Journal of Undergraduate Research
Volume 7, Issue 2- January/February 2006

Compact Stand-Alone-Power-Source (SAPS) for Wireless Applications

Gabriel Olander

ABSTRACT

A Stand-Alone-Power-Source (SAPS) will be developed to convert electrical energy drawn from a piezoelectric (PZT) source to a usable form. This form will be miniaturizable so it can be used in wireless applications. A PZT source that outputs a sinusoidal wave at low frequencies (about 100 hertz) will be converted to a direct current (DC) in order to charge a battery. The firing angle of circuit controller will be variable. This circuit should have an efficiency of 50-80% depending on conditions.

INTRODUCTION

With the continued expansion in the realm of miniaturized electronic circuitry, the demand for cheap autonomous power sources has become an ever important issue. By transformation of ambient energy sources, wireless miniature electronics can be made without the limitation of single charge batteries. Piezoelectric materials (PZTs) are currently being researched for their ability to convert mechanical vibrational energy into electrical power. Since the functional characteristics of PZTs vary greatly with frequency, load, and many other operating conditions [1], their use requires power conversion circuitry. By developing a control system that determines when to switch on a battery charging system, high efficiency power harvesting can be achieved.

The objective of this research is to develop a power source that converts a PZT alternating current (AC) input to a usable direct current (DC) output. First, a prototype circuit will be developed and simulated. After successful simulation, a working model will be built and tested in a lab with a PZT simulation circuit, and then tested with a PZT. The control system used is designed to optimize circuit efficiency while maintaining an ability to be miniaturized. Without the need for inductors or large capacitors, this circuit system can readily be fabricated on an IC chip. This realization enables use in applications such as wireless sensors, transmitters, or radio frequency identification (RFIDs).

STATE OF THE ART

In order to bring ambient energy supplies to circuitry, PZT based energy harvesting has been researched over the past decade. This research has broadly covered ideas for harvested energy, with tidal flow [2] and human motion [3] as studied examples. Harvested power levels have ranged from tens of mW to many watts – opening the door for various applications.

Many wireless sensors and transmitters require relatively small power levels (mW). Ideally, all circuitry of the SAPS would be designed to enable manufacturing on an integrated chip. In order to cheaply miniaturize a circuit, inductors or large capacitors must be avoided. Current research has shown some success in developing circuits that are efficient power converters or able to be miniaturized but little success has been achieved in both.

The Energy Harvesting Eel [2] explored the possibility of transferring the mechanical energy of water flow (by means of alternating vortices behind a bluff body) into electrical power. The Eel’s design calls for an inductance of ten Henry’s and the use of multiple PZT elements. This will greatly limit the ability of the circuit to be miniaturized. For these reasons, this technology would be unlikely to be of use for wireless applications (even if the Eel could conceivably be redesigned to harness airflow). Having successfully tested lower power versions, a full-scale one watt system that can be strung in series is currently being developed. Such a system would set a new precedent for PZT energy harvesting.

A very different approach was taken in this optimized PZT Energy Harvesting circuit [4]. Here, a PZT input is rectified and fed into a step down converter using discontinuous conduction via pulsed width modulation (PWM) of a switch. To maximize input power over a large range, two separate circuit control systems are used at different input power levels. This circuit was built upon maximization of input power and did achieve a good efficiency at higher voltage levels (> 30V) [4]. Unfortunately, this circuit also requires an inductor, limiting its ability to be miniaturized. Also, the circuit is considerably large and more complicated than the SAPS, making the device considerably more expensive.

Finally, the last example is a PZT circuit developed for IC wireless RF transmission [5]. This relatively simple circuit employs no inductors or large capacitors. The prototype is about the size of a quarter. It has successfully transmitted a signal at 1.9 GHz while being powered by a PZT shaken at 60 Hz [5]. While a promising candidate for many wireless applications, this research also suffers from several problems. First, the circuit was tested without a battery. All energy was stored on a small capacitor (3.3 microfarads which was only charged to 1.2 V). This capacitor stores very small amounts of energy and properly functions only at high frequencies. This greatly limits the range of applications the circuit could power. Also, the harvested energy is about .175 mW at peak, which is also too small to be practical for many applications. The efficiency is, at best, 49.9% [5].

In these examples, we have seen circuitry employ medium to high harvested energy levels ([2] and [4]) and circuits that can be miniaturized with very low power levels [5]. There is little success in the development of circuitry that can harvest power in the milliwatt range while also demonstrating high efficiency and an ability to be miniaturized.

PZT MODELING

The qp15n QuickPack PZT actuator was chosen to model because of its low input impedance and high levels of power available for extraction [6].

In order to use a model with a high degree of accuracy, the 100 nF input capacitance of the qp15n was used to scale a resonant frequency model of for the PZT [7]. This model (fig. 1) consists of a sinusoidal current source in parallel with a large resistance and a capacitance.

