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Impedance Matching

  • C. W. Davidson
Chapter

Abstract

The condition for maximum power transfer between generator and load for a simple system with fixed generator resistance is well known (figure 5.1a). The power transferred to the load is
$$W = {{{V^2}} \over 2}{{{R_1}} \over {{{({R_1} + {R_{\rm{g}}})}^2}}}$$
(5.1)
Differentiating with respect to R1 to find the value that maximises the load power, we have
$${{{\rm{d}}W} \over {{\rm{d}}{R_{\rm{1}}}}} = {{{V^2}} \over 2}\left[ {{1 \over {{{({R_1} + {R_{\rm{g}}})}^2}}} - {{2{R_1}} \over {{{({R_1} + {R_{\rm{g}}})}^3}}}} \right] = 0$$
(5.2)
for a maximum, so that
$${{{R_1}} \over {({R_1} + {R_{\rm{g}}})}} + {1 \over 2},\;\;{\rm{or}}\;\;\;{R_{\rm{1}}} = {R_{\rm{g}}}$$
(5.3)

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References

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    J. R. Whinnery, et al., ‘Coaxial-line Discontinuities’, Proc. I.R.E., 32 (1944) p. 695.CrossRefGoogle Scholar
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    P. I. Day, ‘Transmission-line Transformation between Arbitrary Impedances Using the Smith Chart’, I.E.E.E. Trans. Microwave Theory and Techniques, 23 (1975) p. 772.CrossRefGoogle Scholar
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    P. Bramham, ‘A Convenient Transformer for Matching Coaxial Lines’, Electronic Engineering (January, 1961) p. 42.Google Scholar
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    B. J. Minnis, ‘A Printed Circuit Stub Tuner for Micro Integrated Circuits’, I.E.E.E. Trans. Microwave Theory and Techniques, 35 (1987) p. 346.CrossRefGoogle Scholar

Copyright information

© C. W. Davidson 1989

Authors and Affiliations

  • C. W. Davidson
    • 1
  1. 1.Heriot-Watt UniversityUK

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