The 2014 International Power Electronics Conference

Load-Independent Current Output of Inductive Power Transfer Converters with Optimized

Efficiency Wei Zhang, Siu-Chung Wong and Chi K. Tse

Department of Electronic and Information Engineering

The Hong Kong Polytechnic University, Kowloon, Hong Kong

Qianhong Chen Nanjing University of Aeronautics and Astronautics

Nanjing 210016, China

Abstract-Inductive power transfer (IPT) systems are reso­nant converters whose output characteristics are mostly load dependent. Conditions for ensuring a load-independent voltage­transfer ratio of an IPT system have been studied. However, load-independent current output can be more desirable for applications such as battery charging and LED driving. This paper studies the characteristics of IPT systems operating at different frequencies as transconductance converters. Operating frequencies for load-independent transconductance are explored, looking for optimal efficiency. The frequencies interested are found to facilitate the design of a current-output IPT converter with efficient power conversion. The analysis is supported by experimental results.

Index Terms-Inductive power transfer, wireless power trans­mission, compensation topology, efficiency, load-independent transconductance.

I. INTRODUCTION

Wireless power transmission (WPT) technologies are nor­

mally classified according to short-range, mid-range, and long­

range applications, which are mainly distinguished by the

operating principle and the frequency band. The short-range

power transmission technology has a typical transmission

distance from a few millimeters to hundreds of millimeters. It

normally works by means of inductive magnetic coupling at a

relatively low frequency (20kHz to IMHz) [1]. In the recent

decade, this short distance wireless power transmission or IPT

technology has emerged as an attractive and user-friendly solu­

tion to constructing charging platforms for portable electronic

products [2] and electric vehicles [3], [4].

Major research work of IPT focuses on voltage to volt­

age conversion, to select the most appropriate compensation

techniques, isolated to specific application requirements [4]­

[7]. However, in some applications, a load-independent current

output is more desirable. For instance, a constant current

output is preferred to drive an LED or to charge battery packs

of electric vehicles. An extra stage of current regulator which

incurs extra power loss is needed if the IPT converter is an

output voltage power source.

Therefore, voltage to current conversion or transconduc­

tance IPT systems will be studied in this paper. General calcu­

lation and simulation are conducted for the IPT converter using

the secondary series- and parallel-compensations, looking for

This work is supported by Hong Kong RGC GRF project PolyU5258/13E.

[::::::::::::::::::c:,::] Parallel compensation

Primary loop Secondary loop

Fig. I. Series- and parallel-compensation topologies. In this figure, the primary inductance L p is compensated with a series connected capacitor Cp, while secondary inductance Ls is compensated with either a series or parallel connected capacitor Cs. !vI is the mutual inductance of the loosely coupled transformer. Rp and Rs are resistances of primary and secondary coils, and RL is the equivalent loading resistance.

their operating frequencies to achieve maximum efficiency

and load-independent current transfer ratio. The maximum

efficiencies of the two compensation topologies are compared

under the condition of load-independent current output.

II. CIRCUIT MODEL AND EFFICIENCY ANALYSIS

The coils of IPT systems are operating at a frequency

well below their self-resonant frequencies [8], and therefore,

additional compensation capacitors are needed to form the

resonant tanks in both primary and secondary sides of the

loosely coupled transformer. The tuned capacitors of the IPT

system can be series or parallel connected with the transformer

coils. Fig. 1 shows the circuit model for the analysis of steady­

state transfer functions. The primary loop of the circuit is

driven by a modulated AC voltage source which is an equiv­

alent voltage readily generated from a pulse-width-modulated

DC voltage source using either a simple full- or half-bridge

switching circuit. For a parallel resonant compensated primary,

an equivalent current source is needed. Due to the difficulty

of energy storage in the form of a simple current source, extra

components will be needed to transform it on demand from a

978-1-4799-2705-0/14/$31.00 ©2014 IEEE 1425

The 2014 International Power Electronics Conference

voltage source, creating extra loss. Therefore, series resonant

primary compensation will be used in this paper [5], [6]. The

secondary loop is compensated with either series connected or

parallel connected capacitor to form resonant tanks as shown

on the right-hand-side of Fig. 1.

