Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 79

The previous sections have presented the voltage and current waves on the uniform transmission line that has no change in the geometry along the direction of propagation. For a uniform line, the relative permittivity and relative permeability also do not change along the line. For such a uniform lossless or low‐loss transmission line, the voltage and current waves travel at a definite velocity from low frequency to high frequency. The uniform transmission line behaves as a low‐pass filter (LPF) section. The propagation constant for such a uniform transmission line is the same at any section of the line. The line also has a unique characteristic impedance that is independent of the location on a line. However, if the geometry of a transmission line or an electrical property of the medium of a line changes in the direction of propagation, such a line is no longer a uniform transmission line. It is a nonuniform transmission line. Its electrical properties, such as the RLCG primary constants, propagation constant, phase velocity, and characteristic impedance, become a function of the space coordinate along the direction of propagation. The characteristic impedance of a nonuniform transmission line changes from one end to another end; therefore, it finds application in the broadband impedance matching [B.9, B.10, B.12]. It is also used for the design of delay equalizers, filters, wave‐shaping circuits, etc. [J.6–J.9]. It is an essential section of the on‐chip measurement system [J.10]. Unlike a uniform transmission line, it shows a cut‐off phenomenon, i.e. the wave propagates on the line only above the cut‐off frequency. Below the cut‐off frequency, the wave only attenuates with distance. Thus, the nonuniform transmission line behaves like a high‐pass filter (HPF) section [J.11–J.13, B.17].

The present section obtains the wave equations for a nonuniform transmission line. However, like the uniform transmission lines, the nonuniform transmission lines do not have closed‐form solutions for the voltage and current waves. The numerical methods have been used to determine the response of an arbitrarily shaped nonuniform transmission line [J.10, J.11]. However, this section discusses only the exponential nonuniform transmission line to understand its characteristics.