

As mentioned in Introduction, with digital high-tech so advanced the digital hearing aid dominates the market as well as the research and development areas. *Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

However, in addition to its simplicity and cost effectiveness the analog hearing aid technique may still offer some advantages in certain areas. In particular, in comparing the two systems there are some operational factors to consider, and here are a couple of these factors. In digital technique, the incoming voice needs to go through ADC (analog-to-digital conversion), and after being processed the output signal reenters into an inverse process of DAC. This definitely adds to the *path delay* of the signal as well as reducing the *precision accuracy* of the signal due to the double data conversion. In case of analog methodology, however, we have neither of them. The signal stays analog all the way through, and the delay is just equal to the analog propagation delay of the signal through a limited number of devices.

#### **9. Conclusion**

feedback we are losing the gain for high frequencies, and that is why we are not getting a flat response at the end, as we do in the FNP case (Hearing in **Figure 9**). The consequence is that we are loosing the voice quality at high frequencies.

*Hearing aid amplifier using normal negative feedback. Another amplifier is added to prevent the AGC from*

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

**Figure 24.**

*being loaded.*

**152**

This is basically a serious constraint for designing hearing aids when the

superiority of the FNP method compared to the feedback theory.

**8. Some basic comparisons with digital technology**

This concludes our design alternative using negative feedback technique.

As mentioned in Introduction, with digital high-tech so advanced the digital hearing aid dominates the market as well as the research and development areas.

corresponding audiogram (AGC) displays a large loss in higher frequencies. To make it clear, let us assume that we get satisfied with 1% accuracy for the system when we use the feedback method. This means |*A(s)H(s)|* ≥ *100*, for all the bandwidth*.* This means we always need to have the gain of the amplifier 40 dB higher than the largest inverse loss in the feedback. For example, for an AGC with 60 dB loss at high frequency we need an amplifier gain of 100 dB, instead of 60 dB, to satisfy the job, and this makes the system harder to design. The good news, however, is that if we intend to use the setup shown in **Figure 24** for impedance matching purposes then we can split the high gain requirement between the two amplifiers in the feedback loop and make it more distributed amplifier, Of course there are still some consequences involved but we ignore them here for simplicity. In any case, this shows the

This, as it turns out, is due to the lack of impedance matching in the feedback case. For a passive circuit like AGC, the 2R resistive loading creates a clear variation in the AGC response because of loading. However, this is not the case for FNP methodology. Let us look at **Figure 6(b)**. Because a fixator with zero current is connected to the output port the AGC is never loaded. So it stays unchanged no matter what happens to the rest of the circuit. Back to the feedback case, one way to correct the loading problem is to use a buffer stage at the output port of the AGC circuit. This is demonstrated in **Figure 24**, where an extra amplifier is added to the output of the AGC. This of course fulfills the impedance matching and prevents the AGC being loaded. Afterwards, if we simulate the circuit we see the improvement, and the response received is almost the same as given in **Figure 8** for FNP realization. Finally, we need to mention another major difference between the feedback method and the FNP technique. Let us revisit Eq. (7) and compare it with Eq. (3). To have the two equations identical we need to have *A(s)H(s) > > 1*, as stated in Eq. (6).

A methodology is developed and explained in this chapter that uses nullors and FNPs to design amplifiers for certain frequency profiles. The method is applied for designing audio amplifiers for front-end or stand-alone hearing aids.

The method works as follows: For a given hearing profile (audiogram), a circuit model, called Audiogram Generator Circuit (AGC), is initially constructed. This AGC has the same, or close to, frequency response of the audiogram. Now, because of typical losses in hearing, it is shown that this AGC is all passive for a hearingimpaired patient, and it can be made quite simple and modular. Next, an FNP is used to construct an adaptable amplifier inversely following the AGC frequency spectrum. This amplifier converts the frequency profile (transfer function) of the AGC such that the poles and zeros of the AGC are exchanged and become the zeros and poles of the amplifier circuit. So, when the amplifier is used as a hearing aid, the result will be a flat frequency response for the comprehended voice heard by the patient. A second design method is also introduced in the chapter, which use the negative feedback theory. Although not a powerful as the FNP method, the feedback technique is modified for impedance matching.

The FNP design is further extended to cover the cases in which extra gain, and in general some added frequency profile is needed. This feature may help to enhance signals in certain frequencies for clear understanding, or conversely, cancel some unwanted sounds and noises. Here, it is shown how the original amplifier can be modified by adding some sub-circuits to the original AGC without touching any other part in the amplifier (such as Op-Amp circuits). Three examples of actual cases of hearing-impaired patients are worked out.

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

**References**

Hill 1995.

1993.

2015.

**155**

[1] R. Hashemian, "Amplifier Design for Specific Frequency Response Profiles Using Nullors—Hearing Aids, a Case Study", IEEE Trans. Circuits Syst. I, Regular Papers, vol. 65, issue 12, 2018.

*DOI: http://dx.doi.org/10.5772/intechopen.97842*

on the Real Axis," *IEEE Trans. Circuits Syst. II, Exp. Briefs,* vol. 61, no. 8, pp. 624-628, August 2014.

