Ludwig, Reinhold Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, Massachusetts.
- Reflection coefficient
- Impedance and reflection coefficient representation
- Computations with the Smith chart
- Additional applications
- Links to Primary Literature
- Additional Readings
A graphical procedure for converting impedances into reflection coefficients and vice versa. At high-frequency circuit operation, voltages and currents behave like traveling waves propagating over finite-length components. Copper traces on printed circuit boards, coaxial cables, and even simple wires become transmission lines. Changes in the length or operating frequency of these transmission lines result in periodic impedance behaviors not encountered in low-frequency circuits. Frequently, the impedance is replaced by the reflection coefficient, a more convenient way to quantify the transmitted and reflected voltage-current waves. To show how the impedance can be converted into a reflection coefficient and vice versa, P. H. Smith developed an ingenious graphical procedure based on conformal mapping principles. His approach permits an easy and intuitive display of the reflection coefficient as well as the complex impedance in a single graph. Although such a graphical procedure, nowadays known as the Smith chart, was developed in the 1930s prior to the computer age, it has retained its popularity and can be found in every data book describing passive and active high-frequency components and systems. Almost all computer-aided design programs utilize the Smith chart for the analysis of circuit impedances, design of matching networks, and computations of noise figures, gain, and stability circles. Even instruments such as the ubiquitous network analyzer have the option to represent certain measurement data in a Smith chart format. See also: Conformal mapping; Electrical impedance; Reflection and transmission coefficients; Transmission lines
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