Tuned-Resonant Inductive Wireless Power Transfer (TRIWPT)

Prepared by Aaron Scher and Nicholas Babcock
[email protected]
Oregon Institute of Technology

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1. Objectives

The objectives of this lab are to:

  1. Use MATLAB to determine the inductive and capacitive values for designing a tuned-resonant inductive wireless power transfer (TRIWPT) system.
  2. Simulate a TRIWPT system using LTSpice.
  3. Build and test LC resonator circuits based on MATLAB findings and tune them to specified frequencies.
  4. Measure mutual inductance, coupling coefficient, and unloaded quality factor of LC resonator circuits.
  5. Measure wireless power transfer efficiency of a TRIWPT system.
  6. Construct an improved, impedance-matched "4-loop" TRIWPT system and find maximum distance (minimum k-value) to drive an LED load.

2. Equipment

  1. Oscilloscope (an oscilloscope with a bandwidth of at least 50 MHz or above is preferable).
  2. Hand-held LCR meter (in this lab we use the Keysight U1733C LCR Meter)
  3. Function generator
  4. Two 12 inch inductor jig stands (photos and build directions here)
  5. Scotch tape
  6. Wire strippers and cutters
  7. Spool of coated 24 AWG magnet wire, such as Remington PN155
  8. Two PCB component boards (Download the PCB component board build instructions, schematics and block diagram and the PCB component board BOM.) These boards contain the following components mounted and soldered:
    1. 470 pF capacitor
    2. 100 pF capacitor
    3. Tuning capacitors in 0 - 200 pF range (in this labe we use simple variable capacitors designed for low-cost AM radios)
    4. two pin terminal blocks
  9. Two red LEDs with leads
  10. One 50 Ohm resistor

3. Report guidelines

For the lab report, you will create a PowerPoint presentation (or use a similar presentation program), save it as a PDF, and submit it on-line according to the instructions given in class. The presentation should be tutorial in nature; your target audiences are other engineers and scientists who are interested in learning more about circuits and electromagnetism.

Your presentation will have 22 slides. Please include a slide number in the footer of each slide. To earn full credit your presentation must contain the slides in the order asked for in this lab. If you miss a slide, please leave a blank slide in its place so that you have still have exactly 22 slides total. Your first two slides should be:

4. Introduction

In this lab you are going to simulate and construct two tuned resonance inductive wireless power transfer circuits like those shown in Figure 1 and Figure 2. These figures are screenshots of schematics in LTspice. The Spice directive K1 L1 L2 "K-value" shown in Figure 1 is called a K-statement. The last entry of this statment, "K-value", is the mutual coupling coefficient of inductors L1 and L2. A specific example of a K-statement would be K1 L1 L2 0.5. This statement declares the mutual coupling coefficient of the inductors L1 and L2 is equal to 0.5, and assigns this coupling coefficient the variable K1. Similar K-statements are shown for the four-loop case in Figure 2. For more information regarding the K-statement in LTSpice see Using Transformers in LTSpice.

A MATLAB script is provided (see TRIWPT background and MATLAB design tool) to assist you in your analysis. Given the operating frequency and a set of physical parameters describing a pair of circular loops (coil radius, number of turns, coil pitch, frequency, distance between coils, wire radius, wire conductivity), this Matlab script will calculate self- and mutual-inductances, the coupling coefficient, resistance of each wire, capacitance needed for resonance, maximum achievable efficiency, etc.

For this lab exercise to be successful and to allow maximum time for experimentation, a pre-lab consisting of the component calculation (via MATLAB) and circuit simulation (via LTSpice) is necessary. A basic configuration of the TRIWPT system consists of two LC resonator circuits that are tuned to resonate at the same frequency. This allows the TRIWPT system to achieve higher power transfer efficiencies and longer transmission distances than simple induction wireless power transfer systems without tuned resonators. The medium for power transfer in these circuits is magnetic fields, so careful design and construction of the inductors is critical to maximize quality factor, enabling efficient power transfer and maximizing separation distance. The links referenced in TRIWPT background and MATLAB design tools summarize some critical relationships regarding coupled coils and TRIWPT, revealing the interrelation between coupling coefficient, mutual inductance, resonator figure-of-merit, and optimal attainable efficiency.


Figure 1. Two loop configuration.



