Transmission lines are needed for connecting various circuit elements and systems together. Open-wire and coaxial lines are commonly used for circuits operating at low frequencies. On the other hand, coaxial line, stripline, microstrip line, and waveguides are employed at radio and microwave frequencies. Generally, the lowfrequency signal characteristics are not affected as it propagates through the line. However, radio frequency and microwave signals are affected signi®cantly because of the circuit size being comparable to the wavelength. | Radio-Frequency and Microwave Communication Circuits Analysis and Design Devendra K. Misra Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-41253-8 Hardback 0-471-22435-9 Electronic 3 TRANSMISSION LINES Transmission lines are needed for connecting various circuit elements and systems together. Open-wire and coaxial lines are commonly used for circuits operating at low frequencies. On the other hand coaxial line stripline microstrip line and waveguides are employed at radio and microwave frequencies. Generally the low-frequency signal characteristics are not affected as it propagates through the line. However radio frequency and microwave signals are affected significantly because of the circuit size being comparable to the wavelength. A comprehensive understanding of signal propagation requires analysis of electromagnetic fields in a given line. On the other hand a generalized formulation can be obtained using circuit concepts on the basis of line parameters. This chapter begins with an introduction to line parameters and a distributed model of the transmission line. Solutions to the transmission line equation are then constructed in order to understand the behavior of the propagating signal. This is followed by the concepts of sending end impedance reflection coefficient return loss and insertion loss. A quarter-wave impedance transformer is also presented along with a few examples to match resistive loads. Impedance measurement via the voltage standing wave ratio is then discussed. Finally the Smith chart is introduced to facilitate graphical analysis and design of transmission line circuits. DISTRIBUTED CIRCUIT ANALYSIS OF TRANSMISSION UINES Any transmission line can be represented by a distributed electrical network as shown in Figure . It comprises series inductors and resistors and shunt capacitors and resistors. These distributed elements are defined as follows 57 58 TRANSMISSION LINES Figure Distributed network model of a transmission line. L .