[10] R. Hashemian, " Fixator-Norator Pairs vs Direct Analytical Tools in Performing Analog Circuit Designs," *IEEE Trans. Circuits Syst. II, Exp. Briefs,*

vol. 61, no. 8, pp. 569 - 573,

August 2014.

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching*

[2] R. Hashemian, "Application of Fixator-Norator Pairs in Designing Active Loads and Current Mirrors in Analog Integrated Circuits," *IEEE Trans. Very Large Scale Int. (VLSI) Syst.*, vol. 20, no. 12, pp 2220 – 2231, Dec. 2012.

[3] T.L. Pillage, R.A. Rohrer, C. Visweswariah, *Electronic Circuit & System Simulation Methods*, McGraw-

[4] R. Hashemian, K. Golla, S.M. Kuo, and A. Joshi, "Design and Construction of an Active Periodic Noise Canceling System Using FPGAs," 36th IEEE Midwest Symposium on Circuits and Systems, Detroit, MI, August 16-18,

[5] A. S. Sedra, and K. C. Smith,

[6] V. Valkenburg, *Introduction to Modern Network Synthesis*, John Wiley &

Sons, New York, 1960.

*Microelectronic Circuits*, Eighth Edition, Oxford Univ A. S. Sedra, and K. C. Smith, *Microelectronic Circuits*, Eighth Edition, Oxford University Press, 2020.

[7] R. Hashemian, " S-Plane Bode Plots - Identifying Poles and Zeros in a Circuit Transfer Function," Proceedings of the IEEE LASCAS 2015 Conference,

Montevideo, Uruguay, February 24 – 27,

[8] R. Hashemian, "Application of Nullors in Designing Analog Circuits for Bandwidth", IEEE Inter. Conf. on Electro/Information Technology, *EIT2016 conference proceedings*, Grand

Forks, ND, May 19 - 21, 2016.

[9] R. Hashemian, "Extraction of Poles and Zeros of an RC Circuit with Roots

#### **Author details**

Reza Hashemian

Department of Electrical Engineering, Northern Illinois University, DeKalb, Illinois, USA

\*Address all correspondence to: reza@niu.edu

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching DOI: http://dx.doi.org/10.5772/intechopen.97842*

#### **References**

[1] R. Hashemian, "Amplifier Design for Specific Frequency Response Profiles Using Nullors—Hearing Aids, a Case Study", IEEE Trans. Circuits Syst. I, Regular Papers, vol. 65, issue 12, 2018.

[2] R. Hashemian, "Application of Fixator-Norator Pairs in Designing Active Loads and Current Mirrors in Analog Integrated Circuits," *IEEE Trans. Very Large Scale Int. (VLSI) Syst.*, vol. 20, no. 12, pp 2220 – 2231, Dec. 2012.

[3] T.L. Pillage, R.A. Rohrer, C. Visweswariah, *Electronic Circuit & System Simulation Methods*, McGraw-Hill 1995.

[4] R. Hashemian, K. Golla, S.M. Kuo, and A. Joshi, "Design and Construction of an Active Periodic Noise Canceling System Using FPGAs," 36th IEEE Midwest Symposium on Circuits and Systems, Detroit, MI, August 16-18, 1993.

[5] A. S. Sedra, and K. C. Smith, *Microelectronic Circuits*, Eighth Edition, Oxford Univ A. S. Sedra, and K. C. Smith, *Microelectronic Circuits*, Eighth Edition, Oxford University Press, 2020.

[6] V. Valkenburg, *Introduction to Modern Network Synthesis*, John Wiley & Sons, New York, 1960.

[7] R. Hashemian, " S-Plane Bode Plots - Identifying Poles and Zeros in a Circuit Transfer Function," Proceedings of the IEEE LASCAS 2015 Conference, Montevideo, Uruguay, February 24 – 27, 2015.

[8] R. Hashemian, "Application of Nullors in Designing Analog Circuits for Bandwidth", IEEE Inter. Conf. on Electro/Information Technology, *EIT2016 conference proceedings*, Grand Forks, ND, May 19 - 21, 2016.

[9] R. Hashemian, "Extraction of Poles and Zeros of an RC Circuit with Roots

on the Real Axis," *IEEE Trans. Circuits Syst. II, Exp. Briefs,* vol. 61, no. 8, pp. 624-628, August 2014.

[10] R. Hashemian, " Fixator-Norator Pairs vs Direct Analytical Tools in Performing Analog Circuit Designs," *IEEE Trans. Circuits Syst. II, Exp. Briefs,* vol. 61, no. 8, pp. 569 - 573, August 2014.

**Author details**

Reza Hashemian

\*Address all correspondence to: reza@niu.edu

*Hearing Loss - From Multidisciplinary Teamwork to Public Health*

provided the original work is properly cited.

USA

**154**

Department of Electrical Engineering, Northern Illinois University, DeKalb, Illinois,

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

**157**

Section 5

Implementation Strategies

in Public Health

### Section 5
