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Faculty of Engineering and Information Technology
Subject: (^) 48530 Circuit Analysis
Task Title: (^) Lab 2 – Optimum Wireless Power Transfer ONCAMPUS Version Your details:
Student Number Family Name First Name
This Lab is a Groupwork Assignment. You will work on the Prework theory individually prior to the lab.
Your collaboration must follow NSW Health and Australian Government and UTS guidelines on “social distancing”.
For the Assignment associated with this Lab, go to the Assignments Tab in Canvas and select Lab 02. This link include details on mark allocation, submission date , lateness penalty and other important information relevant to submission. It also includes a Declaration of Originality that both students in the team must sign.
This version of the Lab Notes is for the real ONCAMPUS lab. You must prove your attendance by initialling the attendance sheet.
Lab 2 – Optimum Wireless Power Transfer
1. OBJECTIVES
- To see mutual inductance in action
- To apply linear transformer theory to an air-cored wireless power transfer circuit
- To apply phasor impedance circuit solution techniques for sinusoidal voltages
- To determine the Thevenin equivalent circuit and deduce the load for maximum power transfer
- To test the theory on a pair of high frequency “pancake” coils with variable gap
- To appreciate the challenge of component value sensitivity in a “high Q” system
- To propose and test a design variation to the given circuit which might increase the power transfer
2. INTRODUCTION
2.1. Background and Overview
Wireless power transfer is an emerging technology in various applications including battery charging, e.g. in electric toothbrushes and smart phones and watches, and powering implanted medical devices, e.g. artificial hearts (where it is called a Transcutaneous Energy Transfer System, TETS) [1]. There are competing standards for wireless charging of mobile devices, namely Qi developed by the Wireless Power Consortium [2] and AirFuel Inductive developed by the AirFuel Alliance [3] and used by Powermat [4]. In this lab, you will explore this technology, applying phasor analysis of linear transformers to strive for maximum power transfer across an air-gap.
The transformer you will use comprises simply a pair of spiral-wound “pancake” coils of Litz wire, which is very finely stranded to minimise eddy currents, enabling very high frequency. Many manufacturers sell such coils, often with ferromagnetic backing sheets placed outside the coils, as illustrated in Fig. 1. Here we will use no ferromagnetic sheets so that our transformer has precise linearity and only copper losses (no “iron loss” in the ferromagnetic sheets).
Fig. 1 A wireless charging transmitter coil and ferromagnetic shield made by Vishay [5].
2.2. Specification
Test frequency f and coil spacing are given as follows:
Number of 1 mm spacer sheets = Nss = 3 Frequency = f = 830 kHz Infer angular frequency: ω = ............ rad/s.
In the following and throughout this lab:
- use rms quantities including for phasors (which our text book calls “effective” values) – the modulus of a phasor will be called its “amplitude”, but this is still an rms value ;
- perform calculations to 4 significant figures (needed because of parameter ranges); and
- record measurements to 3 significant figures (to help find the maximum).
2.3. Parameters
For the Function Generator (F.G.) power supply, as depicted in Fig. 2, assume that the supply peak-peak voltage is the maximum it can give, namely 20 V, and is at zero phase, hence that:
V s = 7.071 V rms.
The F.G. internal impedance is:
R s = 50 Ω
and you will use a 1% accurate current sense resistor of value
R c = 10 Ω.
A high value is used to ensure it exceeds the reactance associated with the resistor leads and for accurate voltage subtraction.
The coils you will use can be assumed to have equal inductance and series resistance, with values typically:
L = 5.9 μH R = 0.18 Ω.
These values were measured on one of the coil types used in the kits by an Instek LCR Meter LCR-819. There are several batches of coils used in the kits and so values will vary slightly.
3. PREWORK
3.1. Optimum Power Transfer Theory – Resistors Only
Q1. a) For the the circuit of Fig. 3 comprising the Function Generator and the combined total resistance
R t = R s + R c
what load must be applied in terms of R t to obtain maximum power dissipation in the load?
b) What is the resulting maximum power P max delivered to the applied load? Give your answer as a formula involving V s and R t, then evaluate it for the parameter values stated in Sec. 2.3,.
