**8. Simulation results**

66 Wireless Communications and Networks – Recent Advances

TMA width, we have calculated the *START f* (onset cutoff frequency) of the curve tapered

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

> 5,94 6,85 8,03 9,51 11,52 Frequency [Ghz]

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

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

<sup>2</sup> *<sup>c</sup>* 1 23

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

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

*<sup>c</sup>* ), obtained varying the frequency (the cutoff frequency *fc* is the

*<sup>c</sup>* ) , for different width and length of each microstrip section as

*cf cf c* (18)

) opportunely, at the end of the

LWA, than, choosing the survival power ratio ( <sup>2</sup> *i i <sup>L</sup> e*

together (as the Type II antenna in Fig. 17.a).

*c* = 

Type I antenna and Type II antenna.

*c* = 

constant curve (

frequency at which

Fig. 17.1 Cutoff frequency of multisection microstrip LWA.

shown in Fig. 17.1, employing the following simple equation (18):

[rad/m]

repeated, until the upper cutoff frequency of the last microstrip section.

An asymmetrical planar 50 Ω feeding line was used to excite the first higher-order mode while a metal wall down the centerline connecting the conductor strip and the ground plate was used to suppress the dominant mode for Type I - III. The chosen substrate had a dielectric constant of 2.32 and a thickness of 0.787 mm, while the total length of the leaky wave antenna was chosen to be 120 mm.

The leaky multisection tapered antenna Type I was open-circuited, with a 15 mm start width, and 8.9 mm of final width obtained according to [23]. For LWA layout Type I, we used four microstrip steps, for layout Type II we tapered the steps linearly, while the curve contour of the LWA layout Type III, was designed through equation (18).

Fig. 17.b shows the simulated return loss of three layouts. We can see that the return loss (S11) of Type I is below -5 dB from 6 to 10.3 GHz, but only three short-range frequencies are below -10 dB. S11 of Type II is below -5 dB from 6.1 to 9.1 GHz, and below -10 dB from 6.8 to 8.6 GHz. At last, S11 of Type III is below -5 dB from 6.8 to 11.8 GHz, and below -10 dB from 8.0 to 11.2 GHz. In Fig.17.c are shows the mainlobe direction at 9.5 GHz for the different Type I to Type III. We can see a reduction of sidelobe and only few degrees of mainlobe variation between Type I to Type III. Moreover, in Fig. 18 is shown the variation of mainlobe of antenna Type III, for different frequency, while in Fig. 19 is shown the trend of gain versus frequency of the same antenna. It is clear that, the peak power gain is more than 12 dBi, which is almost 3 dBi higher than uniform LWAs.

Finally the simulated VSWR is less than 2 between 8.01 and 11.17 GHz (33%), yielding an interesting relative bandwidth of 1.39:1, as shown in Fig. 20, compared with uniform microstrip LWAs (20% for VSWR < 2) as mentioned in [24].

Fig. 17a. Layout of leaky wave antennas Type I-III. A physical grounding structure was used to connecting the conductor strip and the ground plane.

Fig. 17b. Simulated Return loss of Type I-III LWA.

These results indicate a high performance of Type III LWA: high efficiency excitation of the leaky mode, increases of the bandwidth, improves the return loss and reduction of 19% of metallic surface with respect to uniform LWA. Moreover, these results are in a good agreement whit the experimental results of return loss and radiation pattern of a prototype made using a RT/Duroid 5880 substrate with thickness of 0.787 mm and relative dielectric constant of 2.32, as shown in Fig.21 and Fig.22.

Fig. 17b. Simulated Return loss of Type I-III LWA.

constant of 2.32, as shown in Fig.21 and Fig.22.

These results indicate a high performance of Type III LWA: high efficiency excitation of the leaky mode, increases of the bandwidth, improves the return loss and reduction of 19% of metallic surface with respect to uniform LWA. Moreover, these results are in a good agreement whit the experimental results of return loss and radiation pattern of a prototype made using a RT/Duroid 5880 substrate with thickness of 0.787 mm and relative dielectric

Fig. 17c. Radiation patterns of Electric field (H plane) of Type I-III, LWA at 9.5 GHZ.

Fig. 18. a) Simulated radiation patterns of E field of LWA Type III for different frequency. b) 3-D radiation pattern of Electric field.

Fig. 19. The gain versus frequency of the LWA Type III.

a)

Fig. 20. Simulated VSWR of LWA Type III.

Fig. 21. A prototype of tapered LWA Type III with holes made in the centerline of the antenna.

Fig. 22. a) Measurement set-up of LWA Type III. b) Experimental and simulated return loss of LWA Type III.

Fig. 23. A prototype of half tapered LWA.

Fig. 21. A prototype of tapered LWA Type III with holes made in the centerline of the antenna.

a) b) Fig. 22. a) Measurement set-up of LWA Type III. b) Experimental and simulated return loss

Fig. 20. Simulated VSWR of LWA Type III.

of LWA Type III.

Moreover the use of a physical grounding structure along the length of the antenna, as suggested in [21-22], allows the suppression of the dominant mode (the bound mode), the adoption of a simple feeding, and due to the image theory, it is also possible to design only half LWA (see Fig. 23) with the same property of one entire, as shown in Fig. 24 and in Fig. 25, reducing up to 60% the antenna's dimensions compared to uniform LWAs [24].

