A Design of Size-Reduced Negative Group Delay Circuit Using a Stepped Impedance Resonator Heungjae Choi #1 , Younggyu Kim #2 , Yongchae Jeong #3 , and Jongsik Lim *4 # Dept. of Electronics and Information Engineering, Chonbuk National University Jeonju, Chonbuk, Republic of Korea 1 streetpoet@jbnu.ac.kr 2 fan09@jbnu.ac.kr 3 ycjeong@jbnu.ac.kr * Soonchunhyang University, Asan, Choongnam, Republic of Korea 4 jslim@sch.ac.kr Abstract — A design method to reduce the size of the planar negative group delay circuit (NGDC) is proposed by using a stepped impedance resonator (SIR) concept. From the conventional transmission line resonator, an equivalent stepped impedance resonator with reduced size is derived. To validate the derivation, the reflection coefficient and group delay response are compared between the two types of one-port NGDC. Finally, the reflection topology NGDC using a stepped impedance resonator is fabricated and tested. Maintaining its intrinsic electric properties, total size of the circuit is reduced to 72% from its original size. Index Terms — Negative group delay, stepped impedance resonator, transmission line resonator. I. INTRODUCTION In a specific band of frequency with signal absorption or attenuation condition, the group velocity is observed to be greater than that of c, the speed of light in a vacuum, or even to be negative. Faster-than-c phenomenon was defined as the superluminal group velocity, and negative group velocity is also referred as the NGD [1][2]. The negative group delay (NGD) concept had little use in a radio frequency (RF) circuit design because of its extremely narrow bandwidth and poor input/output return loss. Researchers have been investigating some topologies for the NGD and found some useful practical applications in the RF circuit design. In the early stage, the NGDC typically consists of the lumped element LC (inductor-capacitor) resonator loaded with the termination resistor [3]-[6]. Due to the limited feasibility of the lumped element circuits, the NGDC with the distributed element topology was proposed [7]. Applicability of NGDC to a signal cancellation loop that deals with signals with arbitrary waveform in time domain is discussed in [8]. A research on the efficiency enhancement of an analog feed-forward power amplifier was proposed for commercial WCDMA base- station application by using the distributed element NGDC [9]. NGDC is also successfully applied to an analog RF feedback amplifier to increase the distortion cancellation bandwidth [10]. However, even in a product form implemented by a commercial 3 dB hybrid coupler, the NGDC of the distributed element topology occupies a large area due to the /4-transmission line resonator. To reduce the size of the circuit, the NGDC with the SIR is proposed in this paper. From the conventional transmission line resonator, an equivalent SIR with reduced size is derived. To validate the derivation, the reflection coefficient and group delay response are compared between the two types of the one-port NGDC. Finally, the reflection type NGDC using the SIR is fabricated and tested. II. THEORY Fig. 1 (a) shows the schematic diagram of the reflective parallel (RP) one-port NGDC using a transmission line resonator. And its SIR equivalence is shown in Fig. 1(b). Transmission line resonators are widely used because of their simple structure and easy-to-design features. In practical design, however, such resonators have a number of intrinsic disadvantages, such as the limited design parameters due to their simple structure and spurious responses at integer multiples of the fundamental frequency [11]. The SIR was proposed to overcome those problems. The typical features of SIR are summarized as follows: (1) a wide degree of freedom, (2) derivation of generalized concept for transmission line resonators, (3) development of an expanded concept for nonuniform impedance resonators, (4) size reduction, and (5) spurious reduction [12]. (a) (b) Fig. 1. Schematic diagram of the reflective parallel one-port NGDC using: (a) transmission line resonator, and (b) stepped impedance resonator. The ratio of the impedance step by Z 1 and Z 2 is defined as m, which can be expressed using the resonance condition as follows [12]: Proceedings of Asia-Pacific Microwave Conference 2010 Copyright 2010 IEICE TH1G-17 1118