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A class E power amplifier with coupling coils for a wireless power transfer system.


A wireless power transfer (WPT) system transfers and receives electric power wirelessly. It removes the constraint of a power cord from electrical devices, circumvents aesthetic issues related to the cord, and protects against the risk of fire or destruction of electronics due to unwanted short-circuit of the devices [1, 2]. WPT systems are classified into three areas according to frequency range, quality factor of the WPT network, method of transferring the energy, and other factors: use of inductive coupling, resonant coupling, and radiative transmission [3]. Notably, systems using resonant coupling on the HF bands can transfer power over a longer range than those using inductive coupling. They also have higher efficiency than those using radiative transmission [4, 5].

The transmitted power and transmission efficiency are important factors in the WPT system [6]. A class E amplifier is used as the general circuit topology of a power transmitter in a WPT system on the HF bands because it can obtain high output power and theoretically 100% power added efficiency (PAE) with a simple design [7]. However, the PAE is degraded by the switching transistor on-resistance, losses in the output filter and matching network, and discrete components for the dc feed and additional output capacitance [8]. In addition, it is practically difficult to optimize the performance of the amplifier on these bands due to the restriction of the components in high power applications [9].

This paper proposes a class E power amplifier (PA) for use in a WPT system. The amplifier with a WPT network, which is composed of source and load coils and two resonant coils, can eliminate discrete components for harmonic rejection filters and dc feed inductors. The degradation of the PAE is accordingly minimized. The differential amplifier operating at 6.8 MHz is implemented using LDMOS transistors and passive components, which are for input matching and additional output capacitance.


The proposed differential amplifier consists of a passive balun, input matching blocks, power transistors, and the WPT network as shown in Fig. 1. The drain of the transistors is directly attached to the source coil of the network, and the supply voltage is applied to the center of the coil. The output power in each transistor is combined in the coil. The harmonics are decreased in the output without an additional filter because the network can be described as a band-pass filter with a high quality factor in a class E operation. Power loss in the drain node is also decreased in the amplifier. Because of the reduction of the passive components, a highly efficient amplifier is obtained.

The coupling efficiency [eta] can be expressed with S-parameters of the WPT network as

[eta] = [[absolute value of [S.sub.21]].sup.2] x 100. (1)

The measured S-parameter of the WPT network cannot be used in the proposed amplifier due to the impedance mismatch between the input and output of the network. The output impedance [R.sub.o] shown in Fig. 1 is fixed to 50 ohms. The input impedance of the WPT network is defined by the load condition of the PA due to the direct connection between the drain of the transistor and the network. The coupling efficiency must be calibrated with the modified S-parameter considering different impedances. The load impedance [R.sub.L] in the class E operation, which is the input impedance of the network, is expressed as in [10]

RL = 1.365[[V.sup.2.sub.DD]/[P.sub.out]] (2)

where [V.sub.DD] is the supply voltage and [P.sub.out] the output power. When the input and output impedances are different from each other, the S-parameters can be expressed with the Z-parameters as


where [S.sub.0] represents the calibrated S-parameters, [Z.sub.ij] the measured Z-parameters with the reference load [Z.sub.0], [Z.sub.S] the input port impedance, and [Z.sub.L] the output port impedance. RL is the same as [Z.sub.S] of the network in the amplifier. Using (1) and (3), the calibrated coupling efficiency [[eta].sub.0] can be expressed as

[[eta].sup.o] = [eta] x [[absolute value of [([Z.sub.11] + [Z.sub.0]) ([Z.sub.22] + [Z.sub.0]) - [Z.sub.12][Z.sub.21] [square root of [[Z.sub.S][Z.sub.L]/[Z.sub.0]]]/([Z.sub.11] + [Z.sub.S]) ([Z.sub.22] + [Z.sub.L]) - [Z.sub.12][Z.sub.21]].sup.2] (4)

Therefore, the efficiency of the network must be calibrated by using (4) when RL is not the same as Z0 by VDD and Pout of the amplifier. The transmission efficiency in the output can be defined as

[[eta].sub.trans] = [[eta].sup.o] x PAE. (5)

The proposed amplifier is designed using the Agilent Advanced Design System (ADS). Freescale LDMOS MRF6VP11KH transistors are used as the switching transistors, and discrete passive components by Murata Manufacturing Co., Ltd. are used for input matching and additional output capacitance. A 1: 1 transformer, SBT-A1-30G manufactured by RCL Technology is used for the input balun. The network is demonstrated with copper and litz wires to obtain a high quality-factor. The diameter of the source and load coils with one turn is approximately 5.5 cm, and that of the resonant coils with four turns is approximately 11.5 cm. The distance from the source to the load is 14 cm. There is no cooling device in the system except a metal plate incorporated as a heat sink.


The WPT network is designed by using [11]. The operating frequency of the system is 6.8 MHz. The simulated data of the WPT network are shown in Fig. 2. The coupling efficiency [eta] is 79.9% using (1). The parasitic resistance in each coil is one of the main factors affecting the efficiency degradation of the network. With a one-ohm additional parasitic resistance RP in each resonant coil, the efficiency is changed to 65.2% at 6.8 MHz. As shown in Fig. 3, the efficiency has a maximum value as shown in Fig. 3 when the impedance at the input port is 50 ohms. The efficiency degrades rapidly when the impedance is below 30 ohms, but the variation in the efficiency near 50 ohms is small.

Figure 4 shows the measured S-parameter of the WPT network. The magnitude of [S.sub.21] is -2.58dB at 6.8 MHz. The coupling efficiency [eta] is 55.2%, as determined from the measured data. The differences between the simulations and the measurements can be understood in the observation that the parasitic resistance is more than one ohm in each coil, particularly the resonant coil.


