Theory of fractional order elements based impedance matching networks

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Ahmed G. Radwan, et al., "Theory of fractional order elements based impedance matching networks." IEEE Microwave and Wireless Components Letters 21 (3), 2011, 120.

Fractional order circuit elements (inductors and capacitors) based impedance matching networks are introduced for the first time. In comparison to the conventional integer based L-type matching networks, fractional matching networks are much simpler and versatile. Any complex load can be matched utilizing a single series fractional element, which generally requires two elements for matching in the conventional approach. It is shown that all the Smith chart circles (resistance and reactance) are actually pairs of completely identical circles. They appear to be single for the conventional integer order case, where the identical circles completely overlap each other. The concept is supported by design equations and impedance matching examples.