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Technical Tidbit - August 2012
Novel Equivalent Circuit for Zin of an Arbitrarily Terminated Transmission Line
(Written by Timothy J. Maloney)

Transmission line with source and load impedances

Figure 1.
Transmission Line With Input and Load Impedances

Abstract:  A new equivalent circuit for Zin of an arbitrarily terminated transmission line is presented, one which employs only lumped impedances and short and open line stubs in series‐parallel combination. The new picture readily illustrates concepts of line matching and impedance inversion at quarter‐wave frequencies, and also offers insights into transient and off‐resonance response.

Discussion: Tim Maloney of Intel Corporation has devised a simple, intuitive, and useful equivalent circuit for a transmission line using shorted and open transmission line segments and submitted it for publication on this site. In essence, his equivalent circuit transforms the transmission line of Figure 1 above into the configuration of Figure 2 below. This is a very useful equivalent circuit.

To read Tim's paper in pdf format, click here. Don't be scared by the look of the equations you see on the page. Tim does an excellent job of simplifying their interpretation into an easy to understand concept.

Transmission line equivalent circuit

Figure 2.Equivalent Circuit for Transmission Line With Input and Load Impedances

Summary: Tim Maloney's paper on an equivalent circuit for transmission lines is an intuitive and very useful treatment of transmission lines. Many engineers will find this equivalent circuit useful in their work.

Tim Maloney's paper:
  1. Novel Equivalent Circuit for Zin of an Arbitrarily Terminated Transmission Line
    Timothy J. Maloney, Intel Corporation
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Copyright 2012 Douglas C. Smith