**2. Antenna array design**

Considering only the two current VHF frequency ranges of the openly TV in Mexico, we chose as operation frequency to 71 MHz for the design of the rectangular patch antenna, which will be used as the base of the prototype patch antenna array. This frequency corresponds to the central frequency of the first sub-range of frequency of VHF. The rectangular antenna was designed using the well-known equations (Balanis, 2005 and Garg et al., 2001):

For the patch width:

$$\mathcal{W} = \frac{c}{2f\_0\sqrt{\frac{\varepsilon\_r + 1}{2}}} \tag{1}$$

Low Cost Prototype of an Outdoor Dual Patch Antenna

Table 2. Sizes of the individual patch antenna.

they are established by FEKO program) .

Table 4. The rectangular antenna array sizes (in meters).

Fig. 2. Geometry of the rectangular patch antenna array.

edge of the cuts is also given by *λg/8*, as in the case of the single antenna.

Array for the Openly TV Frequency Ranges in Mexico 229

The wave group of length *λg* determines to the Length edge (*Le*, in Figure 1) of the cuts. *Le*

With the reduced sizes, the antenna array has been designed using a superposition of two rectangular patches, as it can be seen in Figure 2. Some adjustments in length were required in order to locate both central frequencies of the VHF TV channels transmission, with a minimal error (a shift of 0.14% in 71 MHz and of 0.1% in 195 MHz). As it can be noted, the orthogonal lengths have the same length (*W=L+L1*), as it is desirable for dual polarized antennas (Smith, 2008). The sizes of the rectangular antenna array are given in Table 4.

Patch antenna array sizes (m)

Feed point location (m)

Table 3. Feed point location of the individual patch antenna(coordinates are considered as

Sizes W L W1 L1 W2 Patch 0.167 0.132 0.017 0.035 0.127 Substrate 0.176 0.142 0.027 0.045 0.1366

Cuts on the array were also implemented in order to increase the corresponding gain. The sizes of the array with the cuts implemented on its corner are given in Table 5. The length

Wp 0.1272564 Lp 0.1621136

X 0.065 Y -0.04

has a value of *λg/8* (see Figure 1), which in this case is of 0.0161184 m. .

where *c* is the constant speed of light in vacuum, ε*<sup>r</sup>*, the dielectric constant substrate and *f0*, the operating frequency equal to 71 MHz.

The effective dielectric constant:

$$
\varepsilon\_{reff} = \frac{\varepsilon\_r + 1}{2} + \frac{\varepsilon\_r - 1}{2} \left( 1 + 12 \frac{h}{W} \right)^{-1/2} \text{ if } \frac{W}{h} > 1 \tag{2}
$$

The effective length is calculated using:

$$L\_{eff} = \frac{c}{2f\_0 \sqrt{\varepsilon\_{ref}}} \tag{3}$$

The two increments in the length, which are generated by the fringing fields, make electrical length slightly larger than the physical length of the patch:

$$\Delta L = 0.412h \frac{\left(\varepsilon\_{reff} + 0.3\right) \left(\frac{W}{h} + 0.264\right)}{\left(\varepsilon\_{reff} - 0.258\right) \left(\frac{W}{h} + 0.8\right)}\tag{4}$$

The patch length is given by:

$$\text{mL} = \text{L}\_{\text{eff}} - \text{2\Delta L} \tag{5}$$

The length and width of ground plane (and the substrate), are given by:

$$L\_{\mathcal{R}} = \mathfrak{G}h + L \quad \text{and} \quad \mathcal{V}l\_{\mathcal{R}} = \mathfrak{G}h + \mathcal{V}\mathcal{V} \tag{6}$$

The rectangular patch designed at 71 MHz is shown in Figure 1, considering a reduction factor of 8, required to decrease the patch and substrate sizes. The sizes of the patch are given in Table 2 and the feed point location in Table 3. FR-4 was used as substrate; it has a height of 0.0016 m and a dielectric permittivity of 4.2.

Fig. 1. Single rectangular patch antenna.

