A Novel Common Mode Multi-phase Half-wave Semi-synchronous Rectifier for Inductive Power

Transfer Applications

Kerim Colak, Erdem Asa, Mariusz Bojarski, Dariusz Czarkowski Department of Electrical & Computer Engineering

New York University, Polytechnic School of Engineering, New York, USA kcl353@nyu.edu, ea 1 145@nyu.edu, mb4496@nyu.edu, dc 1677@nyu.edu

Abstract-In this study, a novel common mode multi­phase half-wave semi-synchronous rectifier is investigated for applications in wireless energy transfer. The circuit is intended to alleviate variations of the load resistance or coupling coefficient factor while maintaining high efficiency. The proposed rectifier structure is based on the connection of semi-controlled multiple half-wave rectifier topology through multiple inductors. The receiver side semi-synchronous switches are controlled to increase the system efficiency by a symmetrical phase-shifted PWM signals in response to load variations. A 700 W laboratory prototype system is designed to validate the proposed topology in terms of current, power, and efficiency. Experimental results are provided for various loads using 8 inches air gap coreless transformer, which has dimension 2.5 by 2.5 feet, with a 120 V input and a maximum efficiency of 94.8 %.

Keywords- half-wave rectifier, multi-phase, phase-shift, secondary control, semi synchronous, wireless energy

I. INTRODUCTION

An efficient inductive power transfer (lPT) system has been

received recently a growing attention from both academia and

industry for its numerous potential applications [ 1 ]-[3]. The

overall efficiency of the system can be increased by

minimizing conduction and switching losses with a proper coil

winding and magnetic circuit design [4]-[6]. A conventional

inductive energy transfer system is demonstrated in Fig. 1. The

system consists of two main stages: the primary and secondary

platforms as seen in the figure [7]. The first stage role is to

deliver energy to the second stage with an impedance matching

network. The dc output voltage is provided to the load by the

second stage with the impedance matching network, a high­

frequency rectifier, and a non-isolated dc/dc converter.

The impedance matching network is important to improve

the system performance and is usually used at both primary

and secondary sides. However, due to the load resistance or

coupling coefficient variation, the contactless system overall

978-1-4673-6741-7/15/$31.00 ©2015 IEEE

impedance diverges from the designed characteristic, which

means that the designed impedance matching may be not

working effectively causing a decrease in the system efficiency

as compared to the designed performance values. c€l!.%F51 � [-<;--------i DC + i i i �

Source - i AC i i T DC i Load

l······T;:�iiiiite;····.i l·········Receiiiii;·�i'Pick;:; P·=··;

Fig. I. A diagram of a pickup wireless energy transfer system.

Various secondary side controller synthesis, circuit

topologies, and compensation strategies have been presented in

the literature [8]-[22]. A conventional boost converter topology

with low switching frequency [l3] is demonstrated for

impedance matching system in the receiver side. GaN based

transmitter with adaptive receiver using a buck converter is

designed in [ 14]. In [ 15]-[16], researchers have investigated

reflected power to the transmitter side for low power inductive

power transfer applications by using cascaded boost and buck

or cascaded buck and boost converter. Directional tuning

control [ 17], implicit adaptive controller [ 18], active tuning of

parallel compensated receiver with tri state boost converter

topology [ 19], and self-tuning power regulator have been

introduced for inductive energy transfer applications [20].

Optimal resonant load transformation is analyzed for the

biomedical implants [2 1] and high power applications [22]­

[23].

In this paper, a novel high frequency multi-phase semi

synchronous half-wave rectifier with an interleaved inductor is

proposed for the wireless energy transfer systems. In this

topology, it is possible to control the system receiver side

without using any additional secondary side dc/dc converter or

controller synthesis. With the multiphase feature, the proposed

converter topology can also be used for the wireless high

power applications by splitting the current in each phase. The

proposed interleaved converter semi synchronous switches are

driven by a phase-shifted signal to obtain a higher efficiency

considering the variable load variation. This novel approach

brings an easy and cost effective solution considering the

existed methods in the secondary side. The converter model

controllability is analyzed and the transfer function of the

converter is derived. The system performance is confirmed

with experimental results at 8 inch air gaps in coreless

transformer, 150 kHz operating frequency, and a 700 W load

with a maximum efficiency of 94. 8% in the laboratory

conditions.

II. CIRCUIT ANALYSIS OF THE WIRELESS POWER LINK The proposed common mode multi-phase semi controlled

half wave rectifier circuit topology for the inductive power

transfer is shown in Fig. 2. It consists of a dc/ac inverter, an

impedance matching network, an air gap coreless transformer,

and multi-phase interleaved inductor with semi synchronous

half wave rectifier. The proposed rectifier is comprised of

transistors with anti-parallel diodes in the lower part of

switching legs and diodes in the upper parts. The symmetrical

phase-shift angle of the secondary side transistors regulates

the output power in terms of variable load conditions.

