2a/t for two-wire w/t for two-strip

Figure 7.18 Relationship between Zc and wire radius a in terms of t (from [10]).

Figure 7.9, Z0 is expressed as shown in Figure 7.18. These are useful for designing an antenna consisting of two parallel strip-type meander lines.

A practical model having h = 0.11λ (144.4 mm), d = 0.057λ (74.8 mm), and N (number of segments) = 6, is considered. In this case, f0 is set to 228 MHz, Sm = 1.5, and the thickness of the substrate (Teflon, ε = 2.6) is 0.0006λ (0.8 mm). From Figure 7.14 and Figure 7.15, um is 1.1 and RBW is 0.013. When the elements 1 and 2 are connected at the end to form the folded structure, L/λ becomes 0.75, and Z0 is found to be 9.58 . From these, w/t is 18, and thus w becomes 0.011λ (14.4 mm), as t = 0.8 mm. RBW is obtained to be about 7.2%. Measured impedance (200 MHz step between 200 and 260 MHz) is shown in Figure 7.19, where a square ground plane of 0.76 λ (1 m) is used. Radiation efficiency obtained was about 90% to 95%. Sm in terms of frequency f is shown in Figure 7.20.

A tapered folded-type MLA is described in [9a], including folded type with a plate top-loaded MLA.

7.2.1.1.1.1.4 Meander line antenna mounted on a rectangular conducting box

When an MLA is mounted on a rectangular conducting box [12], as can be often seen in practical applications (Figure 7.21), the resonance frequency fr varies with the distance S of the antenna element from the surface of the substrate on which the antenna is printed. R and fr with respect to S are given in Figure 7.22. Figure 7.23 illustrates impedance loci on the Smith chart. The locus A is for the MLA mounted on the rectangular box, while the locus B is for the MLA placed on a circular ground plane with a diameter of 1 m. In both cases the impedance loci encircle near the center of the Smith chart, providing evidence of wideband characteristics. The frequency range used in the measurement is between 800 MHz and 900 MHz.

Antenna length (L/λ)

Figure 7.27 Wire length La versus antenna length L at resonance state ([13], copyright C 2004 IEICE).

Antenna length (L/λ)

Figure 7.28 Input resistance Rin and loss resistance Rl with respect to the antenna length L/λ ([13], copyright C 2004 IEICE).

shown. The antenna wire length La/λ in relation with L/λ at the self-resonance state is illustrated in Figure 7.27 for cases d = 0.1 and 0.3, and N = 10, 22, and 38.

Input resistance Rin and loss resistance RL of an antenna in relation to the antenna length L/λ for cases N = 10, 22, and 38, and d = 0.3 are shown in Figure 7.28. The loss resistance Rl of a conductor with the skin depth δ and the conductivity σ is given by

When the conductor has planar structure with length L, width w, and thickness t, loss resistance RL of an antenna is expressed by

√

RL = Rl L/2(w + t) = L σ f π μ/2(w + t). (7.28)

When the conductor is copper, σ is 5.8 × 107 [S/m], then δ = 2.5 mm at 700 MHz.

√

Since RL increases with the antenna wire length La and f , when L becomes less than 0.1λ, it increases notably with increase in N that makes La large.

Figure 7.31 Current distributions on the MLA element: (a) dipole type and (b) folded-back type ([13], copyright C 2004 IEICE).

elements (in the figure), because the directions of their current flows are the same. Contrastingly, the currents on the vertical elements (in the figure) do not contribute to the radiation, because the current flows on parallel elements are opposite in direction, so that their radiations cancel each other. Hence, radiation from a dipole-type MLA (the

line diameter d with the separation w of the two current flows as shown in Figure 7.32(a))

√

is equivalently the same as that of a thicker dipole of the effective radius deff = dw with the length L as Figure 7.32(b) shows. This dipole is driven by a voltage V, and a current I flows on the element. Meanwhile, a folded-type MLA shown in Figure 7.32(c), in which antenna parameters such as a driven voltage V and currents I1 and I2 on each element separated with a distance W are provided. Current flows on these modes can be decomposed into two modes; unbalanced (radiation) and balanced (transmission line) modes as shown in Figure 7.32(d). On the unbalanced mode, current Iu (= (I1 + I2)/2) flows in the same direction on the two lines, while on the balanced mode, current Ib (= (I1 – I2)/2) flows in opposite directions on the two lines. The equivalent representation for these modes is further remodeled as a radiation mode and a transmission line mode as shown in Figure 7.32(e), which depicts a dipole driven by the voltage V, and the current 2Iu flowing on a single element with the thicker diameter dE (=

From these, the impedance Zu of the unbalanced mode is found by (V/2)/2Iu, and that of the unbalanced mode Zb is (V/2)/Ib. The impedance Z of the MLA is thus found by

Meanwhile, the balanced mode is represented by two shorted two-wire transmission lines driven by a voltage V/2 with opposite-direction currents Ib on each line as shown in Figure 7.32(e). The impedance Zb of the balanced mode is given by 2Zb0, which is the parallel combined impedance of the shorted two-wire transmission line of the length L/2. Here Zb0 is given by (V/2)/Ib and by jZ0 tan( β2L ), where Z0 is the characteristic impedance of the two-wire transmission line. From these relationships, the impedance Zf of the folded meander line antenna is derived as