**4. Interface electronics**

620 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

**3.3. Experimental assessment of the single taxel behavior** 

which also allowed for the required dynamics.

5 MPa, as reported in section 2.

( )

+

3 d Fh

In order to optimize the design of the skin prototypes we checked the pertinence/limits of the mechanical model, thus quantifying the PVDF electrical response to the external mechanical stimuli and testing the effect of the protective layer (material and thickness) on the PVDF response. We performed the tests on basic single taxel prototypes, where a single circular PVDF film is covered with an elastomeric cover to protect the sensor from physical damage by shocks or chemical contamination by oil and other materials. Attention has been focused on gel/rubber layers, in that they are more controllable and reproducible systems

An experimental campaign has been carried out in order to quantify the sensor output charge in common tactile interaction tasks. The mechanical input stimuli range from 50 Pa to

**Figure 5.** Single taxel skin prototype: comparison between model and experiments.

The "modally tuned impulse force hammer" (see Section 2) has been used to mechanically stimulate the single taxel sample. In this case, we recall that the load cell measures a contact force, which depends both on the indenter and on the protective layer materials. The measured charge over the 5 kPa - 5 MPa stress range has been compared with the model presented in the previous section and results are reported in Figure 5. In this case, on the horizontal axis the peak amplitude of the *time behavior* of the contact force is reported. Similarly, the peak amplitude of the charge response is reported on the y axis. It is

<sup>q</sup> <sup>2</sup> <sup>ˆ</sup> <sup>h</sup> *A r*

π= −

3 33 3 5 2 2 2

(8)

In Figure 6 the basic block diagram of the interface electronics is shown. The interface electronics converts the charge developed by the PVDF – as a result of the applied stress – to a voltage signal. It includes a Charge Amplifier (CA) cascaded with a Low Pass Filter (LPF) with high *cutoff frequency*, *fH*. The CA has a high pass response with low *cutoff frequency*, *fL*. The frequency band of interest at constant gain is, therefore, defined as BW = *fH* - *fL*.

**Figure 6.** Basic block diagram of the interface electronics.

The mathematical expression of the charge generated by the PVDF sensor can be found from the piezoelectric constitutive equation (2) of Section 3.1. Considering the op amp as ideal, the electric field *E3* across the PVDF sensor is negligible because of the virtual ground at the op amp non inverting terminal. Therefore, under the assumption of the thickness mode operation, the expression for the electrical displacement reduces to (3). The charge generated by the PVDF sensor can be found by integrating the electrical displacement *D3* over the loading area *Ac*:

$$q = \iint\_{A\_{\mathbb{C}}} D\_3 dA\_3 = d\_{33} A\_{\mathbb{C}} T\_3 = d\_{33} F\_{\mathbb{C}} \tag{9}$$

where the stress *T3* = *Fc* / *Ac* is assumed to be uniform over the loading area, and *Fc* is the applied contact force (see Figure 7).

**Figure 7.** PVDF tactile sensor: The PVDF material (in the middle) is provided of two electrodes *(left)*. Charge amplifier connected to the PVDF equivalent electrical circuit model and the cascaded low pass filter *(right)*.

Figure 7 *(right)* shows the simplified equivalent circuit model of the PVDF sensor connected to the CA. In order to find the mathematical expression for the equivalent voltage source *Vp* Equation (2) can be used. In case of open circuit across the electrodes of the PVDF film, *D3* is zero. Therefore, expressing the electric field as the ratio of the open circuit voltage to the PVDF thickness (i.e. *E3* = *Vp*/*tp*) and considering the loading area *Ac* equal to the PVDF area *APVDF*, we found:

$$V\_p = -\left(\frac{t\_p}{\varepsilon\_{33} A\_c}\right) d\_{33} F\_c = -\frac{q}{C\_p} \tag{10}$$

where *Cp* (*= ε33APVDF/tp*) is the equivalent capacitance of the PVDF film and *q* (= *d33Fc*) is the resulting charge. Using (10) and by analyzing the circuit of Figure 7 *(right)*, the transfer function of the CA – in terms of the input charge to the output voltage ratio – can be found:

$$H\_{\rm CA}(\mathbf{s}) = \frac{V\_{o1}}{q} = \frac{sR\_f}{1 + s\mathbb{C}\_1R\_f} \tag{11}$$

The sensitivity of the CA is given by the ratio between the maximum output voltage (i.e. the supply voltage in the ideal case) to the maximum input charge. The sensitivity sets the value to be given to the feedback capacitance *C1* (i.e. *Vo1,max* / *qmax* = 1/*C1*). Moreover, the CA low cutoff frequency defines the value to be given to the feedback resistance *Rf* (i.e. *fL* = 1/(2π*RfC1*)).

