**5. Electrical parameters for the RC circuit amplifier**

*Capacitance:* The capacitance of a parallel plate photovoltaic device with air as a dielectric medium was calculated to be 91.2 picofarads.

**19**

*Developments in Wireless Power Transfer Using Solar Energy*

*Resistance:* The electrical resistance of various components were calculated as: glass coated PV modules were approximated as 5.3 kΩ, air was approximated as 1200 MΩ, and plywood board was approximated as 26.5 Tera Ω. The total equivalent electrical resistance of a parallel plate photovoltaic device was approximated as: 5.3 kΩ.

*Time Constant:* The time constant, which is product of resistance and capacitance, was calculated to be: 0.5 microseconds. The frequency with this time con-

*Capacitive Reactance:* The capacitive reactance was calculated to be: 872.5 Ω. *Impedance:* The impedance of the circuit was calculated to be: 5.4 kΩ. *The Phase angle* θ*:* The phase angle between capacitance and reactance was

*Capacitive Heating***:** The joule law gives instantaneous power absorbed by the capacitive impedance and is converted to heat. The heat capacities under critical operation of buoyancy-induced hybrid ventilation were calculated to be 59.6 kJ, 0.755 kJ and 510.7 kJ for PV module, air and plywood board respectively [28]. The total average value of joule heating for the parallel plate photovoltaic device was

*Induction Losses:* The induction losses due to thermal storage effect in the parallel

(t) = Im 2 sin2

= θ − ω −θ (1)

(ωt + θ), the

*Power Factor:* The power factor was calculated to be cos θ = 0.911 lag.

*Voltage function:* The voltage function is defined as per the sine wave:

*Power function:* The instantaneous power is given by the expression:

effective (root mean square) value of current was calculated to be 10.4 amps and

v = Vmsin(ωt). The effective value of the voltage was calculated to be 60.4 volts and

( ) ( ) ( ) VI VI m m m m p t cos cos 2 t 2 2

*The Plots:* The time diagram for current, voltage is plotted in **Figure 5(a)**. The

*The Phasor representation***:** Z = 5.300 – *j* 0.8725 = 5.4 kΩ ∟-9°.

plate photovoltaic device was calculated to be 15.9 KJ [28].

*Current function* **(i2(t)):** Using the current function, i2

maximum value of current was calculated to be 14.71 amps.

maximum value of the voltage was calculated to be 85.42 volts.

time diagram for power is plotted in **Figure 5(b)**.

*DOI: http://dx.doi.org/10.5772/intechopen.97099*

stant was calculated to be 2 MHz.

*Potentiometer taper as a function of percentage voltage output.*

calculated to be 9°.

**Figure 4.**

calculated to be 571 kJ.

*Developments in Wireless Power Transfer Using Solar Energy DOI: http://dx.doi.org/10.5772/intechopen.97099*

*Wireless Power Transfer – Recent Development, Applications and New Perspectives*

*A star connected 3-phase generation using a parallel plate photovoltaic device.*

a potentiometer [17]. For determining electric power output with a series electrical circuit connection of a pair of vertically inclined PV modules installed on a wooden frame, the current–voltage measurements were obtained. The electrical measurement results of currents, voltages and power with varying electrical resistance of potentiometer are presented in **Table 1**. The results of the power output from a potentiometer with rotation of circular knob are illustrated in **Figure 4**. The phenomenon of photovoltaic amplification has been observed from the graph of **Figure 4**. The gain in steady state electrical for a photovoltaic device is a factor of its volume or resistance. This operational characteristic is similar to the operation of a