Figure 2. Four loop configuration.

5. Prelab

    Matlab

  1. The following specifications for the TRIWPT system are:

    2. With the above specifications, utilize the MATLAB script to calculate following five parameters:

    Present the above five calculated parameters in Slide 4. As a check, the value of the ideal generator/load impedances to achieve maximum power transfer should be relatively close to 50 Ohms.

    LTspice simulation

  2. Given the parameters calculated above, simulate TRIWPT two-loop configuration in LTSpice (as shown in Figure 1). Remember to include inductor losses (you can model inductor loss as an equivalent series resistors in series with the inductor). Since the actual source impedance in the following experiment will be that of a function generator (50 Ohms), set the source impedance in your LTSpice simulation to 50 Ohms. It is assumed that the source and load impedances are matched. Therefore, also set the load resistor to 50 ohms. Set the source voltage to 10V. To assist you, you can download an LTspice simulation of a TRIWPT and change the parameters in the simulation (like the inductor, capacitor, and resistor values) to match those you calculated above. Present a screenshot of your circuit in LTSpice in Slide 5.

    Perform an AC analysis and sweep the frequency of the voltage source from 500kHz to 900kHz and observe the amplitude of voltage across the load resistor. Present a plot of the voltage sweep across the load resistor in Slide 6. What behavior do you observe in output amplitude? Present our observations in Slide 6 as well.

    Increasing and decreasing the k-value simulates bringing the distance between source and receiver coils closer and farther away, respectively. Set the coupling coefficient to a value larger than the critical value (this simulates bring the coils close together). Perform another 500 - 900kHz frequency-sweep and present a plot of the amplitude of the voltage across the load resistor voltage in Slide 7. Comment on how an over-coupled condition affects the amplitude in Slide 7. Now set the coupling coefficient to a value smaller than the critical value (this simulates bring the coils further apart). Perform another 500 - 900 kHz frequency-sweep and present a plot of the amplitude of the voltage across the load resistor voltage in Slide 8. Comment on how an over-coupled condition affects the amplitude in Slide 8.

    The TRIWPT is nothing but a good old-fashioned double-tuned transformer network. Such networks have been used for many decades in the world of radio as coupling networks in IF/RF circuits. For example, Figure 3 shows a typical double tuned amplifier. Old AM radios had double tuned amplifiers like this. Notice that this schematic shows two double tuned transformer networks. By and large, modern radios are not built using discrete parts like they used to be. They are built using integrated circuits. For Slide 9 do a little research and describe the use of double tuned transformer circuits in traditional radio electronics (and how do they compare to single tuned transformer circuits?). Cite your sources at the bottom of the slide. This webpage on resonant coupling networks may also help.


    Figure 3. Typical double tuned amplifier from Wikipedia's page on Double Tuned Amplifiers.

    Simple remote LED lighting is a potential real-world application of TRIWPT. In the two-loop TRIWPT circuit, replace the 50 ohm load resistor with two LEDs in parallel with opposite polarities (i.e. in a head-to-tail configuration). Use the default LED model in LTSpice. Then, reduce the coupling coefficient until the peak current through the LED drops just below 20 mA. What is the minimum coupling coefficient k necessary to maintain 20 mA through the LEDs? Use the MATLAB script to predict what coil-to-coil distance this corresponds to. Present a screenshot of your schematic and results in Slide 10.

    Lastly, you shall design a four-loop TRIWPT configuration as shown in Figure 2. Set the inner resonator component values (L2/C1 and L3/C2) to the same values used in the two-loop configuration and set the source voltage to 10V. Set the values of L1 and L4 to 2 uH and coupling coefficients for L1/L2 and L3/L4 pairs to 0.68. Replace the load resistor with a pair of LEDs in parallel with opposite polarities (i.e. in a head-to-tail configuration). Find the lowest k-value for L2/L3 to supply the LEDs with 20mA of peak current. What is the lowest L2/L3 coupling coefficient possible to provide a 20mA peak current to the LEDs? How much lower is that than the two-loop configuration? Present a screenshot of your schematic and answers to these questions Slide 11.

