**4.1. Mixer circuit**

To obtain conduction parameters in foil ferrite samples, the parameter *α* was initially calculated

reactions) during sintering cycle in processing technology of Mn-Zn bulk ferrites in contrast to

the processing temperature during sintering cycle. Finally, knowing *α* and *μ* parameters, *ε*<sup>0</sup> *<sup>ε</sup><sup>r</sup>* was estimated for both longitudinal and transverse bias. **Table 3** summarizes the conduction parameters at longitudinal bias where L = 2 mm, W = 1 mm (physical width of each foil ferrite under test), and *S* = *t* × *W* with *t* as the thickness previously estimated by XRD analysis in Section 3.1, while the conduction parameters at transverse bias are registered in **Table 4**, where

is equivalent to *Fe* <sup>∙</sup> *Fe*<sup>2</sup> *<sup>O</sup>*<sup>4</sup>

\_\_\_ ∆*d <sup>d</sup>* )*MnO*

where tensile stress dominated by longer distance and angle of 180°

tion (carrier distribution), resulting *n* in the range from 1020 to 1022 cm<sup>−</sup><sup>3</sup>

**Sample** *α VC* **(***V***)** ∆*G*<sup>∗</sup> **(***eV***)** *VTFL* **(***V***)** *μ* **(***cm***<sup>2</sup>** *V***<sup>−</sup><sup>1</sup>** *s* **<sup>−</sup><sup>1</sup>**

FF-1 0.92 × 10<sup>−</sup><sup>4</sup> 1.12 0.56 2.32 5.49 *x* 10<sup>−</sup><sup>3</sup> 7.61 FF-2 1.32 × 10<sup>−</sup><sup>5</sup> 1.44 0.72 2.88 1.43 *x* 10<sup>−</sup><sup>3</sup> 36.87 FF-3 0.85 × 10<sup>−</sup><sup>5</sup> 1.68 0.84 2.64 4.83 *x* 10<sup>−</sup><sup>4</sup> 632.74

in the octahedral sites. As radius of *Fe*+3

gen ions will define magnetic properties as a function of the distance and angle of the Mn─O─Zn bonds; also, SCLC will depend on different conduction mechanisms related to the exponential distribution of defects (grain boundaries) [13, 27]. From results attained here, it is confirmed that the

> and *y*~( \_\_\_ <sup>∆</sup>*dd* )*Zno*

positive associated to tensile stress while negative in sample FF-1 related to compressive stress. In the samples, *x* and *y* are connected by the coupling type dominant in the Mn-O-Zn bonds,

*pled*, while compressive stress is *ferromagnetically coupled* at shorter distance with angle of 90°

and *VTFL* voltages from **Tables 3** and **4** were extracted to evaluate the charge concentra-

and magnetic ordering are correlating to the charge concentration differences of foil ferrites.

(*ε*<sup>0</sup> *εr*) −1 , and

with value of

in the

and

.

in

for this analysis.

, are found as in earlier methodologies, where both

, should be responsible for the diffusion processes (displacement

) smaller than the activation energy of about 1 eV at *T* > 800° C for

*kT* ), where k is the Boltzmann constant and T is equivalent at

allows explaining structure and conduction properties in foil

than FF-2 and FF-3 samples. Chemical composition approximately

at the bulk of each sample, which reveals that major differences of

with *Fe*+3

, structural disorder will occur; therefore, exchange interactions via the oxy-

can be estimated as a function of *VC*

will be used to evaluate conduction properties in foil ferrite samples as a

is the cross section area of the aluminum electrodes.

, has been well estimated [26, 27]. Also, adia-

ion substituted by *Mn*+2

) in samples FF-2 and FF-3 resulted to be

**)** *ε***<sup>0</sup>** *ε<sup>r</sup>* **(***F cm***<sup>−</sup>1)**

is *antiferromagnetically cou-*

at the surface while *Nt*

is smaller than that of *Zn*+2

from I-V curves. Then, by tracing slopes on I-V curves, the critical voltage, *VC* <sup>=</sup> <sup>10</sup>*en <sup>L</sup>*<sup>2</sup>

the overall activation energy under SCLC. Theoretical studies have reported ∆*G*<sup>∗</sup>