1 2 1 1 1 12

<sup>−</sup> + − =+ + if 1 *<sup>W</sup>*

> 2 *<sup>c</sup> Leff fo reff*

*reff <sup>h</sup> L h <sup>W</sup>*

ε

ε

The two increments in the length, which are generated by the fringing fields, make electrical

⎜ ⎟ ⎝ ⎠

ε

*reff h*

The rectangular patch designed at 71 MHz is shown in Figure 1, considering a reduction factor of 8, required to decrease the patch and substrate sizes. The sizes of the patch are given in Table 2 and the feed point location in Table 3. FR-4 was used as substrate; it has a

0.3 0.264

*W*

⎛ ⎞⎛ ⎞ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

+ +

⎛ ⎞⎛ ⎞ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

− +

0.258 0.8

*r r h reff W*

2 2

 ε

⎛ ⎞

ε

length slightly larger than the physical length of the patch:

Δ =

height of 0.0016 m and a dielectric permittivity of 4.2.

Fig. 1. Single rectangular patch antenna.

0.412

The length and width of ground plane (and the substrate), are given by:

ε

*<sup>r</sup>*, the dielectric constant substrate and *f0*,

> (2)

(4)

*h*

<sup>=</sup> (3)

*LL L* <sup>2</sup> *eff* = −Δ (5)

*L hL g* = + 6 and *W hW g* = + 6 (6)

where *c* is the constant speed of light in vacuum,

the operating frequency equal to 71 MHz.

ε

The effective length is calculated using:

The effective dielectric constant:

The patch length is given by:

The wave group of length *λg* determines to the Length edge (*Le*, in Figure 1) of the cuts. *Le* has a value of *λg/8* (see Figure 1), which in this case is of 0.0161184 m. .

With the reduced sizes, the antenna array has been designed using a superposition of two rectangular patches, as it can be seen in Figure 2. Some adjustments in length were required in order to locate both central frequencies of the VHF TV channels transmission, with a minimal error (a shift of 0.14% in 71 MHz and of 0.1% in 195 MHz). As it can be noted, the orthogonal lengths have the same length (*W=L+L1*), as it is desirable for dual polarized antennas (Smith, 2008). The sizes of the rectangular antenna array are given in Table 4.


Table 2. Sizes of the individual patch antenna.


Table 3. Feed point location of the individual patch antenna(coordinates are considered as they are established by FEKO program) .


Table 4. The rectangular antenna array sizes (in meters).

Fig. 2. Geometry of the rectangular patch antenna array.

Cuts on the array were also implemented in order to increase the corresponding gain. The sizes of the array with the cuts implemented on its corner are given in Table 5. The length edge of the cuts is also given by *λg/8*, as in the case of the single antenna.

Low Cost Prototype of an Outdoor Dual Patch Antenna

the T geometry to realize the prototype.

Fig. 6. Components of the electrical Far Field.

maxima on both directions.

**3. Simulation results** 

MHz.

Array for the Openly TV Frequency Ranges in Mexico 231

For Figure 4(a), the high return loss were obtained (bigger than -5dB), and for (b) the operation frequencies were so far from one to each other. These were the reasons to choose

The 3D far electrical field magnitude patterns as a function of frequency are shown in Figure

(a) (b)

Fig. 5. Radiation pattern of the far electrical field magnitude at (a) 70.98 MHz and (b) 194.8

As it can be observed from Figure 5a, the radiation pattern at 70.98 MHz, corresponds to an omnidireccional antenna, with horizontal polarization, while in Figure 5b, the radiation pattern at 194.8 MHz corresponds to a directive antenna directed on the X-axis, with

5. The electrical far field components, in polar coordinates are shown in Figure 6.


Table 5. Sizes of the patch antenna array with cuts.

Fig. 3. Geometry of the antenna array (T shape), with cuts on its corners.

The feed point and shorting pin location are shown in Figure 3 and its coordinates in Table 6.


Table 6. The feed point and shorting pin location.

Before to obtain the geometry shown in Figure 3, other two geometries were realized (Figure 4), but there were some problems in each one.

Fig. 4. First geometries implemented (L shape) and (b) irregular cuts.

For Figure 4(a), the high return loss were obtained (bigger than -5dB), and for (b) the operation frequencies were so far from one to each other. These were the reasons to choose the T geometry to realize the prototype.
