3732 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 68, NO. 9, SEPTEMBER 2020
A Generalized High-Efficiency Broadband
Class-E/F
3
Power Amplifier Based on Design
Space Expanding of Load Network
Zhenxing Yang , Mingyu Li , Member, IEEE, Zhijiang Dai , Member, IEEE, Changzhi Xu,
Yi Jin, Tian Li, and Fang Tang
, Senior Member, IEEE
Abstract— This article presents an analytical and coherent
design method for the generalized high-efficiency broadband
parallel-circuit (PC) Class-E/F
3
power amplifier (PA). By import-
ing the initial phase shift of the third harmonic and adding series
reactive element to the load network, a free design parameter can
be defined and the design space of the load network parameters
are expanded. The design equations of the idealized waveforms
and the optimum values of the load network components are
derived in detail, and the performance of the peak drain voltage,
maximum operating frequency, and power output capability can
be improved. In addition, with the expanding space of load
network, the generalized PC Class-E/F
3
structure exhibits broad-
band capability. A matching method with the real frequency
technique (RFT) and the de-embedding technique is presented
to design the optimal broadband matching network. To verify the
validity of the proposed method, a broadband high-efficiency PA
working from 1.7 to 2.6 GHz (fractional bandwidth of 42%) is
designed. The experimental results of the fabricated PA present
high-efficiency characteristics of 68.5%–81% drain efficiency and
62%–75.8% power-added efficiency with 38.8–40.5 dBm output
power over the whole operation bandwidth.
Index Terms— Broadband, Class-E/F3, high efficiency,
impedance, parallel-circuit (PC), power amplifiers (PAs).
I. INT RODUCTION
H
IGH-EFFICIENCY p ower amplifiers (PAs) with
extended bandwidth are important solutions to save the
energy consumption and transmitter costs in modern wireless
communication systems. To improve efficiency of the PA,
several k inds of configurations have been widely investigated,
such as Class-D [1], Class-E [2], Class-F/F
−1
[3], and Doherty
PA [4], [5]. Among them, Class-E PA is one of the most
popular switching-mode amplifiers due to its higher efficiency
and relatively simple circuit topology. Theoretically, Class-E
PA can reach 100% collector or drain efficiency (DE) with
nonoverlap of the transient voltage and current waveforms.
Manuscript receiv e d February 3, 2020; re vised April 7, 2020 and May 24,
2020; accepted June 17, 2020. Date of publication July 23, 2020; date of
current version September 2, 2020. This work was supported by the National
Natural Science Foundation of China under Grant 61801377. (Corresponding
author: Mingyu Li.)
Zhenxing Yang, Mingyu Li, Zhijiang Dai, Tian Li, and Fang Tang are with
the School of Microelectronics and Communication Engineering, Chongqing
Uni versity, Chongqing 400044, China (e-mail: myli@cqu.edu.cn).
Changzhi Xu and Yi Jin are with the Xi’an Branch, China Academy of
Space Technology, Xi’an 710100, China.
Color versions of one or more of the figures in this article are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMTT.2020.3009530
However, the obvious disadvantage of Class-E PA is its
typical narrow bandwidth performance. To overcome this
problem, various design approaches have been proposed to
extend the bandwidth of Class-E PA. For example, Class-E
mode PA with parallel-circuit (PC) can achieve the broadband
capability using reactance compensation technique in [6 ].
Although Class-E PA can achieve good performances with
a simple load network, it still suffers from its high peak switch
voltage (V
MAX
) stress of 3.56 times of the DC supply voltage
(V
DD
), which will limit the practical circuit im plementation
even for moderate output power level. Recently, some new
Class-E amplifier configurations were constantly studied to
improve the PA performance, where V
MAX
, maximal operating
frequency ( f
MAX
), and output power capability (c
p
) of the PA
should be taken into account together [7]–[25].
Among them, the harmonic tuning method can effectively
improve the amplifier performance by adopting the resonance
network, which is widely used in conventional Class-F or
inverse Class-F PAs [12]–[19]. Correspondingly, the combined
mixed Class EF or E/F operation modes can be provided. It is
obvious that Class-EF is a hybrid of Class-E and Class-F, and
Class-E/F is a hybrid of Class-E and inverse Class-F. These
mixed modes lead to a tradeoff between circuit simplicity of
Class-E and benefits of Class-F or inverse Class-F by reducing
the peak voltage at the device output. The mixed Class-EF
and its variants have been reported in [12]–[14]. For example,
the performance of Class-EF
2
circuit is analyzed in terms of
its duty cycle in [12], which can offer a V
MAX
of 3.46 V
DD
at a duty cycle of 0.5. The Class-FE PA presented in [13]
offers a low V
MAX
of only 2V
DD
for duty cycles less than
50% as in Class-F. In [14], two new variants of Class-EF
PA with harmonic-peaking structure are proposed to enhance
the maximal operating frequency. In [15]–[19], the mixed
Class-E/F family is defined and analyzed, which have the
hybrid features of Class-E and inverse Class-F. In these modes,
the zero-voltage and zero-voltage-derivative Class-E switching
conditions can be obtained and some number of harmonics can
be tuned in the fashion of inverse Class-F, and the desirable
voltage and current waveforms can be achieved for improved
circuit performance. Generally, tuning the second harmonic
tends to increase the drain peak voltage even higher than
in Class-E mode, while tuning the third harmonic tends to
reduce the peak voltage [15]. For example, the Class-E/F
2
PA
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