Coupling coefficient

TABLE I DEFINITION OF VARIABLES.

Primary winding quality factor

Secondary winding quality factor

k= � LpLs Qp = wR: Qs = *,S

Circuit quality factor of series compensation Q fLs 1 L-S = ds RL Circuit quality factor of parallel compensation QL-P = VC8 RL L8 Circuit quality factor of series compensation Q _ CJ8Ch-8

including RL 0- QS+QL-S

Resonant frequency of primary loop wp= � LpCp Resonant frequency of secondary loop w s = -:rt;c;; v L8C8

A thorough efficiency analysis of both secondary series

and parallel compensations has been carried out [5], [6]. The

system efficiency derived is given as

�(Zr) �(Zs) - Rs T) = T)pT)s = Rp + �(Zr) �(ZS) , (1)

where rip and rls are the efficiencies of primary and sec­

ondary loops. The parameters and variables are summarized

in Tables I and II. The tailing subscript -S or -P of Q L indicates that it is of secondary series or parallel compensation

respectively.

For the secondary series compensation, there exists a local

maximum of 'T) at W = W M which is load-dependent.

(2)

Variable operating frequency is needed for achieving this

theoretical maximum efficiency. Fig. 2 shows two types of

power transfer efficiency and the corresponding W M versus

Qo [5], where

Qos = J 2\ (1 + )1 - 3),), and (3)

The two types of efficiency curves are identified as follows:

TABLE IT PARAMETERS NEEDED FOR EFFICIENCY AND Gi CALCULATION,

Series topology Parallel topology

Zs jwLs + jw �s + Rs + RL jwLs + Rs + ' Ie_ I IRL 7W s J'wLp + ,IC + Rp 7f...1..,' P

Zr

iout

rT----,-------------,--------, 2,5ws

0, 91-_____ -+----------*"">=<>A-- 1 2ws �

0.7 e-e--e Efficiency ofii<1I3 -a--e--e Efficiency of A2:1/3

0.6 fr-ts--t:s: Frequency

QO,critical 0.9 12 1,9 3,7

§ g.

1.5OJs I " "

0,5ws Qs

" o '<

Fig, 2, Simulated efficiency and optimal frequency (w AI) versus Qo,

CD For)' < i, the optimal efficiency peaks at Qos' The

value of WM is just slightly higher than Ws in a reasonable

range of loading (close to Qos) to achieve high efficiency.

Therefore, Ws, which is load-independent, is an ideal constant

operating frequency for the best efficiency operation of the

converter.

@ For ). :;0. i, the optimal efficiency increases monotoni­

cally with decreasing Qo by increasing WM to 00. However,

the operating frequency is affected by the self-resonant fre­

quency of the coils, switching losses and voltage stresses. In

addition, it can be seen from Fig. 2, when). :;0. i, the effi­

ciency improvement with increasing frequency is insignificant.

Therefore, Ws can be a constant operating frequency to achieve

high efficiency.

As a result, operating at constant Ws , rl maximizes at

a 2 T)max = --------;>2 ' where a = k QpQs· (l+�)

(4)

rlmax is only decided by the value of a, which is the product

of k2 and the two winding quality factors. Therefore, for an

IPT system whose coupling is usually higher than 0.1, the

requirement for high Qp and Qs is not demanding in order

to achieve a high efficiency.

For the secondary parallel compensation, the efficiency

maximizes at W N, which is load independent.

Ws WN= (1+k2)�' (5)

Fig. 3 gives a comparison of maximum achievable efficien­

cies of secondary series and parallel compensations versus

the loading condition QL. In the figure, Qp = Qs = 100. It shows that the two compensation topologies can achieve

nearly identical theoretical maximum efficiency except when

). :;0. i (i.e. k > 0.577 if Qp = Qs). For instance, if k = 0.8, the theoretical maximum efficiency of the converter with

secondary series compensation operating at a much higher

operating frequency can be slightly better than that of the

secondary parallel compensation converter.

