8.2.5Application of DBE (Degenerated Band Edge) structure

Figure 8.97 Concept of creating a DBE surface on a microstrip substrate using a pair of coupled and uncoupled transmission lines ([83], copyright C 2009 IEEE).

be explained by using the dispersion diagram of Figure 8.96(b), which is generated by using a half of the loop as the unit cells to form the periodic structure shown in the Figure 8.96(a). The loop consists of two unit cells formed by the top and bottom half loops. Two traces on the dispersion diagram (Figure 8.96(b)) indicate two propagating modes of either positive or negative k, and resonance frequencies are given at points k = ± π and 0, because these points are associated with phases of matching for two propagating waves on the loop. To achieve lower resonance frequency, it is necessary to lower the k–ω curve at k = π as shown in Figure 8.96(c). This can be achieved by using DBE structure, which exhibits a 4th-order k–ω curve, descending more sharply around the band edge than conventional EBG structure having a 2nd-order k–ω curve as shown in Figure 8.96(d).

A practical structure to replace a volumetric DBE material (crystal) composed of misaligned anisotropic layers can be equivalently implemented by coupled and uncoupled transmission line pairs printed on a uniform substrate as shown in Figure 8.97 [83]. A microstrip (MS) DBE antenna composed of two-circularly cascaded unit cells designed for resonance at 2.59 GHz is illustrated in Figure 8.98. The antenna has broadside gain of 6.9 dB at 2.59 GHz with 0.8% bandwidth for |S11| < –10 dB. A physical footprint of the antenna on the Duroid substrate (εr = 2.2) is λ0/4.3 × λ0/5. The radiated field is linearly polarized and the radiation efficiency is over 95%. The narrow bandwidth can be improved by using a thicker substrate. By changing the substrate thickness from 250 mils to 500 mils, the bandwidth increased to 8.7%, but with lowered resonance frequency to 2.3 GHz and reduced gain to 6.2 dB. As the antenna features a highly concentrated field at the center of the antenna, it is suited to an array that can be tightly arranged. Figure 8.99 depicts an example of such an array, which is a 4 × 4 array, constructed in the size of 1.2λ0 × 1.2λ0, with separation of each element λ0/15 at the center frequency f0 = 2.55 GHz. The directivity is 13 dB and the bandwidth is 2%.

A DBE antenna with reduced size and yet wide bandwidth is designed. The antenna depicted in Figure 8.100(a) has reduced footprint of 0.85 × 0.88 (in inches) (λ0/9.6 × λ0/9.3 × λ0/16 at 1.45 GHz) etched on 2 × 2 inches alumina substrate (εr = 9.6, tan δ = 3 × 10−4) with thickness of 500 mils, having a metal plate as the ground plane on the back surface. On the alumina substrate, the resonance frequency is down to 1.455 GHz