and I. These are expressed by using either the impedance matrix [Z], or the admittance matrix [Y] as

Ordinary matching at the load terminals is made in the Immittance Domain, where the input impedance Zi of an antenna is matched to the load impedance, usually 50 ohms. The space matching is done in the near field of an antenna as follows. Consider the complex Poynting vector S, where S = E × H* = Re S + Im S. If Im S can be compensated by some vector P produced by a source F so that Im S + P = 0, only real part Re S remains, and Re S is varied to make Re Zi = Ri to be 50 ohms, then the matching process is completed, without regarding the size of antenna. The additional vector F should produce such a field that × F, will be zero by taking divergence so that

This implies that × F is a near-field component, corresponding to a reactive power. This × F component can be replaced by a metamaterial that provides the corresponding quantity to the × F component which is equal to –Im S so that the resonance in space can be attained. In a short dipole case, Im S is a reactive (capacitive) power, so the× F component should be a reactive (inductive) power, which can equivalently be represented by an ENG material. The ENG material also affects Re S, so Zi, (now Ri since Xi = 0), will be adjusted to 50 ohms, by varying the material parameters such as size, location, geometry, and so forth. Even when the resistive component Ri could not be made equal to 50 ohms, at least the resonance condition Xi = 0 in the near field can be achieved and the matching at the load terminal with low loss can be achieved very easily. In the mean time, MNG materials can be employed for the space matching when a small magnetic source like a small loop, which produces inductive field in the near field, is used. DNG materials can also be adapted for small antennas to enhance the radiation [46, 47].

6.2.5.1Application of SNG to small antennas

6.2.5.1.1 Matching in space

The concept of matching in space is to realize compensation of the reactive components in the near field of an antenna. The conjugate component is produced by an extra field in the near field of the antenna so that resonance condition is obtained, and at the same time the real component in the near field is varied so that the total antenna impedance is made equal to the complex conjugate of the load impedance. By this means, a very high efficiency small antenna would be realized. The bandwidth depends on the range of frequency over which the material can compensate the reactive component in the near field. The extra field is produced by an additional radiation source to the antenna; however, it can also be represented by a metamaterial located in the proximity to the antenna, which produces the conjugate field equivalent to that of the near field so that

ENG

monopole

ground plane

Figure 6.42 An example of an ENG application to a short monopole antenna.

MNG

loop

ground plane

Figure 6.43 An example of an MNG application to a loop antenna.

Figure 6.44 An NIC network.

resonance and matching can be achieved in the near field of the radiation source. In practice, an epsilon-negative (ENG) material is placed near an electrical radiator like a small monopole (Figure 6.42), while a mu-negative (MNG) material is used near a magnetic radiator, for example a small loop (Figure 6.43). Stuart reported application of a negative permittivity material to a short monopole, by which the size reduction of an antenna was achieved (Figure 6.42) [44]. Bilotti et al. published a paper [45], in which they discussed application of a negative permeability material to a patch antenna to realize downsizing of an antenna (Figure 6.43).

The space matching can be achieved by using not only materials but also hardware that represents metamaterials. Some examples are shown in [46–48], where both ENG and MNG are realized by using a meander line, and an inter-digital capacitor circuit, respectively.

6.2.5.1.2 Matching at the load terminals

It is taken for granted that matching occurs at the load terminal of an antenna; however, it is also well known that the smaller the size an antenna becomes, the harder the matching at the load terminal becomes, because the impedance tends rapidly to high reactive impedance and low resistive impedance. In order to overcome this problem, making use of an NIC (Negative Impedance Converter) at the matching circuit is considered very useful. The NIC is represented by a two-terminal network as Figure 6.44 shows [49].

Figure 6.45 An NIC application to antenna matching.

Figure 6.46 A practical NIC implemented by a transistor circuit [49a].

The NIC network transforms an impedance Z to its negative –Z, as shown in Figure 6.44, where the network parameters are given. By inserting an NIC network between the antenna output terminals and the matching circuit as shown in Figure 6.45 [50], the antenna impedance Za of, for instance, a very short dipole, which has very high capacitive impedance, is converted into the negative impedance –Za, resulting in high inductive impedance at the output terminals of the NIC. The high inductive impedance can be compensated by high capacitive impedance, which has low loss. This is advantageous for matching a short dipole antenna, because it does not require high inductive impedance that has big loss, thereby reducing efficiency in an ordinary matching process. Practical NIC circuits can be implemented by a transistor circuit and some excellent results have been reported by Sussman (Figure 6.46) [49a]. This is an application of Non-Foster circuitry to the antenna matching circuit [51]. However, use of a transistor circuit has disadvantages, because of its uni-directionality against bi-directionality of the antenna. Recently real (not artificial) metamaterial, which exhibits negative permeability, has been developed by using composite ferrite material [52]. This material is doubly advantageous to be used in the antenna matching circuit, because the circuit is made bi-directional, and the material is made in a very small piece, so it does not take space as compared with other metamaterials like transmission lines.