Self-Complementary Antennas

An antenna with a self-complementary structure has a constant input impedance, independently of the source frequency and shape of the structure. The practical realization of such a structure, and an explanation of the remarkable principle of constant impedance, were accomplished by Yasuto Mushiake [1.1– 1.3] in 1948. Various other types of self-complementary structures were then developed successively over a fairly long period of time until quite recently [1.4–1.9].

For the purpose of developing the theory of self-complementary antennas, some preliminary considerations will be made in this chapter, and electromagnetic fields for a pair of mutually dual structures will be discussed in this section.

For the purpose of investigating the relationship between the input impedances for mutually complementary planar structures, an arbitrarily shaped plate antenna and its complementary hole antenna, as shown in Figs 3.1(a) and (b) are considered.

According to the result obtained in Chapter 3, section 3.1, the input impedances, Z₁and Z₂, for mutually complementary planar structures are given by relationship (3.3), that is \(Z_{1}Z_{2}= (Z_{0}/2)^{2}\) where Z₀ is the intrinsic impedance of the medium, which is approximately equal to 120 π[Ω] in free space. This relationship was derived by the author in 1948 [1.1–1.3]. As mentioned in section 3.1, however, the same expression had already been obtained by several other investigators, after making various assumptions, as the relationship between the input impedances for a slot antenna and its complementary wire antenna [3.1–3.4]. However, expression (4.1) in the present theory is derived without any assumptions being made, and it is always exact for any shape of mutually complementary structure. Therefore, expression (4.1) is an innovative and generalized relationship for a pair of arbitrarily shaped complementary planar structures. Nevertheless, the originality or novelty of the author’s theory was not appreciated when it first appeared.

A simple and typical example of a rotationally symmetric multi-terminal selfcomplementary planar structure is shown in Fig. 5.1, where all of the eight contour Unes of the four conducting planar sheets are generated with a single bent line by rotating it by 45° steps.

A cross of infinite planar sheets of compound perfect conductors, as shown in Fig. 6.1(a) will now be considered, where the crossing angle is rectangular and the shapes of the perfect electric conductor (PEC) and the perfect magnetic conductor (PMC) are both symmetrical with respect to the crossing axis. Furthermore, in the two mutually perpendicular infinite sheets, the shapes of the portions of the PEC and the PMC are identical, but their properties are interchanged. In such a structure, the whole space is divided into four perfectly shielded and independent partial spaces. For these four partial spaces, we assume four symmetrical electric source currents J₀₁, J₀₂, J₀₃ and J₀₄, respectively.

In order to improve the radiation characteristics of antennas, especially to increase their directivities or power gains, the stacked antenna technique is often utilized effectively in practice. In such cases, there are mutual interactions between the element antennas, mainly owing to the effects of the mutual impedances. Accordingly, the constant-impedance property of self-complementary antennas is not necessarily preserved when they are introduced as element antennas into a stacked antenna. However, the author has proposed various types of stacked self-complementary antenna, where all the element antennas have constant impedance, independently of the source frequency and their shapes.

According to the theory of the self-complementary antenna (SCA), the basic structures of this type of antenna consist of infinitely extended planar sheets of perfect electric conductors. In addition, in the case of stacked antennas, an infinite number of element antennas are arranged periodically. Therefore, the theoretically obtained self-complementary antenna can only be approximated by limited size of structure and limited number of element antennas, when this principle is applied to extremely broad-band practical antennas.

In the process of developing extremely broad-band practical antennas on the basis of the theoretical principle of self-complementary antennas, it is always necessary to make some additional experimental studies as mentioned in Chapters 1 and 8. For this reason, any basic information related to the measured characteristics of practical self-complementary antennas (SCA) will be helpful for their developmental investigations in general. Therefore, it is worthwhile obtaining various experimental data to the greatest extent possible.

As an example of an axially symmetric self-complementary antenna for practical application, an equally spaced unipole (or monopole)-notch type array antenna with tapered distribution of the unipole-lengths as shown in Fig. 10.1 has been experimentally studied [8.1–8.3, 10.1–10.4]. According to the theory described in Chapter 4, this has a constant input impedance of 607π Ω under the condition that the end terminals are terminated by a lumped resistance or a transmission line with 60πΩ. However, the end terminals of the tested structure are opened as shown in the same figure.

The radiation of the three-dimensional SCA shown in Fig. 6.7 is separated into two portions which are respectively in the upper and the lower half-spaces divided by the infinite horizontal plane of the conducting sheet. By taking this property into account, a practical application of this antenna is conceivable, where only the upper half of its radiation is utilized.

Self-complementary antennas have constant input impedance, independently of the source frequency and of the shapes of their structures. This nature has its origin in the “principle of self-complementarity”, and various types of extremely broad-band antennas have been developed from this basic principle as its practical applications. In this book, such types of self-complementary antenna and their origin, the “principle of self-complementarity”, are treated in detail.