#### **4.1. Effects of the operational amplifier non idealities**

The objective of the present section is to analyze the limitations which come into play when the op amp non idealities are taken into account. The non-idealities influence the behavior both of the op amp and of the PVDF tactile sensor.

#### *4.1.1. Finite op amp open-loop gain*

622 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

filter *(right)*.

*APVDF*, we found:

1/(2π*RfC1*)).

**Figure 7.** PVDF tactile sensor: The PVDF material (in the middle) is provided of two electrodes *(left)*. Charge amplifier connected to the PVDF equivalent electrical circuit model and the cascaded low pass

Figure 7 *(right)* shows the simplified equivalent circuit model of the PVDF sensor connected to the CA. In order to find the mathematical expression for the equivalent voltage source *Vp* Equation (2) can be used. In case of open circuit across the electrodes of the PVDF film, *D3* is zero. Therefore, expressing the electric field as the ratio of the open circuit voltage to the PVDF thickness (i.e. *E3* = *Vp*/*tp*) and considering the loading area *Ac* equal to the PVDF area

33

 *A C* = − = − 

*c p*

1

*f*

(10)

(11)

33 *p p c*

ε

*<sup>t</sup> <sup>q</sup> <sup>V</sup> d F*

where *Cp* (*= ε33APVDF/tp*) is the equivalent capacitance of the PVDF film and *q* (= *d33Fc*) is the resulting charge. Using (10) and by analyzing the circuit of Figure 7 *(right)*, the transfer function of the CA – in terms of the input charge to the output voltage ratio – can be found:

1

The sensitivity of the CA is given by the ratio between the maximum output voltage (i.e. the supply voltage in the ideal case) to the maximum input charge. The sensitivity sets the value to be given to the feedback capacitance *C1* (i.e. *Vo1,max* / *qmax* = 1/*C1*). Moreover, the CA low cutoff frequency defines the value to be given to the feedback resistance *Rf* (i.e. *fL* =

The objective of the present section is to analyze the limitations which come into play when the op amp non idealities are taken into account. The non-idealities influence the behavior

*f o*

*V sR*

*q sC R* = = <sup>+</sup>

( ) <sup>1</sup>

*CA*

**4.1. Effects of the operational amplifier non idealities** 

both of the op amp and of the PVDF tactile sensor.

*H s*

The open-loop gain of an op amp, *a*, is not infinite, therefore, the electric field, *E3* across the electrodes of the PVDF is not negligible. Hence, the dielectric contribution due to the electric field cannot be neglected in the piezoelectric constitutive Equation (2). Therefore, the total charge in input to the CA, is:

$$q\_{tot} = \left(d\_{33}F\_3\right) + \left(-\frac{\varepsilon\_{33}A\_{PVDF}}{t\_p}\frac{V\_{o1}}{a}\right) = q\_F + q\_E \tag{12}$$

where the first term *qF* is due to the applied force (i.e. direct piezoelectric effect), while, the second term *qE* is due to the electric field caused by the op amp finite open-loop gain (i.e. inverse piezoelectric effect).


(a) The LPF has a unity gain

(b) Open-loop gain OPA703

**Table 2.** Charge amplifier and low pass filter component values.

In order to quantify how the finite open-loop gain could contribute to the generated charge let us give the following example. Let the op amp be the OPA7035 which is supplied at ±5 V. The CA parameters are the ones reported in Table 2; let the range of contact forces be 0.1 N ÷ 25 N (where the maximum force makes the CA output to saturate to 5 V); and let us assume *APVDF* = *AC*. Finally, let the PVDF parameters be the ones reported in Table 3. Using Equation (12) the charge contribution due to the op amp finite open-loop gain is reported in Table 4.

<sup>5</sup> http://www.ti.com/lit/ds/symlink/opa703.pdf

As it can be seen from the values reported in Table 4, the charge, *qE* due to the electric field contribution can be considered negligible, with respect to the dielectric contribution, the higher the op amp open-loop gain is.


(a) Piezo Film Sensor Technical Manual, Measurement Specialties, Inc.

(b) Refer to Figure 7.

