The Nonuniform Transmission Line as a Broadband Termination

Classical transmission line analysis leads to the propagation of a wave in which neither the electric nor magnetic fields have components in the direction of propagation. 1 These transverse electromagnetic (TEM) waves are characteristic not only of the usual transmission line structures such as parallel wires and coaxial cable; they are also characteristic of plane-wave propagation in isotropic media. It is often convenient, when dealing with TEM-wave propagation, to make use of results of classical transmission line analysis. Some care must be exercised, however, in applying these results at microwave frequencies. Consider, for example, the problem of terminating a lossless line. Classical analysis tells us that, if the line is terminated in its charac913 914 THE B E L L SYSTEM T E C H N I C A L J O U R N A L , JULY 1958 teristic impedance (which is a pure resistance for a lossless line), the termination will be reflectionless. Two difficulties arise at microwave frequencies, where the physical dimensions are no longer small compared to the wavelength. First, as the frequency increases, the concept of a lumped circuit element becomes less meaningful. For example, a resistive disc termination for a coaxial line will have an effective impedance which is strongly influenced by the geometry and has very little correlation with the dc resistance of the disc.2 The second difficulty is that, even if the appropriate effective lumped impedance is obtained, the analysis assumes that this impedance is connected across an open circuit.