III. TRANSCONDUCTANCE

The output current iout through RL of the series- and

parallel-compensated secondary are calculated with parameters

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G' .: (1)

·0 � 0+-W

0.8

0.6

0.4

0.2 1--++-!'"++----f.'l+ I-I-I1

.. .. o . .... . 0.01 0.1

Series @WM ---

Parallel @WN .... .... ....

10

,00=0.1 II--++'IH--+ I ,00=0.2 1\, ,00=0.8

100 1000

Fig. 3. Efficiency comparison of series and parallel compensations.

C '-' '"

r5

0.4,--------------;---------,

0.3

0.2

0.1

Frequency (kHz)

(a)

O.081--I---�==;�==;�--�

.-.. 0.06 1-- --=+----t-+-\-------t----1

g 0;: 0.041----+---+---+-----\;------t---- 1 c5

Frequency (kHz)

(b)

Fig. 4. Transconductances of (a) series and (b) parallel compensations.

given in Table II. The transconductances Gi-S and Gi-P of

secondary series- and parallel-compensations are expressed in

(6) and (7).

G _ iout _ wl'vl i-S - Vin - ZpZS-S + W2 lvI2'

Gi-P = iout = wlvI

Vin ZpZS-P + w2l'v12

(6)

1 1 + jWCSRL' (7)

where Z p and Z s are the impedance of the primary and

secondary networks. In this section, Rp and Rs are neglected

for their small values and insignificant impact on the transcon-

ductance [6]. From (6), Gi-S can be RL-independent when

Zp equals zero, i.e. the operating frequency W equals wp. This frequency can also be found by solving for w from the

equation 8Gi-.s = o. 8RL

The RL-independent transconductance is a very desirable

feature for power converters. It guarantees constant output

current while the loading changes. If Rp is neglected, Zp = 0 requires w = wp. Hence,

1 1 IGi-S(wp)1 =

------'--1 = k JLPLS ' (8)

Wpl> Wp p S which is load-independent.

Fig. 4 (a) depicts the SPICE simulation results of transcon­

ductance at various loading conditions of the secondary series

compensated circuit with zero Rp and Rs. In the simulation,

k is set as 0.2 and Cp is selected to resonate with Lp at

wp/(27r) = 200 kHz and Wp = Ws. The QLmin, QLs and

QLmax represent different loading conditions of 1.19, 5.00

and 21.05 respectively, which are calculated by the method

introduced in [5].

Similarly, for the secondary-parallel-compensated converter,

the transconductance in (7) is simplified as

1 Gi-P = . L Z ' where wl'vl + JW w'ivI P + 5RL

5 . 2MC + Zp(1-w2LsCs)

=JW ' s wM .

(9)

(10)

From (9), Gi-P is RL-independent when 5 = o. Solving

for the roots of (10), the frequencies at which Gi-P is RL-

independent can be obtained as

WL = w� +w� -�

2(1 _ k2) and WH = W� +w� +�

2(1 -k2) (11)

(12)

The load-independent transconductances of the converter op­

erating at frequencies WL and WH are usually not equal to each

other except when

Wp=Ws�.

Under this condition, we have

1 IGt-P(WL)1 = IGt-P(WH)1 =

JLPLS Wp LpLs

(13)

(14)

The simulated I G i-P I curves are shown in Fig. 4 (b)

by using the parameters of series compensation except the

condition (13).

IV. COMPARISON OF SERIES AND PARALLEL

COMPENSATIONS

The foregoing analyses on the frequencies operating for

load-independent transconductance and maximal efficiency are

derived independently on Sections II and III, and summarized

in Table III.

For a secondary series compensated transconductance con­

verter, the Wp and Ws that realize load-independent IGil and

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1�--II--��=hCTffiI�TTI�TTITI �. I " � ' " � 0.8 .' 1,.('- . -.

� 06

W, " I v/ . .. �� ;g : / " . 1\ � 0.4 • I. \ Senes Parallel

.

@OJs @OJH '" 1\ 0.2 / -- .... k�O.l " :,. r'\ J4 = :::: :�� · · · ··f:l> � . 0.01 0.1 10 100 1000

Fig. 5. Efficiency comparison of secondary series compensation converter working at w s and W H versus loading quality factor.