    You should have found that the four-loop configuration is superior to the two-loop configuration. What I mean is that both four-loop and two-loop configurations can transfer from source to load the same power, but the four-loop configuration requires a comparatively much lower coupling coefficient between resonators. In other words, the four-loop configuration is better at transferring power over a longer distance compared to the two-loop configuration. How is this possible? The answer is that inductive coupling is a form of impedance transformation. With inductive coupling, the generators and load do not "look like" 50 Ohms to the inner resonator pair. Instead, the inner resonator pair sees lower generator and load impedances, which in turn yields a smaller critical coupling coefficient to achieve the same amount of power transfer. For example, see Figure 9 in this link. This figure demonstrates how we can transform 50 Ohm generator and load impedances to look like 3.2987 Ohm impedances.

Experimental Procedure

Initial setup and fine-tuning

  1. Now that component values have been determined using the MATLAB script (from the Pre-lab), use the 24 AWG wire to create your first inductor, by wrapping the wire around the 12 inch inductor jig. Use the attached PCB board component holder to hold the ends of your coil in place. Figures 4 and 5 will help you in this task.
    Figure 4. Block definitions.


    Figure 5. PCB schematic with block definitions.

    More information regarding the PCB board is given in this document: PCB component board build instructions, schematics and block diagram. It is recommended that you connect the two ends of your coil to terminal block number 5. You can measure the inductance across the the leads using terminal block 4. Leave all other terminal blocks open. Next, calibrate the handheld Keysight U1733C LCR meter using the "Cal" function in inductance mode. After calibrating the LCR meter, measure the resulting self-inductance of the coil. Perform your measurements at different frequencies (use the "Freq." button to toggle between frequencies). Record the resulting inductance values at 100 Hz, 1 kHz, 10 kHz, and 100 kHz. Does the inductance value change as a function of frequency? Do the inductance values measured match the simulated value (determined with MATLAB)? Discuss and present answer to these questions in Slide 12.
  2. Adjust the inductor coil as necessary to achieve the similar self-inductance value you found in the MATLAB script in the Pre-lab. You may need to readjust the spacings between the wires or possibly even add or subtract turns to achieve a close match. Record the number of turns required to achieve the required inductance value in Slide 12. Then, wrap the second inductor coil with the same number of turns as the first. Measure the inductance value of the second coil and verify a close match between two coils. Present a photo of the two coils and the measured self-inductances of the two coils in Slide 13.
  3. Mutual inductance is the phenomenon in which a change of current in one coil causes an induced emf in another coil placed near to the first coil. Face the coils to each other, and place them a 0.1 meters (approximately 4 inches) apart. Recall that this distance corresponds to critical distance you designed for in the Pre-lab using the MATLAB script. Measure the mutual inductance of the two coils using the LCR meter. There are a few different ways to do measure the coupling coefficient, as described in the following links: Present the measured mutual inductance in Slide 14.
  4. Achieving a close match of resonant frequencies for the two resonant circuits is critical for maximizing power transfer efficiency. Therefore we must determine the resonant frequencies of each circuit independently. Using the LCR meter and the capacitor value prescribed in the MATLAB script (determined in the Prelab exercise), create the equivalent capacitance using a 470 pF, 100 pF, and tuning capacitor in parallel (to make this step a little easier, these capacitors are pre-mounted and soldered on the PCB board for you). Once the appropriate equivalent capacitance is reached, connect it to one of the inductive coils in parallel. Then, connect the function generator in parallel with the circuit, using the 10pF capacitor to loosely couple the power supply to the resonant circuit. Connect the oscilloscope across the equivalent capacitor to measure the output voltage. An illustration of this setup is shown in in Figure 6. In this figure, R1 represents the internal 50 Ohm impedance of the generator (it does not correspond to a real discrete resistor). Set the function generator for a 1V sinusoid at the target frequency (700 kHz) and fine-tune the variable capacitor until the maximum output voltage is reached. This will indicate that the circuit has been tuned to that frequency. Record the peak voltage Vpeak. Once tuned, leave the adjustable capacitor as it is (don't change it). Perform the same procedure for the second coil after creating another equivalent tunable capacitor. Present your results and discuss your experience for this step in Slide 15.