*L*2 (*ε*<sup>0</sup> *εr*) −1

∆*G*<sup>∗</sup> \_\_\_\_\_

trap-filled limit voltage, *VTFL* <sup>=</sup> <sup>6</sup>*<sup>e</sup> Nt*

batic activation energy, ∆*G*<sup>∗</sup>

198 Iron Ores and Iron Oxide Materials

0.5 eV for pure hematite (*Fe*<sup>2</sup> *<sup>O</sup>*<sup>3</sup>

function of the mobility *μ*~*exp*(<sup>−</sup>

L = 1 mm and *S* = 3.14 × 10<sup>−</sup><sup>2</sup> cm<sup>2</sup>

Chemical formula *Mnx Zny Fe*<sup>2</sup> *<sup>O</sup>*<sup>4</sup>

ferrites where magnetite *Fe*<sup>3</sup> *<sup>O</sup>*<sup>4</sup>

sample FF-1 exhibits lower ϵ2*<sup>θ</sup>*

the range from 1015 to 1017 cm<sup>−</sup><sup>3</sup>

**Table 3.** Conduction parameters at longitudinal bias.

proportional to the average strain (*x*~(

tetrahedral sites and *Zn*+2

greater than that of *Mn*+2

The *VC*

*ε*<sup>0</sup> *ε<sup>r</sup>*

Thus, ∆*G*<sup>∗</sup> <sup>=</sup> 0.5 *VC*

conductivity [28]; then as reference ∆*G*<sup>∗</sup>

carrier concentration, *n*, and trap concentration, *Nt*

Modulation is the process of converting information one wants to obtain into one or more properties of a sinusoidal signal called the carrier. This information can be analogic signal, such as a varying voltage or current, or a digital signal, which consists of sequence of bits, i.e., 0 and 1 values. In general several modulation schemes can be represented by using mixer circuits. The main type of modulator recently employed is the quadrature mixer [29].

To disclose the performance of a foil ferrite as mixer circuit to modulation process, a basic schematic diagram of **Figure 7** has been built. A full-rectified signal with amplitude of 15 V was applied on first outer node at operating frequency of 120 Hz. In the middle node, a sinusoidal signal with amplitude of ±7.5 V at operating frequency of 500 Hz was applied. The full-rectified signal was obtained by a variable self-transformer of alternating voltage from 0 to 150 V. A resistor of 1 kΩ is connected in the second outer node to monitoring of mixing signal (see **Figure 7**). It is observed that the mixing signal follows the shape of the full-rectified signal when it is larger than the sinusoidal signal, producing an output signal with amplitude of ±3.5 V. Otherwise, when the amplitude of the sinusoidal signal is greater with respect to the full-rectified signal, mixing process is negligible, because there are strong anisotropy differences among longitudinal and transverse paths on foil ferrite samples related to its structural disorder. Therefore, a foil ferrite will operate in the electronic signal processors integrated by mixer circuits to drive control systems as a function of complex signals at low-power excitation [30].

produces unity gain, and as a result, the PLL provides an online estimate of the synchronized fundamental component, y(t), and its phase angle, φ(t), with output frequency equal to that of the input during phase lock. The PLL is an adaptive system which follows variations in amplitude, phase angle, and frequency of signal u(t). Hence, the structure of a PLL is simple, and this

Mn-Zn Ferrite as Recycled Material Resource Based on Iron Oxide Suitable to Functional Green…

The schematic circuit of **Figure 9** was used to evaluate the performance of the foil ferrite

put signal. To simulate phase difference between two sinusoidal signals, a low-pass filter built with a simple RC circuit was implemented [33]. Signal connected to the RC circuit input

and *V*<sup>2</sup>

is 22.5°

.

and *V*<sup>1</sup>

to monitoring of out-

, 9.2°

signals is close to zero when

and when

, and 1.2° ,

,

201

. Such signals are applied on

at operating frequency in the range of 0.5 to 5 kHz.

, while to 1 kHz is 40.5°

. Meanwhile, at the output node *V*<sup>0</sup>

http://dx.doi.org/10.5772/intechopen.72418

makes it suitable for real-time applications for hardware implementations [32].

sample as phase detector. A resistor of 10 kΩ is connected in node *V*<sup>0</sup>

, while signal collected from RC circuit matches with *V*<sup>2</sup>

when frequency is 0.5 kHz, 1 kHz, and 5 kHz, the phase angle corresponds to 4.5°

**Figure 9.** Schematic circuit to evaluate the performance of the foil ferrite FF-3 as phase detector.

signals shift from 0 to 90°

where ±10 V is fixed in *V*<sup>1</sup>

At 0.5 kHz, the phase angle between signals *V*<sup>1</sup>

The resulting waveforms are shown from **Figure 10(a)**–**(c)**.

