Microwave Slow-Wave Structure and Phase-Compensation Technique for Microwave Power Divider

214 J.-L. LI, ET AL., MICROWAVE SLOW-WAVE STRUCTURE AND PHASE-COMPENSATION TECHNIQUE FOR … Microwave Slow-Wave Structure and PhaseCompensation Technique for Microwave Power Divider Jia-Lin LI1,2, Wei SHAO1, Jian-Peng WANG3, Xue-Song YANG1, Shan-Shan GAO4 1 University of Electronic Science and Technology of China (UESTC), Chengdu 610054 2 State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096 3 School of Optoelectronics, Nanjing University of Science and Technology (NJUST), Nanjing 210094 4 School of Electronic Information, Chengdu University, Chengdu610106 , , , , Abstract. In this paper, T-shaped electromagnetic bandgap is loaded on a coupled transmission line itself and its electric performance is studied. Results show that microwave slow-wave effect can be enhanced and therefore, size reduction of a transmission-line-based circuit is possible. However, the transmission-line-based circuits characterize varied phase responses against frequency, which becomes a disadvantage where constant phase response is required. Consequently, a phase-compensation technique is further presented and studied. For demonstration purpose, an 8-way coupled-line power divider with 22.5 degree phase shifts between adjacent output ports, based on the studied slow-wave structure and phase-compensation technique, is developed. Results show both compact circuit architecture and improved phase imbalance are realized, confirming the investigated circuit structures and analyzing methodologies. Keywords Slow wave, phase imbalance, phase compensation, microwave circuit, microwave power divider 1. Introduction In microwave engineering, transmission lines are generally utilized to constitute all kinds of components, circuits, and matching networks, as well as antenna feeding networks. Moreover, quarter-wavelength transmission lines, i.e., electric lengths of 90, are extensively employed to, for example, parallel-coupled filters [1]-[3], directional couplers [4]-[7], power dividers [8]-[11], impedance transformers and so on. However, circuit areas of these components may be bulky since they basically consist of quarter wavelengths (even half wavelengths). Therefore, compact circuit topologies are attractive for system volume and cost considerations. In general, compactness of a circuit can be implemented by loading transmission line stubs [12], [13], meandering quarter-wavelength transmission lines [14], [15], enhancing capacitive coupling [16], [17], periodically loaded electromagnetic bandgaps (EBGs) [6], [18], loading transmission line with lumped components [19], [20], etc. It seems that transmission line loading stubs can exhibit some interesting characteristics like achieving large division ratio in microwave power divider designs [21], while meandering a section of transmission line has a disadvantage of increasing discontinuities. Also, using inter-digitallike technique can enhance distributed capacitance but, it suffers from fabrication difficulty when coupling fingers become too small. The lumped components, especially for lumped inductors, will exhibit resonance and loss at high frequencies, hence, it cannot be applicable to RF/microwave frequency band. The EBG structure, realized generally by etching some holes or other shapes on the ground plane, can create slow-wave effects, correspondingly, reducing circuit area. But, it results in a patterned ground, thus destroying the ground integrity. Another technique to implement slow-wave effects is by etching patterns on a transmission line itself, which is also a kind of EBG structure. It is an interesting concept since the ground integrity holds, thus facilitating practical engineering. In 2000, Xue et al. [22] first proposed such a method and subsequently, some improved topologies were studied extensively [23]-[25]. Also, many potential applications are investigated [26]-[28]. On the other hand, phase imbalance is an important parameter in engineering such as balanced mixers, pushpull amplifiers, antenna feeding networks, and so on. However, transmission-line-based microwave circuits achieve a matched state only at the center operation frequency. This means its phase response is related to the frequency. When offsetting from the center frequency, the phase also deviates from the desired value. Therefore, the phase imbalance must be compensated, especially for the case where constant phase response is required. In 2000, Piernas et al. [29] first introduced a short-circuited transmission-line stub with quarter wavelength at the center frequency. The stub is attached to one of output ports of a rat-race hybrid. Results indicate that the phase imbalance is greatly improved. Later, Eom et al. [30] further studied an improved topology where two pairs of short/open circuited stubs are shunt on both sides of a coupled transmission line. With this archi- RADIOENGINEERING, VOL. 23, NO. 1, APRIL 2014 The paper is organized as follows: Section 2 presents and analyzes a coupled transmission line with EBG cells etched on the line itself. The phase-imbalance compensation technique is formulated in Section 3. In Section 4, a demonstration circuit that incorporates slow-wave effects and phase-imbalance compensation on an 8-way coupledline power divider is designed and its performance is investigated. Finally, a conclusion is drawn in Section 5. a s 1 2 3 4 w0 hg w,g h symmetry plane In this paper, we first investigate a planar slow-wave structure with EBG cells, where the cell is etched on a pair of coupled transmission line itself. Its equivalent circuit model, based on the distributed inductance and capacitance of transmission lines, is formulated and further simplified based on the even- and odd-mode analyses. The slow-wave effects are also studied, and results show that size reduction is achievable. Subsequently, we study a pair of short/ open circuited stubs attached to a section of transmission line. Its phase response against frequency is analyzed. It indicates that by properly setting the characteristic impedance of the pair of short/open stubs, wideband phase compensation can be implemented. For demonstration, an 8-way coupled-line power divider with 22.5 phase shifts between adjacent ports is designed. Good results from simulations and experimental data confirm the studied circuit architecture and analyzing methodology. T-shaped stub has a width and a height of w and hg, respectively. Also, this narrow strip can be equivalent to distributed inductance denoted by L1. Finally, each horizontal section of the T-shaped stub primarily creates distributed capacitance marked by C0. Based on this formulation, the pair of coupled transmission line with T-shaped stub loading can be equivalent to a lumped LC circuit model illustrated in Fig. 1(b). (a) L0 1 L0 C0 C1 C0 C1 L1 C1 Cc Cc C0 L1 2 Symmetry plane tecture, wideband phase shifter having good phase response is observed. 215 C1 C0 4 3 L0 (b) L0 (...truncated)