Design and Analysis of Microstrip-Line-Coupled NRD Guide Filter Based on Integral Equation Techniques Duochuan Li, 1 Francois Boone, 1 Ke Wu 2 1 Department of Electrical and Computer Engineering, University of Sherbrooke, Canada 2 Poly-Grames Research Center, Department of Electrical Engineering, E ´ cole Polytechnique de Montre ´ al, Canada Received 18 September 2007; accepted 3 February 2008 ABSTRACT: Integral equation techniques which include an order-reduced volume integral equation approach for NRD guide circuits and a generalized surface-volume integral equa- tion approach for planar-NRD guide hybrid circuits have been presented in this article. A gap-coupled NRD guide filter is designed based on the order-reduced volume integral equa- tion method. The two identical high-quality microstrip-line-to-NRD guide transitions are designed by means of the generalized surface-volume integral equation approach. Finally, the optimized length of the NRD guide feed-line is determined and a compact microstrip- line-coupled NRD filter is obtained. Simulated results are in good agreement with measured results. V V C 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE 19: 80–90, 2009. Keywords: electromagnetic fields; filters; integral equations; microwave and millimeter wave circuits; moment methods; dielectric waveguide I. INTRODUCTION Since the hybrid planar/NRD waveguide integration technology was proposed, many experimental proto- types including passive components and active devi- ces based on this hybrid technology have been stud- ied and shown to be very promising in the design of microwave and millimeter-wave circuits and systems [1–4]. In this technology, the microstrip-line-coupled NRD guide filter is one of the important components for microwave and millimeter wave applications. Figure 1 shows a design example of two NRD guide bandpass filters using the two integrated transitions of microstrip line to NRD guide. The two filters pres- ent two different arrangements in which input and output, in the form of the microstrip line, may be located either on the same side or on the two opposite sides of the layered block. This hybrid technology has proved itself useful for millimeter-wave applica- tions where it may be difficult or even impossible to design a high-Q bandpass filter only with a microstrip line unless expensive superconducting technology is used. The design process of the microstrip line coupled NRD guide filter includes the design of an NRD guide filter and two high-quality microstrip line to NRD guide transitions as input and output. Electrical performance of the structure is mainly determined by the NRD guide filter. However, the two transitions may affect the characteristic in a significant way. Such electrical performance of the three parts can be modeled with commercial software separately and S- parameters of the whole structure can be obtained by Correspondence to: D. Li; e-mail: duochuan.li@polymtl.ca DOI 10.1002/mmce.20318 Published online 5 June 2008 in Wiley InterScience (www. interscience.wiley.com). V V C 2008 Wiley Periodicals, Inc. 80