**Figure 8.** Block diagram of a conventional phase-locked loop (PLL) system.

operating frequency increase until 5 kHz resulted to be 58.5°

respectively. It is observed that the phase angle between *V*<sup>0</sup>

and *V*<sup>2</sup>

relates *V*<sup>1</sup>

nodes *V*<sup>1</sup>

and *V*<sup>2</sup>

phase angle between *V*<sup>1</sup>

**Figure 6.** Foil ferrite equivalent at the self-inductor with hysteresis.

**Figure 7.** Schematic of the mixer circuit done with foil ferrite FF-1 when it is operating under full-rectified and sinusoidal signals to produce mixing signal.

#### **4.2. Phase detector**

A phase detector produces a voltage proportional to e(t) = u(t) – y(t) as the phase difference between the signals u(t) and y(t) in the block diagram of **Figure 8**. This block diagram corresponds to phase-locked loop (PLL) system. A PLL is comprised of three blocks: phase detector, filter, and voltage-controlled oscillator (VCO).

The voltage e(t) upon filtering is used as control signal for the VCO. The VCO produces a frequency proportional to input signal u(t), and any time variant signal appearing on the filter output will modulate the VCO frequency [31]. A feedback path among VCO and phase detector Mn-Zn Ferrite as Recycled Material Resource Based on Iron Oxide Suitable to Functional Green… http://dx.doi.org/10.5772/intechopen.72418 201

**Figure 8.** Block diagram of a conventional phase-locked loop (PLL) system.

produces unity gain, and as a result, the PLL provides an online estimate of the synchronized fundamental component, y(t), and its phase angle, φ(t), with output frequency equal to that of the input during phase lock. The PLL is an adaptive system which follows variations in amplitude, phase angle, and frequency of signal u(t). Hence, the structure of a PLL is simple, and this makes it suitable for real-time applications for hardware implementations [32].

The schematic circuit of **Figure 9** was used to evaluate the performance of the foil ferrite sample as phase detector. A resistor of 10 kΩ is connected in node *V*<sup>0</sup> to monitoring of output signal. To simulate phase difference between two sinusoidal signals, a low-pass filter built with a simple RC circuit was implemented [33]. Signal connected to the RC circuit input relates *V*<sup>1</sup> , while signal collected from RC circuit matches with *V*<sup>2</sup> . Such signals are applied on nodes *V*<sup>1</sup> and *V*<sup>2</sup> where ±10 V is fixed in *V*<sup>1</sup> at operating frequency in the range of 0.5 to 5 kHz. The resulting waveforms are shown from **Figure 10(a)**–**(c)**.

At 0.5 kHz, the phase angle between signals *V*<sup>1</sup> and *V*<sup>2</sup> is 22.5° , while to 1 kHz is 40.5° and when operating frequency increase until 5 kHz resulted to be 58.5° . Meanwhile, at the output node *V*<sup>0</sup> , when frequency is 0.5 kHz, 1 kHz, and 5 kHz, the phase angle corresponds to 4.5° , 9.2° , and 1.2° , respectively. It is observed that the phase angle between *V*<sup>0</sup> and *V*<sup>1</sup> signals is close to zero when phase angle between *V*<sup>1</sup> and *V*<sup>2</sup> signals shift from 0 to 90° .

**Figure 9.** Schematic circuit to evaluate the performance of the foil ferrite FF-3 as phase detector.

**4.2. Phase detector**

signals to produce mixing signal.

filter, and voltage-controlled oscillator (VCO).

**Figure 6.** Foil ferrite equivalent at the self-inductor with hysteresis.

200 Iron Ores and Iron Oxide Materials

A phase detector produces a voltage proportional to e(t) = u(t) – y(t) as the phase difference between the signals u(t) and y(t) in the block diagram of **Figure 8**. This block diagram corresponds to phase-locked loop (PLL) system. A PLL is comprised of three blocks: phase detector,

**Figure 7.** Schematic of the mixer circuit done with foil ferrite FF-1 when it is operating under full-rectified and sinusoidal

The voltage e(t) upon filtering is used as control signal for the VCO. The VCO produces a frequency proportional to input signal u(t), and any time variant signal appearing on the filter output will modulate the VCO frequency [31]. A feedback path among VCO and phase detector

use, availability, and recycling have not been taken into account. Nevertheless, to ensure availability of the materials for future generations, the transformation of waste into usable materials has been discussed here, as more environmentally beneficial which implies that resource disposal and material flow will require well-designed systems into manufacturing stages. The latter is a challenge for engineers and scientists responsible with the current state of the nature resources. The Mn-Zn ferrites have been chosen as recycled material resource because it provides suitable uncommon physical properties when it is converted from bulk ferrite to foil ferrite. Also, negative environmental impact such as emission of toxic gases during powder preparation, higher use of energy resources into sintering cycle, and electronic waste from consumer electronics has demonstrated that Mn-Zn ferrites in bulk shape take their final placement often in landfills. But, to take advantages of the properties in foil ferrites, a recycling model has been employed here as a methodology based on Life-Cycle Green Strategy (LCGS) to ensure recy-

