Scattering-Matrix-Based Parametric Characterization of a Two-Port Bridged-T Network for Microstrip Filter Applications

TL;DR

This paper presents a parametric characterization of a two-port Bridged-T network using scattering matrices, deriving key parameters for microstrip filter design and demonstrating a high-pass filter with sharp roll-off.

Contribution

It introduces a mathematical derivation linking T and S matrices for the Bridged-T network and designs a high-pass filter with specific scattering parameter features.

Findings

Derived S-parameters from T and S matrices for the network.

Designed a high-pass filter with a 1 GHz corner frequency.

Achieved sharp roll-off ratios of -30dB/GHz and -32dB/GHz in simulation.

Abstract

The purpose of this study is to characterize a two-port Bridged-T network using transmission (T) and scattering (S) matrices. Using mathematical derivations, scattering parameters including S11, S12, S21, and S22 have been derived from the T and S matrices to permit a detailed investigation of the network's performance. As two of the most relevant parameters in the design of microstrip filters, both the magnitude and phase of S11 and S21 have been parametrically calculated after normalizing the frequency. Furthermore, when the inductors L1 and L2 are identical, all even coefficients of the numerator polynomial in the S11 transfer function are eliminated, leaving only the odd coefficients behind. Based on this feature, the bridged-T circuit is designed to operate as a high-pass filter. Therefore, the magnitude and phase of both S11 and S21 have been simulated for the designed filter with a corner frequency of 1 GHz. Simulation results performed by Keysight ADS show that S11 and S21 for the high-pass filter built upon the bridged-T network have sharp roll-off ratios of -30dB/GHz and -32dB/GHz respectively.