794 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 27, NO. 9, SEPTEMBER 2017 Predistortion Linearizer for Wideband AM/PM Cancelation With Left-Handed Delay Line Dawei Zhang, Student Member, IEEE, Xin Xu, Hongxi Yu, Jun Li, Thangarasu Bharatha Kumar, Member, IEEE, Kaixue Ma, Senior Member, IEEE, and Kiat Seng Yeo, Fellow, IEEE Abstract—In this letter, a modiﬁed predistortion linearizer model is proposed to enable wideband synthesis of phase predis- tortion function. Additional time delay based on an artiﬁcial left-handed transmission line is introduced in the model to characterize the frequency-dependent phase conversion function, which can be utilized for wideband cancelation of the AM/PM distortion in microwave power ampliﬁers. Based on the proposed model, a microwave monolithic integrated circuit predistorter is designed to generate both positive gain and phase conversion according to the input power, and to realize increasing phase conversion as frequency increases. Large signal measurement of the design is performed at 20, 20.75, and 21.5 GHz. Result shows that +4.8-dB gain conversion is achieved, while phase con- version increases from +12.9° to +30.8° as frequency increases from 20 to 21.5 GHz. Index Terms— Left-handed transmission line (LHTL), microwave monolithic integrated circuit (MMIC), predistortion linearizer, wideband. I. I NTRODUCTION L INEARIZATION of microwave power ampliﬁers (PAs) has been a major consideration for nowadays communi- cation system because of the demanding linearity speciﬁcation for high data-rate transmission. To improve linearity, it will allow a PA to operate at higher output power, which also means that the power added efﬁciency will be improved indirectly. Predistortion technique has been developed and widely used to improve the linearity of PAs [1]–[5]. The basic idea of predistortion linearization is to form inverse gain and phase nonlinearity to that of the PA in order to compensate for the distortion. Generally, the AM/PM distortion of high PA varies with frequency, and the predistorter’s nonlinearity should be tailored to match the PA’s nonlinearity over fre- quency [1]. Therefore, the inverse frequency-dependent phase nonlinearity should be created as the predistorter accordingly, as illustrated in Fig. 1(a). However, frequency dependence is not considered in the conventional predistorter model. Therefore, in this letter, we introduce left-handed transmis- sion line (LHTL) time delay to the conventional predistor- tion linearizer model as the architecture shown in Fig. 1(b). Manuscript received March 29, 2017; revised May 25, 2017; accepted June 27, 2017. Date of publication August 18, 2017; date of current version September 1, 2017. (Corresponding author: Dawei Zhang.) D. Zhang, X. Xu, H. Yu, and J. Li are with the Department of Microwave, China Academy of Space Technology, Xi’an 710049, China (e-mail: dawei_zhang_1989@hotmail.com; jerry_1019@163.com; yuhongxi123@aliyun.com; lij@cast504.com). T. B. Kumar and K. S. Yeo are with the Singapore University of Tech- nology and Design, Singapore 487372 (e-mail: bharatha_kumar@sutd.edu.sg; kiatseng_yeo@sutd.edu.sg). K. Ma is with the University of Electronic Science and Technology of China, Chengdu 610054, China (e-mail: makaixue@uestc.edu.cn). Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identiﬁer 10.1109/LMWC.2017.2734760 Fig. 1. (a) Wideband phase predistortion function for compensation. (b) Proposed predistortion linearizer model with LHTL time delay. Based on the value of time delay in each path, frequency- dependent phase conversion function can be synthesized. As a validation, a predistorter design is implemented in GaAs 0.25-μm pHEMT process based on the proposed model. Performance of the design has been veriﬁed experimentally. II. WIDEBAND PREDISTORTER MODEL As shown in Fig. 1(b), LHTL time delay τ i (i = 1, 3, 5 ...... n, the nth path represents the nth-degree nonlin- earity) is introduced to the nonlinear model [2], [3]. A 1 is the linear gain, R n and θ n are the amplitude and phase coefﬁcients of the nth-degree response. Considering single-tone signal excitation with amplitude of a and angular frequency of ω e i (t ) = a · cos(ωt ). (1) Then, by summing all the fundamental signal components generated from each path, the combined output fundamental signal can be written as e o (t ) = A 1 a · R(a ) · cos[ω(t - τ 1 ) - θ 1 + ψ(a )]. (2) In (2), contributions from all paths are absorbed in R(a ) and ψ(a ), which can be used to represent gain and phase conversions, respectively. If n higher than 4 is neglected, according to [2], R(a ) and ψ(a ) can be calculated by R(a ) =  1 + 3 2 a 2  R 3 A 1  cos φ 3 + 9 16 a 4  R 3 A 1  2 (3) ψ(a ) = tan -1  3a 2 R 3 4 A 1 sin φ 3   1 + 3a 2 R 3 4 A 1 cos φ 3  (4) 1531-1309 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.