P max =
This will be an upper bound for your wireless power transfer.
Fig. 3. Function Generator and current sense resistor, open circuit.
3.2. RL Series Circuit Analysis
Consider the circuit of Fig. 4, in which the primary coil of the air-cored transformer is connected to the F.G. in series with the current sense resistor, and the secondary coil is open circuit and so carries no current, indicated by subscript “oc” below.
Fig. 4 Connected primary coil in series with a current sense resistor, secondary coil open.
Q2. a) Sketch a voltage phasor diagram for V 1 when the secondary is open, i.e. for V 1oc , with arbitrary relative lengths assuming I 1oc is real (you don’t need to specify its value, just include its amplitude as “ I 1oc ” in your phasor diagram). Draw R 1 I 1oc from the origin, then draw
3.4. Thevenin Circuit Analysis for the Transformer
Consider the wireless power transfer circuit of Fig. 4. You will obtain the Thevenin equivalent impedance Z th, once you know M , in two ways: Q4, a quick way; and Q5 using the conventional open circuit and short circuit method, using the theory of Sec. 9.10 of our textbook [6].
Q4. This quick method establishes a formula for Z th by analysing the circuit of Fig. 4 with the voltage source shorted V s = 0, a method stated in Sec. 4.11 of our textbook [6]. The theory of Sec. 9.10 of our textbook [6] reflects the impedances of the secondary circuit onto the primary circuit. But here, to just obtain Z th, we instead reflect the impedances of the primary circuit onto the secondary circuit.
a) After studying Sec. 9.10, give a formula for the reflected impedance from the primary to
the secondary Z r12 in terms of ω , M , and Z 11 , where Z 11 is the sum of the impedances around
the primary circuit, i.e.
Z 11 = Rs + Rc + R 1 + j ω L 1.
Z r12 =
b) State a formula for the Thevenin equivalent impedance Z th in terms of Z r12 , R 2 , ω and L 2
Z th =
Q5. Now we obtain both the Thevenin voltage V th and impedance Z th using the conventional open circuit and short circuit analysis, along the way deducing the current in the primary circuit in both cases, i.e. for the secondary circuit open and closed.
a) For open-circuit secondary, express the complex phasor I 1oc as a formula in terms of the primary circuit V s and parameters R s, R c, R 1 , ω and L 1. I 1oc =
b) Evaluate I 1oc for the given parameters and frequency.
I 1oc = Evaluate its (rms) amplitude. I 1oc =
c) From your answers to Q3c and Q5a, give a formula for the Thevenin Voltage in terms of V s, R s, R c , R 1 , ω , L 1 and M.
V th =
d) For the circuit of Fig. 2 with arbitrary load impedance Z L, give a formula (from our textbook [6] Sec. 9.10) for the reflected impedance from the secondary to the primary Z r
(just called Z r in Sec 9.10) in terms of ω, M , and Z 22 , where Z 22 is the sum of the impedances
around the secondary circuit, i.e.
Z 22 (^) = j ω L 2 (^) + R 2 (^) + Z L.
Z r21 =
e) Z r21 is the impedance that can be inserted in the primary circuit to enable solving for I 1 neglecting the secondary circuit (as if it weren’t there). So what is I 1 as a formula involving V s, R s, R c, R 1 , ω , L 1 and Z r21?
I 1 =
f) For the secondary circuit short-circuited, i.e. Z (^) L = 0 , indicated by subscript “sc”, you must
first determine I 1sc using your answers to d) and e), with Z L = 0 in the Z 22 expression. Once
I 1sc has been determined, what formula relates the short-circuit secondary current I 2sc in terms of I 1sc , ω , M, R 2 and L 2?
I 2sc =
g) Recap the above, by listing the calculation steps you will undertake in the lab to determine both I 1sc and I 2sc , once you have measured M :
h) What is the formula for the complex Thevenin impedance Z th in terms of V th and I 2sc?