Figure 1. PZT Resonant Model For QP15N.

In order to calculate the conjugate match and optimal resistive match load ratios, the power extracted over these loads need be determined by simulation. To do this, the Thevenin’s Series Equivalent Circuit for each frequency was calculated and simulated.

SYSTEM FUNCTIONING

Given that there are multiple means to realize the power conversion system, selection criteria must be determined in order to select between given systems. Below are three main systems considered with a synopsis of the relative performance.

Rectifier

The Rectifier Circuit is the simplest power conversion system considered. Input current is fed through a diode rectifier and placed directly onto a battery without any specific control.

Figure 2. Rectifier System.

The labeled curves (fig. 3) demonstrate functioning and show output voltage and current achieved when using a 1mA input current at 100 Hz. The top two curves show the input voltage and current, labeled input2 (fig. 3), and the bottom two curves show the corresponding battery voltage and current, labeled r_batt2 (fig. 3).

Figure 3. Rectifier Function with 1mA Input Current at 100 Hz and a 90K Load.

MOSFET Current Source

The MOSFET current source will be used by placing a MOSFET in series with the battery. The MOSFET will be driven by a separate voltage source which will be swept to achieve optimal circuit performance.

Figure 4. MOSFET Current Source System.

The voltage source (fig. 4) labeled “test” need be swept in order for an optimal level to be found. This level will leave the MOSFET in saturation mode and output a steady current when the input voltage is at a high enough level. Figure 5 shows that sweeping Vgs places the MOSFET into saturation mode, forcing it to conduct as a current source into the battery. The top set of curves show a set of positive V_ds values while the bottom set of values show a positive set of V_gs- values.

Figure 5. MOSFET Current Source Function with 1mA Input Current at 50 Hz and a 90K Load. V_gs is Swept From 4 to 10 V.

MOSFET Switch

The MOSFET switch gives direct control of when to connect and disconnect the circuit. This switch will be used by a MOSFET in series with the battery that is powered as a switch. The gate voltage will alternate between high and low, effectively setting the MOSFET to “short” and “open.”

Figure 6. MOSFET Switch System.

This switch will allow two degrees of freedom, “turn on” and “turn off” (sometimes referred to as “firing angle”). “Turn on” will designate at what input voltage level the MOSFET will be made a short. “Turn off” will designate at what input voltage level the shorted MOSFET will be made “open.”

For simplicity sake, turn on and turn off will be set by setting time delay (phase) and pulse width (duty ratio) of a gate driver. Time delay (fig. 7) is set to 2.25ms and pulse width is set to 2ms. The top two curves show the input voltage and gate signal, which is when the circuit is switched on. Notice that the input voltage drops to battery voltage while the circuit is switched on, and approaches the open circuit voltage level while the circuit is switched off. The two bottom curves show battery voltage and current.

Figure 7. MOSFET Switch Function with 1mA input current at 100 Hz and a 90K Load.

System Performances

Since all three systems discussed above have been shown to successfully transform a PZT simulated AC input voltage to a DC battery voltage, their relative performances will be evaluated in terms of total power extracted, efficiency, conjugate load ratio, and optimal resistive load ratio.
Performance measurement definitions are as follows:

1. Power extracted (in or out): The instant value of P(t) = V(t)_{in or out} * I_{in or out} (1)
2. Joules J= (2)
3. Complex Conjugate Match Ratio is the power extracted over the battery in one period as in equation (1) divided by the power extracted over the optimal load given the same input conditions. Optimal Load is defined as the complex conjugate of the input impedance:
   
   Zoptimal load = Rin – j*Xin (3)

R_in is the input resistance of the PZT source. X_in- is the input reactance of the PZT source.

Selection between these three systems will be made by determining which system has the maximum potential power harvesting ability. Each system’s given degrees of freedom will be swept in order to determine if one individual system has significantly higher power harvesting capability will performing optimally.

Rectifier Circuit – Conjugate Match Load and Energy Harvested

Since there are no degrees of freedom in such a setup, the only parameters to be swept are input magnitude and frequency. Input magnitude was swept from .5mA up to 10mA. Frequency was swept from 50 Hz up to 400 Hz. The results of extracted energy and conjugate load ratio are shown below in Figures 8 and 9 respectively.

Increasing frequency has a slight lowering effect on joules harvested (fig. 8), though the effect is subtle. Increasing input current (fig. 8) shows increases joules harvested proportionately.

Figure 8. Joules per Second vs. Frequency for a Rectifier Circuit with a Battery Load of 90K.

Figure 9. Joules per Second vs. Frequency for a Rectifier Circuit with a Load of 90K.

Increasing frequency drops the conjugate load ratio linearly (fig. 10). There appears to be a cutoff frequency for each separate input magnitude, above which the circuit will not function and no power is extracted. For increasing input current (fig. 11) there appears to be a turn-on level, below which the circuit will not function. This turn-on level is lower for lower operating frequencies.

