Design Studies for Tapered Transmission Line Matching Circuits

Sprungle, Raymond

Graduate Thesis Or Dissertation

Design Studies for Tapered Transmission Line Matching Circuits Public Deposited

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Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/cj82k895q

Abstract

When two RF circuits or devices are connected, there is often an impedance mismatch causing unwanted reflection if not corrected. Impedance matching can be realized using lumped or distributed circuit elements. When considering transmission line segments, the length of the line with respect to the wavelength of the matched frequency is significant. It has been empirically observed while designing short transmission line matching circuits, that there is a lower limit to the segment length that can provide a perfect match when constraints are placed on the possible values of characteristic impedance. However, this limit has not been extensively studied.

In this dissertation, lengths limits for zero reflection are derived. The length limits are a function of the characteristic impedances used along the non-uniform transmission line. Discontinuities along the transmission line can be used in impedance matching. A study of complex reflection using global and local reflection coefficients is developed to understand the contributions of line length, taper, and impedance discontinuities.

A special case of a nonuniform transmission line that can be used for impedance matching is the exponential line. While past studies of exponential transmission lines have concentrated on the case where there are no discontinuities at the load and input ends of the line, this dissertation allows for an infinite number of exponential lines with various discontinuities at the load and source end of the line. For this case, a closed form solution for the reflection coefficient as a function of distance along the line can be computed. A one-parameter family of designs for an exponentially tapered transmission line needed to match a given resistive load to a real input impedance is derived. Consideration is also given to frequency bandwidth, ripple height, and length of the matching section. Several of these transmission lines have been fabricated and measured.

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