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3 Waves on Transmission Lines – II: (Network Parameters, Wave Velocities, Loaded Lines)
Introduction
The transmission line sections are used to develop various passive components. These are characterized by several kinds of matrix parameters. This chapter discusses the matrix parameters and their conversion among themselves. It also discusses various kinds of dispersion and wave propagation encountered on transmission lines. The transmission lines could be loaded by the reactive elements and resonating circuits to modify the nature of the wave propagation on the lines. Such loaded lines are important in modern planar microwave technology. Such loaded lines are introduced in this chapter. The primary purpose of this chapter is to review in detail the matrix description of lines and wave propagations on the dispersive transmission line that supports various kinds of wave phenomena.
Objectives
To review the matrix representations of the two‐port networks using the [Z], [Y], and [ABCD] parameters.
To discuss the basic properties and use of the scattering [S] parameters.
To understand the process of de‐embedding of true [S] parameters of a device.
To understand the process of extraction of the propagation constant from the [S] parameters.
To understand the phase and group velocities in a dispersive medium.
To discuss the circuit modeling of the reactively loaded line supporting both the forward and backward waves.
3.1 Matrix Description of Microwave Network
At low frequency, the circuit is described in terms of several kinds of matrices that relate the port voltages to the port currents. These matrices could be the impedance matrix [Z], admittance matrix [Y], and hybrid matrix [H]. The transmission matrix is defined as the [ABCD] matrix. It is useful in cascading of two or more networks or transmission line sections. At low radio frequency, the voltage and current are measurable parameters. Therefore, the matrix elements of a network and device could be experimentally determined.
Normally, the microwave passive components, circuits, and networks are constructed around the transmission lines supporting the TEM or the quasi‐TEM mode. Sometimes, the lumped elements are also used. The