**Rotation Volts Amps Watts Rotation Volts Amps Watts Rotation Volts Amps Watts** 240° 18.7 — — 83° 16.3 0.935 15.23 30° 9.7 1.577 15.21 239° 16.5 0.331 5.461 75° 16.0 1.014 16.26 27° 9.0 1.587 14.33 201° 17.4 0.414 7.195 69° 15.8 1.100 17.38 21° 7.1 1.583 11.24 185° 17.5 0.454 7.940 64° 15.5 1.165 18.04 18° 6.2 1.573 9.831 162° 17.3 0.513 8.885 55° 15.0 1.302 19.53 17° 5.7 1.578 9.026 150° 17.18 0.550 9.449 50° 14.5 1.386 20.05 12° 3.9 1.567 6.257 142° 17.19 0.582 10.00 43° 13.2 1.503 19.79 10° 3.2 1.553 4.840 128° 17.1 0.640 10.93 42° 13.1 1.493 19.49 1.5° 0.5 1.593 0.807 107° 16.8 0.750 12.51 37° 11.9 1.536 18.26 1° 0.3 1.59 0.426 89° 16.4 0.884 14.45 32° 10.5 1.567 16.42 0° — 1.643 —

*Capacitance:* The capacitance of a parallel plate photovoltaic device with air as a

**5. Electrical parameters for the RC circuit amplifier**

*Sample electrical measurement results with varying resistance of potentiometer.*

dielectric medium was calculated to be 91.2 picofarads.

**18**

loudspeaker.

**Table 1.**

**Figure 3.**

**Figure 4.** *Potentiometer taper as a function of percentage voltage output.*

*Resistance:* The electrical resistance of various components were calculated as: glass coated PV modules were approximated as 5.3 kΩ, air was approximated as 1200 MΩ, and plywood board was approximated as 26.5 Tera Ω. The total equivalent electrical resistance of a parallel plate photovoltaic device was approximated as: 5.3 kΩ.

*Time Constant:* The time constant, which is product of resistance and capacitance, was calculated to be: 0.5 microseconds. The frequency with this time constant was calculated to be 2 MHz.

*Capacitive Reactance:* The capacitive reactance was calculated to be: 872.5 Ω. *Impedance:* The impedance of the circuit was calculated to be: 5.4 kΩ.

*The Phase angle* θ*:* The phase angle between capacitance and reactance was calculated to be 9°.

*The Phasor representation***:** Z = 5.300 – *j* 0.8725 = 5.4 kΩ ∟-9°.

*Capacitive Heating***:** The joule law gives instantaneous power absorbed by the capacitive impedance and is converted to heat. The heat capacities under critical operation of buoyancy-induced hybrid ventilation were calculated to be 59.6 kJ, 0.755 kJ and 510.7 kJ for PV module, air and plywood board respectively [28]. The total average value of joule heating for the parallel plate photovoltaic device was calculated to be 571 kJ.

*Induction Losses:* The induction losses due to thermal storage effect in the parallel plate photovoltaic device was calculated to be 15.9 KJ [28].

*Power Factor:* The power factor was calculated to be cos θ = 0.911 lag.

*Current function* **(i2(t)):** Using the current function, i2 (t) = Im 2 sin2 (ωt + θ), the effective (root mean square) value of current was calculated to be 10.4 amps and maximum value of current was calculated to be 14.71 amps.

*Voltage function:* The voltage function is defined as per the sine wave: v = Vmsin(ωt). The effective value of the voltage was calculated to be 60.4 volts and maximum value of the voltage was calculated to be 85.42 volts.

*Power function:* The instantaneous power is given by the expression:

$$\mathbf{p}(\mathbf{t}) = \frac{\mathbf{V\_m I\_m}}{2} \cos(\theta) - \frac{\mathbf{V\_m I\_m}}{2} \cos(2\alpha \mathbf{t} - \theta) \tag{1}$$

*The Plots:* The time diagram for current, voltage is plotted in **Figure 5(a)**. The time diagram for power is plotted in **Figure 5(b)**.

**Figure 5.** *Time diagrams: (a) voltage and current; (b) power in the RC circuit amplifier.*

#### **5.1 Discussions on power transfer and effects of inductance**

*Capacitive Reactance and Resistance in Series:* The losses that appear in capacitive circuits are lumped in a resistor connected in series with the capacitor.

