A Synthesis Procedure for Transmission Line Networks

Richards has shown that by a suitable frequency transformation, networks composed of transmission lines all of a fixed length and resistors behave over a range of frequencies zero to as lumped constant networks behave over the frequency range zero to infinity. In this paper the synthesis procedure of a general class of lossless filters using transmission line components is considered. This is the class of filters having all of its transmission zeros at zero frequency and at infinite frequency in the transformed frequency plane, which corresponds to transmission zeros at zero frequency and frequency along the real frequency axis. This class includes the high-pass and low-pass configuration as special cases. It is proven that if a transmission characteristic is realizable using lumped constant elements, it can be realized in the transformed frequency plane using transmission line components. The transmission line components used are series or shunt shorted and open stubs and series lines. The series stubs are discussed and their feasibility demonstrated. It is shown that series transmission lines can be placed between elements whenever necessary, so that it is physically possible to build these networks.