**Table 3.** PVDF parameters.


**Table 4.** Contribution of the op amp finite open-loop gain to the input charge.

Moreover, if we consider the finite op amp open-loop gain, the CA frequency response becomes:

$$A\_{CA,q} \left( jao \right) = \left( \frac{a}{1+a} \right) \left( \frac{t\_p}{\varepsilon\_{33} A\_c} \right) \left[ \frac{jao \mathcal{C}\_p \mathcal{R}\_f}{1 + jo \left( \frac{a}{1+a} \right) \mathcal{R}\_f \left( \mathcal{C}\_1 + \frac{\mathcal{C}\_1 + \mathcal{C}\_p}{a} \right)} \right] \tag{13}$$

The module of (13) at low frequency tends to zero, while for high frequencies, it tends to:

A Tactile Sensing System Based on Arrays of Piezoelectric Polymer Transducers 625

$$\left| A\_{CA,q}(jo) \right| \equiv \left( \frac{t\_p}{\varepsilon\_{33} A\_c} \right) \frac{\mathbf{C}\_p}{\left( \mathbf{C}\_1 + \frac{\mathbf{C}\_1 + \mathbf{C}\_p}{a} \right)} \tag{14}$$

For high values of the op amp finite open-loop gain the term *(C1+Cp)/a* of Equation (14) becomes negligible.

The influence of the finite op amp open-loop gain can be considered negligible both as contribution to the generated charge and as contribution to the output frequency response of the CA. Therefore, for the analysis the op amp can be approximately considered as ideal.

#### *4.1.2. Finite Gain-bandwidth product (GBP)*

624 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

higher the op amp open-loop gain is.

Equivalent PVDF voltage source

(b) Refer to Figure 7.

becomes:

to:

**Table 3.** PVDF parameters.

(a) Piezo Film Sensor Technical Manual, Measurement Specialties, Inc.

( ) ,

ω

*CA q*

1

As it can be seen from the values reported in Table 4, the charge, *qE* due to the electric field contribution can be considered negligible, with respect to the dielectric contribution, the

**Name Parameter Value Unit** 

*Vp = - q/[(ε33 Ac)/tp]* 2e-3 (*Fc* = 0.01N) ÷ 5 (*Fc* = 25N) V

Piezoelectric constant (a) *d33* -20 pC/N Permittivity (a) *ε* 106 pF/m

PVDF thin film Length *lp* 5 mm PVDF thin film Width *bp* 5 mm PVDF thin film Thickness (a) *tp* 110 μm PVDF electrode surface (b) *APVDF=Ae = bp · lp* 25e-6 m2 Static Capacitance (b) *Cp = (ε33 Ac)/tp* 24 pF Input charge *q = d33 Fc* 0.2 (*Fc* = 0.01N) ÷ 500 (*Fc* = 25N) pC

Relative permittivity (a) *ε<sup>r</sup>* 12

Fc [N]

**Table 4.** Contribution of the op amp finite open-loop gain to the input charge.

ε

*qF*  [pC]

0.01 -2 -48.2e-9 25 -500 -120 e-9

Moreover, if we consider the finite op amp open-loop gain, the CA frequency response

1

The module of (13) at low frequency tends to zero, while for high frequencies, it tends

*a t j C R A j a A <sup>a</sup> C C*

*qE* [pC]

33 1

*c p f*

ω

*j RC a a*

1

*p p f*

<sup>=</sup> <sup>+</sup> <sup>+</sup> + + <sup>+</sup>

ω

1

(13)

The gain-bandwidth product (GBP) defines the limit of the op amp amplification, introducing a *cutoff frequency* at high frequency. When choosing an op amp it is worth to check accurately if the op amp has a GBP that allows the CA to achieve the target pass-band frequency range. Table 5 reports the results of the comparison among the three op amps which have been chosen for their suitable features in terms of GBP, open-loop gain, supply voltage and package size for the design of the interface electronics.

Both the package size and supply voltage are two important specs to be considered because of the small space available on the robot. In fact, the use of single supply op amps allows reducing the number of components without degrading the circuit performance – negative voltage regulators are not necessary thus reducing the required number of components. Components with small packages should be preferred to save space. Therefore, according to the considered op amp specs summarized in Table 5 the OPA347 is the better tradeoff.


\* http://www.ti.com/lit/ds/symlink/opa2347.pdf †http://www.ti.com/lit/ds/symlink/opa348.pdf

**Table 5.** Comparison among some off-the-shelf op amps characteristics in terms of GBP, supply voltage and package size.

Figure 8 shows that op amps in Table 5 satisfy the 1 Hz ÷ 1 kHz bandwidth specification for the *frequency band of interest*.

The experimental results validate the proposed circuit approach. The behaviour of the interface electronics is linear in the given frequency range. The input signal range of the interface electronics was able to measure up to 3 orders of input force magnitude range. In order to extend the input range of the detectable signal up to the 5 orders of magnitude expected for the application, a variable gain amplifier is currently under development.

**Figure 8.** Comparison between the ideal and CA frequency responses using an ideal op amp, the OPA703 and the OPA348/7 with their corresponding finite GBPs.
