**7. Design of tapered LWA**

64 Wireless Communications and Networks – Recent Advances

Fig. 16. Possible integration paths C . The three different are denoted as*C*0 for the real-axis path (bound mode solution), *C*1 for the path that detours around only the spectral dyadic Green's function poles (surface-wave leaky modes solution), and *C*2 for the path that also

Nowdays, some applications especially with regard to communication applications like the indoor wireless LAN(WLAN) actually are increasing the use of millimeterwave antennas like leaky-wave antennas (LWA), suited for more purpose. In detail, the transmitting/ receiving antennas with relatively broadbeam and broadband can be obtained from the curved and tapered leakywave structures. In fact, the microstrips (LWA), are very popular and widely used in applications thanks to their advantages of low-profile, easy matching, narrow beamwidth, fabrication simplicity, and frequency/electrical scanning capability. Is well know that the radiation mechanism of the higher order mode on microstrip LWAs is attributed to a traveling wave instead of the standing wave as in patch antennas. Moreover the symmetry of the structure along this physical grounding structure, thanks to the image theory, allows to design only half of an antenna with the same property of one in its entirety, and reducing up to 60% the antenna's dimensions. Using this tapered antenna we can obtained a quasi linear variations of the phase normalized constant and than a quasi linear variations of the its radiation angle. Moreover the profile of the longitudinal edges of the LWA, was designed, by means of the reciprocal slope of the cutoff curve, symmetrically

Nevertheless the variation of the cross section of the antenna, allowing a non-parallel emitted rays, such as happens in a non-tapered LWA. In fact, using the alternative geometrical optics approach proposed in the tapering of the LWA, for a fixed frequency, involves the variation of the phase constant *β* and the attenuation constant *α*, obtained as a cut plane of 3D dispersion surface plot varying width and frequency. We can be determined a corresponding beam radiation interval with respect to endfire direction. As mentioned previously, for a tapered antenna with a curve profile (square root law profile) the radiation angle in the leaky regions, vary quasi linearly whit the longitudinal dimension, so it is possible to calculate the radiation angle of the antenna as a average of the phase constant

passes around the branch points (space-wave leaky modes solution).

to the centerline of the antenna, allows a liner started of leaky region.

**6. Tapered leaky wave antennas** 

using the simple formula.

The radiation mechanism of the higher order mode on microstrip LWAs is attributed to a traveling wave instead of the standing wave as in patch antennas [13,20].

We can explain the character of microstrip LWAs trough the complex propagation constant *k j* , where is the phase constant of the first higher mode, and is the leakage constant. Above the cutoff frequency, where the phase constant equals the attenuation constant (*c* = *<sup>c</sup>* ), it is possible to observe three different propagation regions: bound wave, surface wave and leaky wave.

The main-beam radiation angle of LWA can be approximated by:

$$\theta = \cos^{-1}\left(\frac{\beta}{K\_0}\right) \tag{16}$$

where is the angle measured from the endfire direction and *K*0 is the free space wavenumber. According to (16) we can observe that the leaky mode leaks away in the form of space wave when *K*<sup>0</sup> , therefore we can define the radiation leaky region, from the cutoff frequency to the frequency at which the phase constant equals the free-space wavenumber 0 ( ) *K* . An example of tapered LWA was proposed in [21-22], using an appropriate curve design to taper LWA.

In fact through the dispersion characteristic equation, evaluated with FDTD code, we can obtain the radiation region of the leaky waves indicated in the more useful way for the design of our antenna:

$$\frac{c}{2w\_{eff}\sqrt{\varepsilon\_r}} = f\_c < f < \frac{f\_c\sqrt{\varepsilon\_r}}{\sqrt{\varepsilon\_r - 1}} \ . \tag{17}$$

From equation (17) we can observe that the cutoff frequency increases when the width of the antenna decrease, shift toward high frequencies, the beginning of the radiation region as shown in Fig. 17. 1.

Therefore it is possible to design a multisection microstrip antenna [as Type I antenna in Fig. 17.a], in which each section able to radiate at a desired frequency range, can be superimposed, obtaining an antenna with the bandwidth more than an uniform microstrip antenna. In this way every infinitesimal section of the multisection LWA obtained overlapping different section should be into bound region, radiation region or reactive region, permitting the power, to uniformly radiated at different frequencies.

Using the same start width and substrate of Menzel travelling microstrip antenna (TMA) [13], and total length of 120 mm., we have started the iterative procedure mentioned in [23] to obtain the number, the width and the length of each microstrip section. From Menzel TMA width, we have calculated the *START f* (onset cutoff frequency) of the curve tapered LWA, than, choosing the survival power ratio ( <sup>2</sup> *i i <sup>L</sup> e* ) opportunely, at the end of the first section, we have obtained the length of this section. The cutoff frequency of subsequent section ( *<sup>i</sup> f* ), was determined by FDTD code, while the length of this section was determined, repeating the process described previously. This iterative procedure was repeated, until the upper cutoff frequency of the last microstrip section.

Fig. 17.1 Cutoff frequency of multisection microstrip LWA.

The presence of ripples in return loss curve and the presence of spurious sidelobes shows the impedence mismatch and discontinuity effect of this multisection LWA that reduce the bandwidth. A simple way to reducing these effects is to design a tapered antenna in which the begin and the end respectively of the first and the last sections are linearly connected together (as the Type II antenna in Fig. 17.a).

Alternatively the ours idea was to design a LWA using a physical grounding structure along the length of the antenna, with the same contour of the cutoff phase constant or attenuation constant curve (*c* = *<sup>c</sup>* ), obtained varying the frequency (the cutoff frequency *fc* is the frequency at which*c* = *<sup>c</sup>* ) , for different width and length of each microstrip section as shown in Fig. 17.1, employing the following simple equation (18):

$$
\beta\_c = c\_1 f^2 + c\_2 f + c\_3 \tag{18}
$$

obtained from linear polynomials interpolation, where 1*c* = 0.0016, 2*c* = 0.03, 3*c* = -15.56.

The antenna layout (as the Type III antenna in Fig. 17.a), was optimized through an 3D electromagnetic simulator, and the return loss and the radiation pattern was compared with Type I antenna and Type II antenna.
