¼-Wave Impedance Matching Section Nomograph
March 1959 Radio & TV News

March 1959 Radio & TV News

[Table of Contents] Wax nostalgic about and learn from the history of early electronics. See articles from Radio & Television News, published 1919-1959. All copyrights hereby acknowledged.

This nomograph from a 1959 issue of Radio & TV News magazine simplifies matching a source (sending - s) impedance (Z_s) and a load (receiving - r) impedance (Z_r) using a quarter-wave transmission line. To use it, locate your Z_s value on the left vertical scale and your Z_r value on the right scale. Lay a straightedge across these points; the intersection with the center vertical scale reveals the required surge impedance† - also called characteristic impedance - (Z₀). Surge impedance is the ratio of voltage to current for a wave traveling along an infinite transmission line, dictated by the physical geometry and dielectric properties of the cable, defined as Z₀ = sqrt (L/C), where L is inductance per unit length and C is capacitance per unit length. The quarter-wave transformer relies on the relationship Z₀ = sqrt (Z_s * Z_r). By using a line with this specific surge impedance cut to one-quarter wavelength, you achieve perfect impedance matching, effectively eliminating signal reflections and maximizing power transfer between your source and load systems.

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This chart is used to obtain the surge impedance of a ¼-wave matching section used as an impedance transformer from one real impedance to another.

†  The term "surge impedance" originates from the study of transient phenomena and traveling waves on power transmission lines. In electrical engineering, a "surge" refers to a high-voltage, short-duration transient caused by lightning strikes, switching operations, or sudden faults on a line. When such a surge wave propagates down a conductor, it does not see the entire line as a single lumped element of resistance. Instead, it encounters the line's distributed inductance and capacitance. The wave behaves as if it is charging the line's capacitance through its inductance as it travels. The ratio of the voltage of this surge to the resulting current is constant, determined solely by the geometry of the physical conductors and the insulating medium. Because this ratio represents the "opposition" the surge wave encounters as it travels - before the wave reaches the end of the line or "sees" the terminal load - it was historically termed the "surge impedance." Today, it is more commonly called characteristic impedance, but the legacy term remains common in power systems.