D,

+

V;

Fig. 2. Wireless power transfonner circuit and the proposed common mode multi-phase semi synchronous half wave rectifier.

In order to perform the circuit analysis, the wireless power

link can be represented as two coupled inductors and two

resonant capacitors connected in series as shown in Fig. 3.

Lc.eq

+ ZL,eq Vo

Fig. 3. The equivalent circuit model of the proposed wireless converter.

In this model, input voltage source is Vi, load impedance is

ZL,eq where ZL,eq=ljXL,eq +RL,eq}, phase equivalent inductance

LC,eq={(LCJ+ .. + lILoJln}, LC1,n are assumed identical and n is

number of phase, two coupled inductors are Lp and Ls with

equivalent series resistances Rs and Rp. K is a coupling factor

between the two coils and Cp and Cs are resonant capacitors.

The two coupled inductors can be equivalently modeled as a

transformer with proper leakage and magnetizing inductances.

ZP.eq ZS,eq -:+ � Ip Is +

ZM ZL.eq Vo

Fig. 4. The simplified model of wireless power link.

To simplify analysis, both coils Lp and Ls are assumed to be

identical and equal to L. Then, the model can be equivalently

represented by the circuit in Fig. 4. In this model Vu is a

fundamental component of voltage source Vi, the equivalent

impedances of Zp,eq, ZS,eq, and ZM can be expressed as

Zpeq = Rp +_._1_+ jwLL , jWCp ZM = jWLM

Zs eq = Rs + -. _1_ + jWLL + jwLc eq , jWCs '

where LM can be described by the following equations.

LM = K.JLpLs = KL LL = L - LM = (1 - K)L

(1)

(2)

When the secondary switches are in ZVS region, the

reflected equivalent impedance can be found by using first

harmonic approximation (FHA) as

where fJ is the conduction angle of the half wave rectifier. The

equivalent resistance value can obtained by taking real portion

of (3), as

4RL . 4 (P) RL,eq = nn2 SLn '2 (4)

and taking imaginary portion of the equivalent impedance, the

corresponding reactance value is defined as

4RL . 3 (P) (P) XL,eq = - nn2 SLn '2 cos '2 (5)

With the help of the above described equations, the voltage

transfer function of the system can be calculated as

(6)

III. ANALYSIS OF THE PROPOSED CONVERTER

The operating waveforms and switch state transitions are

presented in Figs. 5, 6, and 7 to show the behavior of the

proposed converter. To simplify the circuit analysis,

secondary side rectifier diodes and switches are ideal, the

output capacitor is assumed to be large enough for a constant

dc output, and filter losses are neglected. The proposed circuit

is examined under these conditions in the following operation

modes:

�1�+-------�------�------�------+

�1 ��------�----��----�------�

Is wt

to 2

Fig. 5. Current and voltage waveforms in the proposed semi synchronous half-wave rectifier.

Mode 1 [to<t<tlj

During this interval, the rectifier diodes D f and D3 are off­

state, while switches Sf and S2 are turned on as demonstrated in

Fig. 6. The current is is shorted from the switches and

circulates through resonant capacitor Cs and interleaved

inductors Lc,eq, the current waveform is depicted in Fig. 5. The

filter capacitor C discharge into the load resistance RL in this

mode.

01 LC1 O2

Cs LC2 -On io

+

LCn +

Va C is Vs

Fig. 6. Mode I analysis, current path and switching transition.

The system differential equation can be described by the

following equations,

( ) 1 I. tl . ( ) disCt) Vs t = - t IS t dt + LC eq --Cs 0 ' dt

Mode 2 [tl<t<t2j

iO Ct) = c dVcCt) dt

(7)

In this mode, both switches Sf and S2 are turn-off and diodes

Df and D2 are on-state as shown in Fig. 7. The current is flows

in positive direction through diodes Df and D2 and the energy

is transferred from the transformer secondary side and the

resonant capacitor Cs and multi-phase inductors Lc,eq to the

filter capacitor C and the load resistance RL.

01 LC1 O2

Cs LC2 -:+ On 10

I +

LCn � +

is Vs Va

Fig. 7. Mode 2 analysis, current path and switching transition.

The differential equation of the system during this time

interval can be written as

Vs(t) - Va = 2.. I.ttz is(t)dt Cs 1

ioCt) = is(t) - cdv;;t) (8)

In both interval, the current is equal divided by interleaved

inductors that provides less current stresses on the switches and

diodes.