*Capacitance and Resistance in parallel:* When a sine waveform voltage is applied across a capacitor and a charging current of sine waveform is transmitted across the circuit. The alternating current source, which is a sine waveform voltage, if applied at a uniform rate, is responsible sinusoidal response of the charging current in the capacitor. The motion of the charging current is transmitted through the capacitor, corresponds to the electron flow in the wires connecting the capacitor to the alternating current source. The alternating current source is responsible for development of the electric stress in the dielectric between the plates of the capacitor. Electron flow does not occur through the capacitor. The electrons flow around the capacitor circuit in one cycle, which causes a negative charge to build up on one place, and a corresponding positive charge on the other, and the next cycle causes a reversal of the polarity of the charges on the plates. Thus, the effective impedance which the capacitor offers to the flow of alternating current can be relatively low while the insulation resistance which the dielectric offers to the flow of direct current is extremely high.

*Power Transfer:* With no voltage or charge, the electrons in the dielectric between the capacitor plates rotate around their respective nuclei in normally circular orbits.

**21**

*Developments in Wireless Power Transfer Using Solar Energy*

When the capacitor receives a charge the positive plate (PV Module) repels the positive nuclei and at the same time the electrons in the dielectric are strained toward the positive plate and repelled away from the negative plate (Plywood Board). This distorts the orbits of the electrons in the direction of the positive charge. During the time the electrons are changing from normal to the strained position there is a movement of electrons in the direction of the positive charge. The movement constitutes the displacement current in the dielectric. When the polarity of the plate reverses, the electron strain is reversed. If a sine-wave voltage is applied across the capacitor plates the electrons will oscillate back and forth in a direction parallel to the electrostatic lines of force. Displacement current, is a result of the movement of bound electrons, whereas conduction current represents the movement of free

The **Figure 5(b)** shows that the instantaneous power is negative whenever the voltage and current are of opposite sign. However, as has been illustrated in the **Figure 5(b)** that positive area of p(t) energy exceeds the negative area. Therefore, the average power is finite. Since the angle, θ, is small between current and voltage, the negative area of p(t) energy become very small. During the first quarter cycle (from 0° to 90°) the applied voltage rises from slightly negative value to a maximum and the capacitor is receiving a charge. The power curve is positive during this period and represents energy stored in the capacitor. From 90° to 180°, the applied voltage is falling from maximum to slightly negative value and the capacitor is discharging. The corresponding power curve is negative and represents energy returned to the circuit during this interval. The third quarter cycle represents a period of charging the capacitor and the fourth quarter represents a

*Induction Losses:* The induction losses due to thermal storage amount to 1.5% in comparison to the capacitive heating [28, 29]. When a circuit containing a coil or source of energy is energized with direct current, the coil's effect in the circuit is evident only when the circuit is energized, or when it is de-energized. However, when the inductive circuit is supplied with alternating current, the induction losses are continuous and much greater than when it was supplied with direct current. For equal applied voltages, the current through the circuit is less when alternating current, is applied than when direct current is applied. The alternating current is accompanied by an alternating magnetic field around the area of the source of energy, which cuts through the area of the source of energy in the circuit. Most of the applied voltage appears across inductance, L, with little remaining for the load in the circuit. In a circuit possessing inductance only, the true power is zero. The current lags the applied voltage by 90°. The areas of induction losses above the X axis represent positive energy and the areas below the X axis represent negative

**6. Development of a receiver using radio waves for wireless information** 

The focus of the current research is to expedite the efforts for development of a receiver using radio waves for wireless information and power transfer using solar energy spectrum. Liang Liu et al. investigated transmit beamforming for simultaneous wireless information and power transfer using radio frequency (RF) transmission [35]. It is essential to have Radio frequency (RF) transmission enabled wireless power transfer (WPT) to power energy-restricted wireless systems (e.g., sensor networks), where dedicated energy transmitters are deployed to broadcast RF signals to charge low-power electric devices (e.g., sensors and RF identification

*DOI: http://dx.doi.org/10.5772/intechopen.97099*

electrons.

discharge period.

energy [28–34].

