Contributed to Wikipedia.

Self-Complementary Antenna (SCA)

1. Definitions of three terms related to SCA.

    Self-complementary antenna is an arbitrarily shaped antenna which is constituted with a half of an infinitely extended planar-sheet conductor such that the shape of its complementary structure is exactly identical with that of the original structure with two terminals for the simplest case. The self-complementary antenna has constant input impedance independent of the source frequency and the shape of the structure.

Explanation of the self-complementary shapes.

    The type of the self-complementary antenna is not limited only to the case of a planar antenna with two terminals, but there are more general types of structures with various grades of complexity in their structures, such as, the number of terminals, the number of reference planes, and others. They also have constant-impedance property independent of the source frequency and the shape of the structure for respective classes of structures with various grades of complexity. This general principle is called “Principle of Self-Complementarity”. (This is also called “Mushiake Principle” on the Internet.) This principle is applicable also to the structures other than antennas.

    Furthermore, the equation which gives the constant value of the input impedance for self-complementary antenna is called “Mushiake Relationship”. The values of the constant-impedance for various classes of complexity in the self-complementary structures depend on the respective grades of the complexity. For example, Mushiake relationship for the simplest self-complementary planar antenna with two terminals is expressed as

Z = Z0/2188.4 [Ω].

Where Z is the input impedance of the antenna and Z0 is the intrinsic impedance of the medium.
Also, some experimental studies
on truncated self-complementary antennas, including radiation properties, are conducted in Japan.

2. An important note.

     The so-called “Log-Periodic Antenna” (commercial name) is a modified self-complementary antenna, and the original structure before its modification has a typical self-complementary shape. The “log-periodic”shape does not provide the broadband property for antennas. This fact is evident from the IEEE definition of “Log-Periodic Antenna”, folding up the structure of SCA, and others.

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