IV. EXPERIMENT AL RESULTS

TABLE I

Symbol Parameter Value

Vi dc input voltage 120 V

Po maximum output power 700 W

Cp,Cs resonant capacitors 40 nF

C filter capacitor 10llF

Lp, Ls coil self-inductances 251lH

LC/, ... Lcn phase inductance 1.51lH

d square coil dimension 2,5 x 2,5 feet

n coil tum number 4

!sw operating frequency 150 kHz

Current Ratio at 10 0 Current Ratio at 20 0 Current Ratio at 30 0

3.5 2 1.5

Current Ratio Current Ratio Current R.atio

1.75 1.25 ;t' 3 ;t' � � 1.5 � "" � ">, - 2.5 � �

1.25 0.75

2 0.5 0 30 60 90 120 150 180 0 30 60 90 120 150 180 o � � � 1� 1� 1�

Alpha fa] Alpha fa1 Alpha (a]

(a) (b) (c)

Output Power at 10 0 Output Power at 20 0 Output Power 30 0 300 600 �-

Output Power

200 400 [ [ 0': 0': 100 200

0 0 0 30 60 90 120 150 180 0 30 60

Alpha fa]

(d)

Output Power

90 120 150 Alpha {a]

(e)

180

� 0':

900

600

300

0

Output Power

0 30 60 90 120 150 180 Alpha (a]

(t)

Efficiency at 10 0 Efficiency at 20 0 Efficiency at 30 0 100 100 100 �-

lit Efficiency lK Efficiency :. Efficiency

96 95 95

� ........ lI:

� "lK �

90 lI:/ll l[ 90 II e- e-

li J:

" lit �

It II 90

"" It 85 85 85

80 80 80 0 30 60 90 120 150 180 0 30 60 90 120 150 180 0 30 60 90 120 150 180

Alpha fa] Alpha fa] Alpha (a]

(g) (h) (i)

Fig. 8. The experimental results of current ratio between seconday and primary side at a) 10 fl, b) 20 fl, c) 30 fl, the output power range at d) [0 fl, e) 20 fl, f) 30 fl, and the proposed converter efficiency at g) to fl, h) 20 fl, i) 30 fl.

In order to prove the idea and show the operating principle,

a two-phase semi synchronous half wave rectifier interleaved

through a multiple inductor is considered to experimentally

verify the proposed converter analysis. The wireless system is

designed for 700 W, 120 V input voltage considering various

output load conditions. The coreless transformer is tested with

8 inch distance between coils which results in 0.3 coupling

factor. The topology parameters of the converter are given in

Table I. The characteristic waveforms of the proposed

converter described in Sections II and III are given to verity

circuit operation with the following waveforms.

The current ratio between secondary and primary side is

presented with the different phase angle a. and different load

conditions RL in Fig. 8( a-c). The different current ratio can be

obtained with the different a. as seen in figures. Fig. 8( d-f)

shows the output power conditions in terms of a. and RL. A

wide output power range can be achievable by controlling a. at

the light and high load conditions. The efficiency

characteristic of the proposed topology versus a. and RL is

demonstrated in Fig. 8(g-i). As seen from analysis results, a

certain power can be acquired at two different a. values; while,

the efficiency results are different in both cases. Thus, the high

IIj:WWlWM

(a) (b) (c)

(d) (e) (t)

(g) (h) (i)

Fig. 9. The resonant tank voltage VR, currentlR, and the secondary side switch voltage VSJ and currentlSJ for 10 Q at a) 30°, b) 90°, c) 150°, for 20 Q at d) 30°, e) 90°, t) 150°, for 30 Q at g) 30°, h) 90°, i) 150°.

efficiency operating area is preferred to control the system

output.

Selected resonant voltage and current waveforms at

different load conditions are given in Fig. 9. The phase-shift

angle controls the output power by changing the transformer

secondary side voltage as shown in the figures.

V. CONCLUSIONS

In this study, a new semi-synchronous multi-phase half­

wave rectifier is analyzed for wireless power transfer

applications. The simple converter topology has reduced

current stresses on the switches by sharing the current through

conunon mode inductance. The converter model analysis with

the steady state equivalent circuit is given using FHA and

voltage/current waveforms are displayed in all operating

modes. The transfer function of the converter is derived

analytically. The proposed control adjusts the output power of

the system by phase shift tuning of the synchronous switches

in the receiver. The concepts presented here can be also used

in multiple output receiver wireless applications since the

output control can be regulated only in the receiver side. The

system performance is confirmed with theoretical and

experimental results at different load conditions. To verify the

proposed converter, a 700 W full power prototype is designed

at 120 V input. The laboratory prototype achieved a 94. 8 %

maximum efficiency.

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