Figure 10. Conjugate Load Power vs. Frequency for a Rectifier Circuit with a load of 90K.

Figure 11. Conjugate Load Power vs. Input Current for a Rectifier Circuit with a Load of 90K.

Peak energy harvesting is about .02 joules per second and occurs at 10 mA of input current at 50 Hz. Peak conjugate load ratio is about 35% and .5mA of input current at 50 Hz.

MOSFET Current Source – Conjugate Match Load and Energy Harvested

The gate to source voltage was set (fig. 13) from 4 to 20 V, which is shown to place the MOSFET in saturation mode at lower values (as a current source should) and reach up to linear mode when the gate voltage is high. This shows that for low frequency, optimum gate voltage is as high as possible and that the circuit functions best when the MOSFET has a gate voltage high enough to push it into linear mode, where it functions as a short. Therefore, at this frequency level, the MOSFET current source gives no advantage.

In order to verify that the above trend holds for some higher frequencies, the simulations (fig. 13) were repeated at frequencies up to 400 Hz (fig. 14). Again, the best power output is achieved at the highest gate voltage. This suggests that at these frequencies and power levels the MOSFET current source will not perform better than the rectifier.

Figure 12. Output power for four different Vgs levels while sweeping input current at 50 Hz with a 90K Load. See Table 1.

Figure 13. Output power (W) for four different Vgs levels while sweeping input current at 400 Hz with a 90K Load. See Table 1.

Figure 14. Output power vs. Gate to Source Voltage for Varying Input Current at 50 Hz with a 90K Load.

Figure 15. Output power vs. Gate to Source Voltage for Varying Input Current at 400 Hz with a 90K Load.

Figure 16. Gate to Source Voltage vs. Output power for Varying Input Current at 50 Hz with a 90K Load.

Figure 17. Gate to Source Voltage vs. Output power for Varying MOSFET current at 400 Hz with a 90K Load.

Setting gate voltage to 20 V, which has been demonstrated (fig. 13 & fig. 14) to give approximately best performance, power levels were swept and conjugate load ratios were computed. If gate voltages were lower, these values (fig. 15-18) would drop.

The energy (in Joules) harvested for this system was just nearly equivalent to the diode rectifier system (fig. 9-12) with slightly lower values at the lowest frequency.

Figure 18. Joules per Second vs. Frequency for a MOSFET Current Source in Linear Mode (V_gs of 10 Volts) With a Load of 90K.

Figure 19. Joules per Second vs. Frequency for MOSFET Current Source with a Load of 90K.

Figure 20. Conjugate Load Ratio vs. Frequency for a MOSFET Current Source With a Load of 90K.

Figure 21. Conjugate Load Ratio vs. Input Current for a MOSFET Current Source With a Load of 90K.

Peak energy harvesting is about .02 joules per second, and occurs at 10 mA of input current at 50 Hz. Peak conjugate load ratio is about 34%, and .5mA of input current at 50 Hz.

These graphs (figs. 15-21) show that as compared to the diode rectifier circuit, the current source circuit is not of any advantage at the tested frequencies and input current levels.

Switch Based Circuit – Conjugate Match Load and Energy Harvested

This circuit has two furthers degrees of freedom that can be swept to determine its viability as compared to the diode rectifier. These two parameters, “turn on” and “turn off” will be swept in terms of time delay and pulse width. If this circuit can perform better than the diode rectifier, than it would be expected that a value other than, always on would be optimal.

To start, time delay will be set to switch the circuit on at a voltage value above the battery voltage and varying pulse widths will be swept. In other words, “turn on” will be set and turn off will be swept. Below (fig. 22) this is done with a circuit an input current of 1mA at 50 Hz. Time delay is set to 2ms which is approximately a 5 V “turn on.” After which, the reverse process will be carried out.

The top curve is the open circuit battery voltage. This is the voltage level the PZT will rise to so long as the switch is kept off. The middle set of curves is the gate voltage that is swept from 2.5ms to 20ms (the entire period, or always on). The bottom set of curves is the battery voltage, which flows when the circuit is switched on.

Figure 22. Voltage Waveforms For Switch Circuit With a Time Delay of 2ms and Swept Pulse Widths (from 1.25ms to full period) for a 1mA Input Current at 50 Hz with a 90K Load.

Below (fig. 23) are the power extracted curves for a similar circuit as previously listed (fig. 22) for several time delays. The top set of curves is for a time delay of 1ms. The second set of curves is for a time delay of 2ms. The third set of curves is for a time delay of 3ms. The bottom set of curves is for a time delay of 4ms.

In order to determine if this trend changes over the tested frequency or power range, a similar sweep was conducted at 10mA of input current at 400 Hz (fig. 24). The results are shown and discussed below.