# A general broadband matching theory and its application

Abstract (Summary)

In the design of communication systems, a basic problem is to design a lossless coupling network between a given source and a given load so that the transfer of power from the source to the load is maximized over a given frequency band of interest. This dissertation solves the problem of designing a lossless reciprocal equalizer to match a given frequency-dependent source to an active or passive loads. The equalizer, when operating between the given source and the given load, yields the desired transducer power gain characteristic. The significance of the approach taken is that it circumvents the need for replacing the source and the load impedances by their Darlington equivalents and is applicable to passive as well as active loads. The prescribed transducer power gain characteristic determines the real-frequency magnitude of the reflection coefficient. The constraints imposed on the output reflection coefficient by the load impedance are determined so that the driving-point impedance looking into the output port of the equalizer is positive-real. To realize the equalizer, this impedance must be compatible with the source impedance. Additional constraints imposed on the output reflection coefficient, and the input reflection coefficient defined with respect to a one-ohm resistor termination at the output port are determined so that the driving-point impedance looking into the output port is compatible with the source impedance. These constraints on the reflection coefficients are shown to be necessary and sufficient for the existence of an equalizer which matches a given load impedance to a given source impedance. If the necessary and sufficient constraints are satisfied, the driving-point impedance looking into the input port with a one-ohm resistor termination at the load end is computed, which is guaranteed to be positive-real. To construct the equalizer, this positive-real impedance is realized as the driving-point impedance of a lossless reciprocal two- port network terminated in a one-ohm resistor. If the impedance facing the one-ohm resistor is equal to that derived from the output reflection coefficient and the load impedance, the two-port network is the desired equalizer. On the other hand, if the realization does not give the desired equalizer, by properly augmenting the desired driving- point impedance before realization by multiplying its numerator and denominator polynomials by the same factor, the resulting Darlington realization can be such that the impedance facing the one-ohm resistor is equal to that derived from the output reflection coefficient and the load impedance. The two-port network in the new Darlington realization is the desired equalizer. A procedure for the design of an equalizer is presented in seven steps. The procedure provides the proper augmentation, when required, for the desired driving-point impedance before it is realized. Several examples are worked out to illustrate the application of the theory presented. The design of an equalizer is illustrated by considering a tunnel diode active load and, a parallel RC or a serial RL source impedance. When the source resistor and generator are replaced by a circulator termination, the system achieves the prescribed approximation of the low-pass Butterworth or Chebyshev transducer power gain characteristic. For an active load with the simplified equivalent network of a tunnel diode, the design procedure for an equalizer that achieves the approximation of the low-pass Butterworth or Chebyshev transducer power gain characteristic of arbitrary order is presented in its full generality. Applying the constraints on the reflection coefficients, gain- bandwidth restrictions are determined in nonintegral form.
Bibliographical Information:

Advisor:

School:Ohio University

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:communication systems reflection coefficient equalizer general broadband

ISBN:

Date of Publication:01/01/1981