Eigenfrequency Based Comparison of Coupling Models with Real Coupled Resonators

Abstract

The most popular design methods for coupled microwave resonator bandpass filters involve ideal inverters to transform a lowpass prototype to a bandpass filter. In a case of wide band filters these methods fail. An application of LC inverters can solve the problem but there are 8 types of LC inverters and much more types of microwave resonators. The eigenfrequency method has been used to assign proper inverters to the real resonators. The resonant frequencies have been computed by means of mode matching method and FDTD method. I. INTRODUCTIONThe direct-coupled resonator filters [1,2] and more advanced multiple-coupled resonator filters [3,4] are based on the application of ideal inverters. The lowpass prototype filter is transformed to the bandpass one employing ideal inverters. The coupling coefficients between resonators and between resonators and input and output are obtained form the computations. The methods work well for narrow band filters and sufficiently well for intermediate bandwidth filters. But in a case of wide band filters design results are often wrong. For example combline filters suffer from bandwidth expansion which can be as high as 100% [5,6]. Although many explanations of the effect can be found there is a possibility that ideal inverters are simply not proper ones. Lets us calculate the coupling coefficient between resonators in 61 % wide two-pole Czebyshev filter having 0.0346 dB passband ripples (RL = 20 dB) applying Cohn's method [1]. The normalized lowpass prototype filter elements are a 1 = 0.666666 and a 2 = 0.545454 [2]. According to [1] the coupling coefficient k 1,2 is equal 1.0116. It is easy to notice that coupling coefficient is higher than 1. But everybody knows that the coupling coefficient between real resonators is always lower than 1. On the base of this example one can exclude ideal inverters form design of wide band filters. But one does still need a reliable design method. LC inverters produce coupling coefficients in the range from 0 to 1 thus can be used in design of coupled resonator filters. This paper does not describe the design method for wide band filters but a proper assignment between real resonators and LC inverters is done.