...... QL�3.44 0.24�-

J � 0.1 ...... QL�6.38

C � 0.12 !-J-,.r�-� r.)

0.06

O+----+----f------I------l

0.08

160 180

-+- QL�2.82 ...... QL�12.4

180

200 220 Frequency (kHz)

(a)

200 220 Frequency (kHz)

(b)

240

240

Fig. 6. Transconductances of (a) series compensation and (b) parallel compensation.

maximum efficiency are independent. They can be adjusted

individually by changing values of compensation capacitors

in each side of resonant tank according to their definitions

shown in Table I. For a secondary parallel compensated

transconductance converter, there is no single frequency that

achieves load-independent IGi I and maximum efficiency as the

frequencies never align.

If wp is selected equal to Ws as in [4], [7], the efficiency

comparison of operation at Ws of series compensation and

that at W H of parallel compensation is depicted in Fig. 5. It is

obvious that series compensation has higher efficiency at full

load.

» u �

0.9

·C 0.8 �

L ...

r 'I�� � ...... � Series co /npensation

f-- Parallel ompensatlon

'-H u.l 0.7

06 o 5 20 25

(a)

0.91 ------:;r ...... -e-te-��=--+--- 1 G' � ·CO.8r-����----r-------------T------ 1 S u.l

0.7

5 10 15 25

(b)

Fig. 7. Efficiencies obtain from (a) measurement and (b) calculation.

TABLE TIT FREQUENCIES TO ACHIEVE LOAD-INDEPENDENT IGil AND MAXIMUM

EFFICIENCY.

Compensation Load-independent I Gi I Max. efficiency Series Wp Parallel WL or wH

Therefore, by adjusting the values of Cp and Cs, a sec­

ondary series compensated current output IPT converter can

have load-independent output and maximum efficiency by

operating at Ws = wp. V. EXPERIMENTAL EVALUATION

Full-bridge prototype circuits are built to verify the results

from the analyses. The prototypes are constructed with a

loosely coupled transformer whose parameters are shown in

Table IV.

Fig. 6 gives the experimental trans conductances of the

secondary series and parallel converters versus operating fre­

quency with three output loading conditions.

The efficiencies versus Q L (adjusted using RL) at a constant

output power of 24 W (adjusted using Yin) are measured

for the two prototype converters. A constant power operation

can maintain a smaller converter temperature variation and

thus a smaller variation of converter component parameters,

leading to a more consistent efficiency measurement. The

calculated and measured efficiencies of the secondary series

compensated converter operating at ws, as well as secondary

parallel compensated converter operating at w H, are compared

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TABLE TV COMPONENTS AND PARAMETERS USED IN THE EXPERIMENTAL

CONVERTERS.

Transformer and compensation k Lp Ls Cp Cs

Value 0.18 32.77 JiB @200kHz 31.77 JiH @200kHz 19.32 nF / 630 V 19.93 nF / 630 V

as shown in Fig. 7. All the efficiencies are measured with

soft switching conditions. From the comparison of efficiency

curves shown in Fig. 7, and some other measurements with

stronger and weaker coupling coefficients, the series compen­

sated IPT current output converter always performs with better

efficiency.

VI. CONCLUSION

The operating frequencies of an inductive power trans­

fer output current converter are studied with primary series

compensation and secondary series or parallel compensation.

Operating frequencies for maximum efficiency and load­

independent transconductance are identified and compared

with the two secondary compensation techniques. Operating

at Ws of the secondary series compensation and operating

at W N of the secondary parallel compensation have a similar

maximum efficiency. However, for the secondary series com­

pensation, the load-independent transconductance operating

frequency Wp and maximum efficiency operating frequency

Ws can be adjusted independently. Thus, the two desired fea­

tures can be achieved simultaneously. While for the secondary

parallel compensation, the two frequencies never align. The

efficiency will be lower than the maximum when it has load­

independent current output. Two experimental prototypes are

built and the experimental results confirm the analysis.

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