Z th =
- Breadboard with 5 terminals, but some contacts are poor, so better to bring your own.
Equipment you must bring
- a calculator which can do complex number arithmetic
- camera (e.g. a phone camera)
Optional equipment you may bring
- your own breadboard (but old ones are available in the lab)
Completion Objective
Proceed through the lab notes below as far as you can in the time available. You will certainly finish Section 4.4, establishing your coils’ mutual inductance. You should strive to finish at least Sec. 4.6, testing your calculated optimum load. Ideally, you should finish Sec. 4.7. If you are not able to complete a section of the lab, try completing the rest through attending an Open Lab session to complete your Assignment.
4.3. Safety
The electromagnetic fields generated at the low power levels of this experiment are considered safe. The maximum electric field generated 1 cm above the mid-plane of one of the coils when carrying rms current 0.5 A (approximately the maximum which will occur here) at 500 kHz has been calculated to be around 3 V/m rms, which is 100th^ of the maximum reference level for General Public exposure to instantaneous electric fields at that frequency, 290 V/m rms, from Table 8 of [7]. Inherently this is because of the low maximum power level, 0.25 W, that the function generator (with its 50 Ohm internal impedance) can provide, much less than the power levels needed to heat a region of human tissue. In TETS for artificial hearts, the transmitted power level is around 10 W, or 40 times higher than this experiment, and there can be some local tissue heating but neurostimulation is not reported.
To ensure safety in this laboratory exercise, the coils must be placed at the back of the bench top away from human proximity – in particular, coils must not be placed on or near the human body (especially the head) during coil operation.
4.4. Mutual Inductance Measurement
Build your air-cored transformer by sandwiching the required number of clear spacer sheets between the coils and placing wooden end-plates outside the coils. Each coil has a lead wire to the centre of the spiral; place these lead wires on the outsides of the two coils, so the coils are closer together. The coils should be aligned vertically and the coil leads should emerge together to ensure that any ribs in the moulding align. Compress the coils by two rubber bands outside the wooden end-plates, one rubber band doubled for each direction. Place the transformer near the back of the bench at least 8 cm from metal. Because of the steel sheet 4 cm below the bench top, you should place the coils on a non-conducting object (such as some
books) of thickness at least 4 cm. The performance will be slightly lower if the coils are placed straight on the bench top because the coupling coefficient will drop by about 1%.
Connect up the open secondary circuit of Fig. 4. The primary coil should be connected across two breadboard terminals and the current sense resistor from one of those terminals to an adjacent breadboard terminal. To minimise inductance of the leads from the F.G. to the breadboard terminals, use short equal-length leads twisted together tightly (about 10 times). As shown in Fig. 4, include an earth wire from Coil 2 to the DSO earth. You must minimise connecting wire lengths in your breadboard as such wires will have an inductance that can be non-trivial compared to the coil inductance. (For example a 100 mm loop of hook-up wire might have inductance of order 10-7^ H, or about 2% of the coil inductance. If you have 5 such loops, then your results will be 10% out.)
Connect coaxial probes to record v 1 on CH1, v 2 on CH2 and v 3 on CH3, all at 1:1. Try Averaging. Use the MATH capability to evaluate the voltage across the current sense resistor, in phasor notation:
V c (^) = V 3 − V 1 = Rc I 1.
Q9. Apply F.G. voltage 7.071 V rms at the given frequency (p. 4).
a) Take a photo of your circuit and include it in your report.
b) Take a photo of the oscilloscope screen showing measurement of V 2oc and include it in your report.
c) Use the DSO’s Measure capability to give the AC rms (N cycles) voltages (include units!):
V 1oc = ; V 2oc = ; V c,oc =
d) From V c,oc , deduce the primary current rms amplitude:
measured I 1oc =
e) Copy your predicted rms amplitude value of Q5b) to here:
calculated I 1oc =
f) Compare the two by evaluating the ratio:
1oc 1oc
measured calculated
I
I
Q10. Use your answers to Q3d) and Q9c) to infer:
a) k ≈
and, using your answer to Q3b) and the nominal L (see Sec 2.3), infer
b) M =
Fig. 5 Circuit with optimum load
Parallel combinations of components in the secondary circuit are much preferred as the effect of stray inductances and contact resistances in the breadboard connections are both reduced for parallel components (compared to added for series components).