Mn-Zn Ferrite as Recycled Material Resource Based on Iron Oxide Suitable to Functional Green…

http://dx.doi.org/10.5772/intechopen.72418

203

Due to the interrelation of the structure and conduction properties as a function on magnetic ordering which is the key issue in green electronic device design, the x-ray diffraction and electrical studies have been done on foil ferrites to know if the operating parameters are useful and when it would be used as functional green device. Those studies have confirmed that structural disorder and carrier concentration under longitudinally and transversally bias conditions are responsible of the nonlinear behavior which obeys at the carriers' conduction into

Finally, it has been shown that fundamental tools such as recycling practices and basic characterization routes are needed to provide theoretical basis for the green materials exploration, converting waste materials into suitable materials in its second life. Discovering the fascinating properties of the materials, especially structure, conduction, and magnetic parameters is a key to continue the trends to green processing and then synthesize adaptive oxide materials

cling efficiency during all overall stages into the green manufacturing.

their small grained crystalline structure.

intended for electronic signal processors.

Address all correspondence to: rbaca02006@yahoo.com.mx

America: John Wiley & Sons; 1972. 357 p

Hall, Inc; 1972. 460 p

Department of Electronics, National Polytechnic Institute, México City, Mexico

[1] Grove AS. Physics and Technology of Semiconductors Devices. 1st ed. United States of

[2] Keyser CA. Materials Science in Engineering. 6th ed. United States of America: Prentice-

**Author details**

Roberto Baca

**References**

**Figure 10.** Waveforms monitored from the schematic circuit of **Figure 9** driven at three operating frequencies: (a) 0.5, (b) 1, and (c) 5 kHz. The input and output signals are shown.

Also, *V*<sup>2</sup> and *V*<sup>0</sup> signals decrease slowly as frequency rises. Results from **Figure 10** indicate that foil ferrite samples of grain-reduced crystalline structure with single magnetic domain offer controllable power losses under low-frequency excitation. Hence, a foil ferrite will operate like PLL system.

### **5. Summary**

Since 1994, initiatives in response to the environmental and ecotoxicological concerns in manufacturing processes based on life-cycle assessment (LCA) have been established. To manufacturing electronic devices with desired characteristics, the conventional selection of raw materials had depended on link between material and function; however, environmental consequences of use, availability, and recycling have not been taken into account. Nevertheless, to ensure availability of the materials for future generations, the transformation of waste into usable materials has been discussed here, as more environmentally beneficial which implies that resource disposal and material flow will require well-designed systems into manufacturing stages. The latter is a challenge for engineers and scientists responsible with the current state of the nature resources.

The Mn-Zn ferrites have been chosen as recycled material resource because it provides suitable uncommon physical properties when it is converted from bulk ferrite to foil ferrite. Also, negative environmental impact such as emission of toxic gases during powder preparation, higher use of energy resources into sintering cycle, and electronic waste from consumer electronics has demonstrated that Mn-Zn ferrites in bulk shape take their final placement often in landfills. But, to take advantages of the properties in foil ferrites, a recycling model has been employed here as a methodology based on Life-Cycle Green Strategy (LCGS) to ensure recycling efficiency during all overall stages into the green manufacturing.

Due to the interrelation of the structure and conduction properties as a function on magnetic ordering which is the key issue in green electronic device design, the x-ray diffraction and electrical studies have been done on foil ferrites to know if the operating parameters are useful and when it would be used as functional green device. Those studies have confirmed that structural disorder and carrier concentration under longitudinally and transversally bias conditions are responsible of the nonlinear behavior which obeys at the carriers' conduction into their small grained crystalline structure.

Finally, it has been shown that fundamental tools such as recycling practices and basic characterization routes are needed to provide theoretical basis for the green materials exploration, converting waste materials into suitable materials in its second life. Discovering the fascinating properties of the materials, especially structure, conduction, and magnetic parameters is a key to continue the trends to green processing and then synthesize adaptive oxide materials intended for electronic signal processors.
