Compact Leaky-Wave Antenna

Generally, the cutoff frequency of a conventional leaky-wave antenna is controlled by the normalized complex propagation constant which includes the normalized phase constant β/k^B0^B and the normalized attenuation constant α/k^B0^B, where k^B0^B is the free space wavenumber. In Fig. 3-5, as the normalized attenuation constant equals the normalized phase constant (α/k^B0^B

=β/k^B0^B), the cutoff frequency can be defined. When the normalized phase constant is less than one (β/k^B0^B < 1), which is called fast wave (β < k^B0^B), the radiation region can be found. The β/k^B0^B, α/k^B0^B, cutoff frequency, and radiation region can be determined by the width of leaky-wave antenna, dielectric constant, and substrate thickness. The theoretical β/k^B0^B and α/k^B0^B of the conventional microstrip LWA as a function of frequency are plotted in Fig. 3-5. They are calculated by employing a rigorous (Wiener-Hopf) solution [3-7] and [3-9]. The cutoff frequency is about 4.15 GHz, and the radiation region is operated from 4.15 to 4.9 GHz. In [3-11] and [3-12], the normalized constant β/k^B0^B and α/k^B0^B relate directly to the maximum radiation angle θ^Bm^B between the broadside direction and the main-beam direction, and the 3-dB radiation beamwidth Δθ. These relations are given by

Figure 3-6(a) compares the theoretical θ^Bm^B of infinite length, and the simulated and measured θ^Bm^B of finite length (about 1.40 λ^B0^B at 4.2 GHz) conventional LWA. The characteristics of the finite length conventional LWA were simulated by Ansoft High Frequency Structure Simulator software. Fig. 3-6(b) illustrates the theoretical Δθ of infinite length, and the simulated and measured Δθ of finite length conventional LWA. The values of theoretical θ^Bm^B and Δθ are determined in Eq. (3-04)~(3-06) by the values of theoretical β/k^B0^B

and α/k^B0^B. The theoretical, simulated, and measured radiation angles of convention LWA are respectively about 16°, 22°, and 15°at the cutoff frequency of 4.15 GHz; therefore, it can be seen that the length of LWA does not influence the value of θ^Bm^B and β/k^B0^B much (see Eq. (3-04)).

However, from Fig. 3-6(b) we can see that the 3-dB radiation beamwidth, Δθ, of the theoretical calculation of infinite length LWA, and the simulated and measured results of finite length LWA are respectively about 95°, 43°, and 60°at 4.15 GHz. This result agrees very well with the thesis in [3-12] that the length of LWA can vary the value of Δθ and α (see Eq.

(3-05) and (3-06)). Furthermore, since the cutoff frequency can be controlled by the width of leaky-wave antenna, the width of LWA can be reduced by reducing the value of β/k^B0^B and α/k^B0^B

or the cutoff frequency.

In order to compact the leaky-wave antenna size, the slot elements with the size of G^B1^B×G^B2^B are etched on the ground plane of the conventional LWA. This method of etching slot

elements on the ground plane can change the current distribution on the ground to reduce the frequency of the first higher order mode. Therefore, the radiation angle θ^Bm^B and 3-dB radiation beamwidth Δθ are also varied. Figure 3-7(a) and (b) show the simulated radiation angle and 3-dB radiation beamwidth results with different number of slot elements. The slot elements are 0, 4, 7, and 10 elements, respectively. For the results of Fig. 3-7(a), we can find that the frequency of θ^Bm^B is strongly dependent on the number of the slot elements. As they are increased to 7 elements, the frequency of 22° radiation angle is decreased from 4.15 to 3.33 GHz. Furthermore, the frequency of 22° radiation angle is converted from 3.33 to 3.25 GHz when the number of the slot elements is increased from 7 to 10. In Fig. 3-7(b), the characteristic of shifting to lower frequency of the Δθ is similar to that of the θ^Bm^B. As the cutoff frequency is shifted to lower frequency, the β/k^B0^B and α/k^B0^B has been varied; therefore, the width of LWA is reduced. For conventional LWA, if it is operated at lower frequency, obviously, the width of LWA must be increased. However, using this technique of etched slot elements on the ground plane, the LWA can be operated at lower frequency without increasing the width of LWA. From these simulated results, it can clearly be concluded that the cutoff frequency is decreased about 900 MHz from 4.15 to 3.25 GHz. Therefore, by this technique, we can compact the width of conventional LWA by more than 20 %.

The θ^Bm^B and Δθ are changed because the current distributions are influenced by etching slot elements on the ground plane. The simulated surface current distributions of the

conventional LWA and the LWA with 10 etched slot elements on the ground at 4.2 GHz are illustrated in Fig. 3-8(a) and Fig. 3-8(b). Comparing the surface current distributions on the LWA of Fig. 3-8(a) with that of Fig. 3-8(b), it can be found that the wavelength on the LWA is different. The LWA with 10 etched slot elements on the ground is less than half of the wavelength of the conventional LWA. Since the current distributions of ground plane are affected by the slot elements, the wavelength on the LWA is decreased. This phenomenon is explained that the fast wave (β < k^B0^B) of the conventional LWA is changed to the slow wave (β

> k^B0^B) by etching the slot elements on the ground at 4.2 GHz. The cutoff frequency and the radiation region are shifted to the lower frequency; therefore, the width of LWA is reduced.

L

Slot-A S

S

S

Slot-B

S

G

G

L

D

Tapered LWA

Ground Plane

Slot Elements Z

X

Y Top-view

Back-view Z

X

Y

Fig. 3-4. Configuration of the proposed leaky-wave antenna.

TABLE 3-1

Width of Section 1 15.0 mm Length of Section 1 15.0 mm Width of Section 2 14.5 mm Length of Section 2 20.0 mm Width of Section 3 14.0 mm Length of Section 3 20.0 mm Width of Section 4 13.3 mm Length of Section 4 20.0 mm Width of Section 5 11.8 mm Length of Section 5 25.0 mm

0

Fig. 3-5. Normalized complex propagation constants of the conventional microstrip LWA.

H = 1.6 mm, W = 15 mm, and εr = 4.4. k0 is the free space wave number.

0

Fig. 3-6. Comparison of the theoretical, simulated, and measured θm and Δθ of a conventional LWA: (a) Radiation angle θm; (b) Radiation beamwidth Δθ.

0

Fig. 3-7. Simulated radiation angle and 3-dB radiation beamwidth of LWA with etched slot elements: (a) Radiation angle θm; (b) Radiation beamwidth Δθ.

(a)

(b)

Fig. 3-8. Simulated surface current distributions at 4.2 GHz: (a) conventional LWA; (b) LWA with 10 slot elements.

Top-view

Back-view

Top-view

Back-view