Q14. a) Decide what single resistance or pair of parallel resistances you will try to be close to R opt.
Component values: ............................................
Hence actual (calculated) load resistance: R L =
b) Decide what collection of parallel capacitances you will try to be close to C opt.
Component values: ............................................
Hence actual (calculated) load capacitance: C L =
To minimise lead lengths it is suggested that you place the secondary coil pins on either side of the centre line of the breadboard. Use the two parallel rails on one side of the centre line for the parallel capacitors. Use parallel resistors to complete the secondary circuit. Minimise the number of hook-up wires and connections in the breadboard because every connection will have some contact resistance (a typical value being 0.02 Ω but varying) causing a loss of output power. Don’t forget to earth the secondary to the DSO earth.
Connect v 1 on CH 1, v 2 on CH2, v 3 on CH3, and v 4 on CH4. Use the MATH capability to evaluate the voltage across the current sense resistor:
V c (^) = V 3 − V 1 = Rc I 1.
Q15. a) Turn on your circuit, and measure the AC rms (N cycles) voltages:
V 1 = ; V 2 = ; V c = ; V 4 =
b) From V 4 , deduce the power dissipated in the resistor R L of your load, showing your working:
P L =
c) How did it compare as a ratio to the optimum you predicted P opt in Q13?
opt
P L
P
...............
...............
d) How did it compare as a ratio to the upper bound you could get from the F.G., P max which
you calculated in Q1?
max
P L
P
.............
..............
4.7. Thevenin Circuit Impedance Evaluation for Transformer and Frequency
You will now examine the open circuit and short circuit secondary cases and compare the Z th you infer with that from Q11.
Q16. a) By your answer to Q5c) and for your M (from Q10), evaluate your predicted V th and its amplitude:
V th =
V th =
b) Compare this to the measured V 2oc (Q9) by giving the ratio (which should be near 1 or your M is wrong): th 2oc
V
V
Q17. Short-circuited Secondary Calculation
a) Suppose the secondary is short-circuited, i.e. Z L = 0 in the circuit of Fig. 2. Using the calculation steps you have planned in Q5g), now that you know M , calculate I 1sc and I 2sc, showing your working:
How does this compare with the Z th you obtained using the quick method (Q11)? Try to debug if they are nowhere near similar.
4.8. Design Challenge Question Q20. If you had a go at Q8 and were able to propose an alternative circuit for greater power transfer, draw that circuit here and try it out!
References (all websites accessed on 12/3/2020)
[1] “Inductive charging”, Wikipedia article https://en.wikipedia.org/wiki/Inductive_charging.
[2] Wireless Power Consortium homepage https://www.wirelesspowerconsortium.com/.
[3] AirFuel Alliance homepage https://www.airfuel.org/.
[4] Powermat homepage https://www.powermat.com/
[5] Vishay Intertechnology Inc. datasheet IWTX5050DZEB6R3KF1, “Wireless Charging Transmitter Coil/Shield”, Document No 91000, 1 Jan 2019, https://www.vishay.com/docs/34485/iwtx5050dzeb6r3kf1.pdf.
[6] James W. Nilsson and Susan A. Riedel, Electric Circuits: Global Edition , 10th Edition, Publisher: Pearson Education, Inc., publishing as Prentice Hall, USA, ISBN-9781292060545 (ISBN-10: 1292060549).
[7] “Maximum Exposure Levels to Radiofrequency Fields – 3 kHz to 300 GHz”, Radiation Protection Series No. 3, Australian Radiation Protection and Nuclear Safety Agency, 8 May 2003.