Fig. 24. Measured return loss of full and half Leaky Wave Antennas

Fig. 25. The measured and simulated radiation patterns of E field of half tapered LWA at 8 GHz.

#### **9. Focusing-diverging property**

As described in [21-22], the profile of the longitudinal edges of the LWA, was designed, by means of the reciprocal slope of the cutoff curve, symmetrically to the centerline of the antenna, allows a liner started of leaky region. 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 as we can see in Fig. 26 and in Fig. 27. Nevertheless the variation of the cross section of the antenna, allowing a non-parallel emitted rays, such as happens in a non-tapered LWA (see Fig. 28). In fact, as was described in the alternative geometrical optics approach proposed in [24] the tapering of the LWA, for a fixed frequency, involves the variation of the phase constant and the attenuation constant , as shown in Fig. 29, obtained as a cut plane of 3D dispersion surface plot varying width and frequency (see Fig. 30).

Fig. 26. The variation of the main beam radiation angle versus length of the antenna, at f= 8 GHz, for linear, square and square root profile of the LWA.

Fig. 27. The variation of the phase constant versus length of the antenna, at f= 8 GHz, for linear, square and square root profile of the LWA.

As described in [21-22], the profile of the longitudinal edges of the LWA, was designed, by means of the reciprocal slope of the cutoff curve, symmetrically to the centerline of the antenna, allows a liner started of leaky region. 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 as we can see in Fig. 26 and in Fig. 27. Nevertheless the variation of the cross section of the antenna, allowing a non-parallel emitted rays, such as happens in a non-tapered LWA (see Fig. 28). In fact, as was described in the alternative geometrical optics approach proposed in [24] the tapering of the LWA, for a fixed frequency, involves the variation of the

Fig. 26. The variation of the main beam radiation angle versus length of the antenna, at f= 8

Fig. 27. The variation of the phase constant versus length of the antenna, at f= 8 GHz, for

, as shown in Fig. 29, obtained as a cut plane

**9. Focusing-diverging property** 

and the attenuation constant

GHz, for linear, square and square root profile of the LWA.

linear, square and square root profile of the LWA.

of 3D dispersion surface plot varying width and frequency (see Fig. 30).

phase constant

From (16) can be determined in the leaky regions of the antenna, a corresponding beam radiation interval [min , max ], , 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 using the simple equation (19).

$$\mathcal{A}\_m = \text{sen}^{-1}\left(-\frac{1}{K\_0 L} \int\_0^L \mathcal{J}(z) dz\right) \tag{19}$$

Alternatively using the geometrical optics it is easy to determine the closed formula to predict the angle of main beam of a tapered LWA. Through simple mathematical passages, the main beam angle *<sup>m</sup>* can be obtained by the equation (20).

$$\mathcal{A}\_m = \text{sen}^{-1}\left(\frac{\text{Asen}\mathcal{B}\_{\text{min}}}{\frac{1}{2}\sqrt{\left(2A\text{sen}\mathcal{B}\_{\text{min}}\right)^2 + \left(L + 2\text{C}\cos\mathcal{B}\_{\text{max}}\right)^2}}\right) \tag{20}$$

Where *A* and *C* are respectively the distance between real focus *F* and the beginning and the end of the length of the antenna *L* . Therefore, if we know the begin width and the end width of the antenna, from the curves of normalized phase and attenuation constant at fixed frequency, we can determine the beam radiation range from (16), and the main beam angle through (20).

Fig. 28. The ray optical model for a tapered Leaky Wave antenna.

Furthermore this focusing phenomena of a tapered LWA can determine a wide-beam pattern in a beam radiation range which is evident when the antenna length is increased ( <sup>0</sup> *L* 50) [25].

Fig. 29. The curve of normalized phase and attenuation constants versus the width, at 8 GHz for the LWA with the angular range [28°, 76°]. The leaky region start from 10.8 mm. (cutoff frequency).

To obtain a broad beam pattern without the use of a longer LWA, we can bend a tapered LWA (see Fig. 31), leading the electromagnetic waves to diverge. This, increases the beam of the radiation pattern and reduce furthermore the back lobes as we can see compared the curves of Fig. 32. Finally in Fig. 33 is shown the measured return loss of half bend LWA Type III.

Fig. 30. The 3D normalized phase constant and attenuation constant of tapered LWA versus frequency and width.

Fig. 29. The curve of normalized phase and attenuation constants versus the width, at 8 GHz for the LWA with the angular range [28°, 76°]. The leaky region start from 10.8 mm. (cutoff

To obtain a broad beam pattern without the use of a longer LWA, we can bend a tapered LWA (see Fig. 31), leading the electromagnetic waves to diverge. This, increases the beam of the radiation pattern and reduce furthermore the back lobes as we can see compared the curves of Fig. 32. Finally in Fig. 33 is shown the measured return loss of half bend LWA

Fig. 30. The 3D normalized phase constant and attenuation constant of tapered LWA versus

frequency).

Type III.

frequency and width.

b)

Fig. 31. a)Layout of a bend tapered LWA. b) A prototype of bend half LWA Type III made using Roger 5880 RT/Duroid.

Fig. 32. a)The radiation patterns of E field of tapered LWA at f= 8 GHz. b) The radiation patterns of E field of bend tapered LWA at f= 8 GHz.

Fig. 33. Experimental return loss of half bend LWA Type III.