**and power transfer**

*Wireless Power Transfer – Recent Development, Applications and New Perspectives*

**5.1 Discussions on power transfer and effects of inductance**

*Time diagrams: (a) voltage and current; (b) power in the RC circuit amplifier.*

circuits are lumped in a resistor connected in series with the capacitor.

*Capacitive Reactance and Resistance in Series:* The losses that appear in capacitive

*Capacitance and Resistance in parallel:* When a sine waveform voltage is applied across a capacitor and a charging current of sine waveform is transmitted across the circuit. The alternating current source, which is a sine waveform voltage, if applied at a uniform rate, is responsible sinusoidal response of the charging current in the capacitor. The motion of the charging current is transmitted through the capacitor, corresponds to the electron flow in the wires connecting the capacitor to the alternating current source. The alternating current source is responsible for development of the electric stress in the dielectric between the plates of the capacitor. Electron flow does not occur through the capacitor. The electrons flow around the capacitor circuit in one cycle, which causes a negative charge to build up on one place, and a corresponding positive charge on the other, and the next cycle causes a reversal of the polarity of the charges on the plates. Thus, the effective impedance which the capacitor offers to the flow of alternating current can be relatively low while the insulation resistance which the dielectric offers to the flow of direct current is extremely high. *Power Transfer:* With no voltage or charge, the electrons in the dielectric between the capacitor plates rotate around their respective nuclei in normally circular orbits.

**20**

**Figure 5.**

When the capacitor receives a charge the positive plate (PV Module) repels the positive nuclei and at the same time the electrons in the dielectric are strained toward the positive plate and repelled away from the negative plate (Plywood Board). This distorts the orbits of the electrons in the direction of the positive charge. During the time the electrons are changing from normal to the strained position there is a movement of electrons in the direction of the positive charge. The movement constitutes the displacement current in the dielectric. When the polarity of the plate reverses, the electron strain is reversed. If a sine-wave voltage is applied across the capacitor plates the electrons will oscillate back and forth in a direction parallel to the electrostatic lines of force. Displacement current, is a result of the movement of bound electrons, whereas conduction current represents the movement of free electrons.

The **Figure 5(b)** shows that the instantaneous power is negative whenever the voltage and current are of opposite sign. However, as has been illustrated in the **Figure 5(b)** that positive area of p(t) energy exceeds the negative area. Therefore, the average power is finite. Since the angle, θ, is small between current and voltage, the negative area of p(t) energy become very small. During the first quarter cycle (from 0° to 90°) the applied voltage rises from slightly negative value to a maximum and the capacitor is receiving a charge. The power curve is positive during this period and represents energy stored in the capacitor. From 90° to 180°, the applied voltage is falling from maximum to slightly negative value and the capacitor is discharging. The corresponding power curve is negative and represents energy returned to the circuit during this interval. The third quarter cycle represents a period of charging the capacitor and the fourth quarter represents a discharge period.

*Induction Losses:* The induction losses due to thermal storage amount to 1.5% in comparison to the capacitive heating [28, 29]. When a circuit containing a coil or source of energy is energized with direct current, the coil's effect in the circuit is evident only when the circuit is energized, or when it is de-energized. However, when the inductive circuit is supplied with alternating current, the induction losses are continuous and much greater than when it was supplied with direct current. For equal applied voltages, the current through the circuit is less when alternating current, is applied than when direct current is applied. The alternating current is accompanied by an alternating magnetic field around the area of the source of energy, which cuts through the area of the source of energy in the circuit. Most of the applied voltage appears across inductance, L, with little remaining for the load in the circuit. In a circuit possessing inductance only, the true power is zero. The current lags the applied voltage by 90°. The areas of induction losses above the X axis represent positive energy and the areas below the X axis represent negative energy [28–34].
