Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 86

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 waveguide sections supporting non‐TEM mode are also used to develop components and circuits. As a matter of fact, the voltage and current can be uniquely defined only for the TEM mode supporting structures. However, for non‐TEM line structures, only the equivalent voltage and current, based on the power equivalence principle, is defined [B.1, B.2].

The abovementioned parameters are discussed in this section, as these are important for the analysis of the line networks and the networks involving both the line sections and lumped circuit elements. The results of the analysis and measurement are also presented using these parameters. The reader can study these parameters in detail from any of the excellent textbooks [B.1, B.3–B.7]. One basic difference could be seen between the lumped elements based low‐frequency circuits and the transmission line sections based on high‐frequency circuits. The low‐frequency circuits are the oscillation type circuits, whereas the high‐frequency microwave circuits are the wave type circuits. In the case of the low‐frequency oscillation type circuits, the port voltage and port current are described by a single voltage or current. In general at any port, for the high‐frequency wave‐type circuits, the port voltage is described by a sum of the incident and reflected voltages, also the port current is a sum of the incident and reflected currents. It is illustrated in the discussions on the evaluation of the parameters.

How to characterize the components, circuits, and network made of the transmission line sections and waveguide sections? At the microwave frequency, port voltage and port current are not the measurable quantities. However, from the analysis point of view, the networks can be characterized by the [Z], [Y], and [ABCD] parameters. But these are not the measurable parameters at microwave frequencies. A different kind of matrix parameter, called the scattering or [S]‐parameters, is used for the practical characterization of the microwave network and the transmission line structures [J.1]. The [S] parameter is a measurable quantity. A Scalar Network Analyzer is used to measure the magnitude |S| of S‐parameter of any microwave circuit and network. For the measurement of the complex [S] parameters, i.e. both the magnitude and phase response of a network, a Vector Network Analyzer (VNA) is used. The Circuit Simulators and the EM‐Simulators (Electromagnetic field simulators) are also used to get the frequency‐dependent [S] parameters response of the microwave circuits.