I. INTRODUCTION

Bandpass filters are indispensable in many microwave systems. Such filters can be realized by electromagnetically coupling several resonators which are synchronously tuned at the band center of the desired filter. A good account of various synthesis techniques for microwave bandpass filters can be obtained from the famous book Mi- crowa¨e Filters, Impedance-Matching Networks, and Coupling Structures by Matthaei, Young, and Jones w1x, considered to be the bible of microwave passive circuit design. The book was first published in the 1960s and it presents the design method for various types of microwave filters, using the circuit and transmission line theory. Physical implementation of all those methods invariably requires post production tuning because the circuit theory approach cannot always take

Correspondence to: Shi Yin

into consideration the second order parasitic effects which in many cases dominate the performance of the designed filter. Consequently, with the steady advancement of computer technology and the availability of cheaper computer power, designers have recourse to the field theory approach to microwave filter design. However, as a result, computer aided design of microwave filters has become a very important area of research and development during the last few decades. During the past few decades many articles have appeared in the literature showing the brute force analysis cum optimization methods for the synthesis of waveguide cavity filters w2x. Such methods need stand alone computer programs for the design of each type of filter and invariably require large computer speed and memory.

In the last decade, the world of computer-aided design CAD. of microwave circuits has witnessed the appearance of a number of three-dimensional

3D. analysis based computer software for the design and analysis of passive microwave circuits. The software are based on the complete 3D electromagnetic solution of Maxwell’s equations for the particular structure to be analyzed or synthesized. The methods use the transmission line matrix TLM. w4x or the finite difference time domain FDTD. w5x method for analysis in the time domain and the finite element method FEM. w6, 7x, the finite difference method FDM. or the moment method MM. w8]11x for analysis in the frequency domain. All these software packages are quite versatile and can accurately analyze any electromagnetic structure that does not involve any active device. In this paper, we have shown how to make use of these general purpose software to successfully design any coupled cavity type microwave bandpass filter. We have chosen a representative waveguide cavity type as our baseline filter configuration. We have chosen all versions of the most commonly used single and double round rod coupled resonator waveguide filters.

II. THE DESIGN APPROACH ACCORDING TO THE MATTHAEI, YOUNG, AND JONES’ HANDBOOK

Consider the half-wave waveguide resonator coupled bandpass filter configurations shown in Figure 1. Figure 2 shows the K-inverter equivalent network of the filter shown in Figure 1. According to the design outlined in Matthaei, Young, and Jones’s handbook, the design steps are as follows:

1.We define the fractional bandwidth of the filter as

where lgL , lgH , and lgo are the guided wavelengths at the lower cutoff, upper cutoff, and the center frequencies, respectively, of the filter.

where g1, g2 , . . . , gNq1 are the lowpass prototype parameters, and see Fig. 2b.,

For purely lumped-inductance discontinuities having shunt reactance Xj, jq1, shown in Figure 3, one can write

The designer may choose any type of waveguide discontinuity in order to realize the required K inverters. A few typical discontinuities and the equivalent scattering matrix networks are shown in Figure 4. The handbook of Matthaei, Young, and Jones provides graphs which directly relate the K-inverter values to the rod diameter in the case of a centrally located single rod filter shown in Figure 4a. The main disadvantage of this structure is that one has to vary the diameters of the rods depending upon the required K-inverter value to be realized. However, the same goal can be achieved by using a constant rod diameter for all K inverters as shown in Figure 4c, where the rods are not symmetrically located. Unfortunately, no design curve is currently available for the structure shown in Figure 4b, c, and d which can be used directly to realize the K inverters. In addition, one cannot use a simple mode matching technique to solve for the scattering matrices of the discontinuities because of the associated complexity of the mixed coordinate system rectangular for the waveguide and