    5. Figure 6. Configuration for fine-tuning the variable capacitor.

  5. The unloaded Q quantifies the ratio of stored-to-dissipated energy in an isolated resonator. Qualitatively, the value Q describes the "sharpness" of the frequency response of a resonant circuit. Using the same apparatus from the resonant frequency tuning step, determine unloaded Q for each resonant circuit by performing a frequency sweep above and below the circuit's resonant frequency. Sweep the frequency of the function generator below the natural frequency until Vout= 0.707Vpeak. Record this frequency. Now, sweep the frequency of the function generator above the natural frequency until Vout= 0.707Vpeak. Record this frequency. The difference between the two frequencies is the 3dB bandwidth of the resonator. The quality factor is equal to the ratio of natural resonant frequency to bandwidth. Determine Q for both resonant circuits. From the measured Q, determine the equivalent series resistance of each inductor. Does this match the results obtained in the Prelab? Record all your finding for this step in Slide 16.

    6. System 1: Two-loop TRIWPT circuit configuration with load resistor

  6. Now that the resonators have been tuned to the operating frequency (700 kHz), the first TRIWPT circuit configuration will be constructed. Construct the two resonant circuits as illustrated below in Figure 7. In the schematic in Figure 7, the voltage source V1 corresponds to the signal generator with an internal resistance of 50 Ohm resistance. The resistor R1 at the receiver side corresponds to a 50 Ohm load resistor. Face the coils (like that shown in Figure 8), and set the closest distance between the coils to 0.1m (approximately 4 inches). This is the the distance between coils considered in the Prelab. Set the function generator for an amplitude of 1 V and a frequency of 700 kHz, and provide power to the first resonant circuit. Measure the power across the 50 ohm load resistor in the second resonant circuit. Determine the efficiency of wireless power transfer at this distance, where efficiency of wireless power transfer is defined as: \begin{equation} \eta_{power} = \frac{\text{Power delivered to load}}{\text{Maximum power available from source}}=\frac{|V_{load}|^2}{|V_{source}/2|^2}=4\frac{|V_{load}|^2}{|V_{source}|^2}, \end{equation} where \(V_{load}\) is the AC voltage amplitude across the load resistor (corresponding to the voltage across R1 in Figure 7) and \(V_{source}\) is the AC generator voltage amplitude (corresponding to V1 in Figure 7). Note that setting the voltage of the function generator to 1V is equivalent to setting \(V_{source} = 2\text{V}\). Present a photo of your setup and the measured efficiency value in Slide 17. How does the measured power transmission efficiency compare to calculated efficiency from the Prelab?

    7. Figure 7. Two-loop TRIWPT circuit configuration.


    Figure 8. TRIWPT experimental configuration with LED load.

    System 2: Two-loop TRIWPT circuit configuration with LED load

  7. Replace the load resistor with two LEDs in parallel in a head-to-tail configuration. Increase the source voltage to 5V, and move the receiver away from the source resonator until the LEDs no longer illuminate. Present a photo of your setup and this measured distance in Slide 18.

    8. System 3: Four-loop TRIWPT circuit configuration with LED load

  8. Now reconfigure the circuit for a four-loop TRIWPT configuration as shown in Figure 9. In this system both the generator and load are inductively coupled to the main pair of tuned resonators. Keep in mind that this "external loading" slightly detunes the two main resonators. For this circuit, you can initially leave the RC resonator inductors (now named L2 and L3) to each be ten windings of wire. To create L1, wrap three turns of wire around L2 and connect it to the function generator. To create L4, wrap three turns of wire around L3 and connect it to the load LEDs. Power the apparatus again at 5V, and find the maximum distance at which the LEDs illuminate. Fine tune the spacings and placement of the cois and adjust the number of turns on L1 and L4 to try and maximize the maximum possible distance for illumination. Present a photo of your setup and this measured distance in Slide 19. Why do you think adding these extra coils allows for an increased range? Present your anser in Slide 20. Check out my online notes on Inductive wireless power transfer systems, which might give you some insight. Five bonus points will be provided to the team with the greatest achieved illumination distance.

    9. Figure 9. Four-loop TRIWPT circuit configuration with LED load.

    Reflections on your experience

  9. In Slide 21 and 22, present your conclusions, summary and any extra information you would like to present for this lab. In these slides you can include additional tables or plots or comments. For example, did you learn anything interesting in this lab? Did you try any other "extra" experiments of your own? What would you change about this lab? Did you have any particular issues or challenges that you met? How did you meet them, etc.?