Extracting Coupling Matrix and Unloaded Q From Scattering Parameters of Lossy Filters

Abstract

Abstract-This paper presents a method for extracting the coupling matrix and the unloaded Q from the measured (or electromagnetic simulated) S-parameters of a narrow band cross-coupled resonator bandpass filter with losses. The Cauchy method is applied to determine the characteristic polynomials of the S-parameters of a filter in the normalized low-pass frequency domain. A five-parameter optimization method is proposed to obtain the unloaded Q and to remove the phase shift of the measured S-parameters, which is caused by the phase loading and the transmission lines at the input/output ports of a filter. Once the characteristic polynomials of the S-parameters with the phase shift removed have been determined, the coupling matrix of a filter with a given topology can be extracted using well established techniques. Two application examples are given to illustrate the validity of the proposed method.

Synthesis of Microwave Resonator Diplexers Using Linear Frequency Transformation and Optimization

“…In this diplexer design, 15 parameters, including 5 main couplings, 6 self-couplings, and 4 external Q values, need to be tuned to obtain the acceptable diplexer responses. To accelerate the diplexer design, the methods presented in [20,21] can be applied to guide the tuning of each channel in the diplexer. After tuning, physical dimensions of the diplexer 1 are obtained as shown in Figure 4(b).…”

Improved Extraction of Coupling Matrix and Unloaded Q From S-Parameters of Lossy Resonator Filters

“…A sequential tuning method was also reported in [4]. However, these methods in [1][2][3][4] have not taken the source-load coupling into account. The methods in [1,2] require assuming all the resonators with the same unloaded Q.…”

“…In recent years, the interest has been growing in methods for extracting the CM of microwave filters from measurements (or simulations) including losses, such as a five-parameter optimization method in [1], Cauchy method in [2] and the analytical method in [3]. A sequential tuning method was also reported in [4].…”

“…However, these methods in [1][2][3][4] have not taken the source-load coupling into account. The methods in [1,2] require assuming all the resonators with the same unloaded Q. The method in [3] is attractive, because it overcomes the assumption of uniform unloaded Q for each resonator.…”

“…The method is based on the presentation in [1] with proper extension to handle the presence of source-load coupling. With respect to the previous method available in [1], the new method has three advantages: 1) the CM extraction of the filter with source-load coupling has been taken into account; 2) unloaded Q for each resonator may be non-uniform; and 3) the new method has the higher accuracy and robustness.…”