The class E operation of the proposed amplifier is shown in Fig. 5. The harmonic signals in the output load decreased extremely due to filtering by the WPT network. Fig. 6 shows the output power and efficiencies in the simulation in the case where the input power is 25.5 dBm and the gate bias of the transistor is 1.0 V. The maximum transmission efficiency is 57.7% with a 21V supply voltage. The variations of all the efficiencies are below 1% depending on the supply voltage from 16 V to 30 V. The black box shown in Fig. 7 represents the coupling efficiency obtained from the power at the drain of the transistor (node A and B at Fig. 1) and the power at the output port (node C at Fig. 1).

The red circle shown in Fig. 7 is the other coupling efficiency obtained from the calibrated S-parameters of the network using (2) and (4). The efficiencies in Fig. 7 are almost the same at a 14 V supply voltage.


The measurement results of the WPT system are shown in Fig. 8 for the case where the input power is 25.5 dBm and the gate bias of the transistor is 1 V, which is the optimum value for high transmission efficiency. With a supply voltage of 14 V, the maximum transmission efficiency is measured at 44.6%, and the transmitted power to the output is 6.95 W. Using (2), the input impedance of the network is 38.2 Q when the supply voltage is 14 V and the output power is 7W. The calibrated coupling efficiency is 48.3%, which decreases by 6.9% due to the impedance difference. The PAE of the transistor is calculated as 92.1% using the coupling and transmission efficiencies. All the efficiencies in Fig. 8 change, depending on the supply voltage from 14.5 V. The variations in the efficiencies are similar to the effects on the increase of the drain impedance of the transistor, which is the input impedance of the network. When the supply voltage is increased from 14 V, the coupling efficiency also increases due to the increase in the input impedance of the network, as shown in Fig. 9. However, the transmission efficiency decreases due to the rapid decrease of the PAE, as shown in Fig. 8. These variations are understood by the thermal degradation in the drain node, depending on the output power. The degradation is not shown in the proposed amplifier with an output power of less than 7W. In other words, the coupling efficiency increases, but the PAE decreases when the input impedance of the network increases due to thermal effects on the impedance of the drain. Therefore, there is an optimum supply voltage for high transmission efficiency in the proposed amplifier depending on the transmitted output power. Because of thermal degradation of the transistors, the transmission efficiency and the transmitted output power decreases to 43.6% and 6.56 W after one hour. However, subsequent performances are not degraded further. All harmonic signals in the output are measured as less than 48 dBc, as shown in Fig. 10.

The performance comparisons are summarized in Table 1. The conventional PA is designed with the same devices as used in the proposed amplifier, but it uses dc feed inductors and an L-type output matching network between the WPT network and the amplifier [10]. The proposed amplifier shows better PAE and transmission efficiency than those of a conventional amplifier under the same bias conditions.


A class E power amplifier with coupling coils is demonstrated for a magnetic induction-based wireless power transfer system. The drain of the transistor in the amplifier links to the source coil of the wireless power transfer network without any devices. The network functions as a harmonic rejection filter and dc feed inductors in the class E amplifier. The optimum supply voltage is determined by obtaining the maximum transmission efficiency because the load impedance in the drain node affects the performance of the network, and thermal degradation by the output power changes the impedance of the drain node. The system with the amplifier shows 6.95 W transmitted power and 44.6% transmission efficiency with a supply voltage of 14 V at 6.8 MHz. Considering the calibrated coupling efficiency of the network, the PAE in the amplifier is 92.1% considering the calibrated coupling efficiency of the network. A highly efficient transmitter of the WPT system can be obtained by using the proposed amplifier with the network designed to consider impedance difference and cooling devices.


This work was supported by the Primary Research Program of Korea Electrotechnology Research Institute (grant 12-12-N0101-47).


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[11.] Son, H.-C., J. W. Kim, D.-H. Kim, K.-H. Kim, and Y.-J. Park, "Self-resonant coil with coaxial-like capacitor for wireless power transfer," Proc. Asia-Pacific Microw. Conf., 90-93, Melbourne, 2011.

Jong-Ryul Yang (1,2), *, Hyeon-Chang Son (1,2), and Young-Jin Park (1,2)

(1) Advanced Medical Device Research Center, Korea Electrotechnology Research Institute (KERI), 111, Hanggaul-ro, Sangnok-gu, Ansan-city, Gyeonggi-do 426-910, Korea

(2) Department of Electrical Equipment Information and Communications Engineering, University of Science and Technology, 217, Gajeongro, Yuseong-gu, Daejeon 305-350, Korea

Received 9 October 2012, Accepted 21 November 2012, Scheduled 25 November 2012

* Corresponding author: Jong-Ryul Yang (

Table 1. Performance comparisons with the conventional
class E power amplifier.

@Vdd = 14 V               [P.sub.out] (W)   Power-added

Conventional Type              6.62            75.7
This Work (simulation)         8.05            92.3
This Work (measurement)        6.95            92.1

@Vdd = 14 V                Coupling    Transmission
                          efficiency    efficiency
                             (%)           (%)

Conventional Type            55.2          41.8
This Work (simulation)       61.1          56.4
This Work (measurement)      48.5          44.6
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Author:Yang, Jong-Ryul; Son, Hyeon-Chang; Park, Young-Jin
Publication:Progress In Electromagnetics Research C
Article Type:Abstract
Geographic Code:1USA
Date:Feb 1, 2013
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