**4. Design procedure and parametric study**

In this section the impact of the bend angle, *ϕ*, length of the flat top, *L*f, size of the ground plane, *L*g, height, *h*, and the permittivity of the substrate, *ε*r are analyzed to

*Three-Dimensional Microstrip Antennas for Uniform Phase Response or Wide-Angular Coverage… DOI: http://dx.doi.org/10.5772/intechopen.108338*

**Figure 8.** *Structural variations: Lf = 10, 30, and 50 mm; Lg = 85, 100, and 120 mm.*

evaluate their effects on the phase response, phase center, pattern coverage, gain, Half-Power-Beamwidths (HPBW), and polarization as compared to the equivalent FMA. The design process is complicated since several interacting parameters must be individually considered to meet the design objectives of the applications considered in this Chapter.

**Figure 8** depicts the downward DMA configurations selected to perform the parametric study. A square patch is placed on three grounded substrates, *L*s = 85, 100, and 120 mm. The substrates are bent at three positions in the center resulting square tops with dimensions of *L*f = 10, 30, and 50 mm as shown in **Figure 8**. Three substrates have been considered with *ε*r = 2.2, 4.2, and 10.

#### **4.1 Phase response**

Some GSP antenna designs have been reported in the literature [2–9, 16, 17]. However, a close scrutiny of the literature revealed that the design focused mainly on the amplitude of the radiation patterns, expressed in terms of the realized gain. On the other hand, the phase response and phase center have been reported in [23] for a flat microstrip antenna installed on a metallic choke ring. It should be noted that depending on the angle of arrival of the satellite signals, the GPS antenna far-field phase response introduces phase distortion effect, hence, the phase response must be taken into consideration to accommodate sub-centimeter positioning accuracy.

To quantitatively assess the phase performance of the DMAs, the measured phase response is matched to an ideal hemisphere using a 5° × 5° grid with equal solid angle

#### **Figure 9.**

*Phase response for different bend angles, Lg = 100 mm, Lf = 30 mm, εr = 4.2.*

weighting. The phase center is next obtained by adjusting the center of the hemisphere by minimizing the RMS error between the 3-D measured and the theoretical hemispherical phase response pattern. The terms, "phase residual" or "phase error" are used to denote the difference between the measured and ideal phase in the 3-D far-field region. As a Figure-of-Merit, the RMS value of the phase error to characterize the stability of the phase center of the antennas introduced in this Chapter.

Elevation cuts of the phase pattern are presented in **Figure 9** for five downward DMAs with *L*g = 100 mm, *L*f = 30 mm, and *ε*r = 4.2. As shown in **Figure 9**, a noticeable improvement is seen in the below-horizon phase response for bend angles below 60°. As shown in **Figure 10**, it is clear that the phase response of the far-field patterns exhibits small variations above the horizon for bend angles ranging from 15° to 30°. Moreover, the RMS error in the upper hemisphere, as shown in **Figure 10**, shows little

**Figure 10.** *RMS phase error using three ground planes, εr = 4.2.*

*Three-Dimensional Microstrip Antennas for Uniform Phase Response or Wide-Angular Coverage… DOI: http://dx.doi.org/10.5772/intechopen.108338*

variations with bend angle or ground plane size. Hence, the antennas proposed in this Chapter provide uniform phase response and stable phase center over the entire upper hemisphere when constructed with a downward scheme for bend angles between 15° and 30°. These antennas are hence suitable for precise geodetic positioning since the phase difference of the antenna outputs corresponding to different view angles is uniform which will lead to reduced positioning errors.

### **4.2 Radiation patterns**

The measured far-field radiation patterns are measured at the resonant frequency of the GPS L1 band inside an anechoic chamber. A sequence of the normalized patterns is presented in **Figure 11** for the *E*θ component in the *E*-plane to illustrate the range of coverage patterns that could be achieved by varying *ϕ*, *L*f, and *L*g. **Figure 11** clearly demonstrates broader beam coverage for *ϕ>*30° and the wide range of fields of view that can be achieved in comparison to the FMA counterparts. As expected,

#### **Figure 11.**

*Elevation patterns versus the droop angle, ϕ (a) Lg = 85 mm, (b) Lg = 100 mm, and (c) Lg = 120 mm. E<sup>θ</sup> component, Lf = 30 mm, εr = 2.2, h = 1.5 mm. All patterns are normalized to 0 dB maximum, 10 dB/division.*

#### **Figure 12.**

*Gain and HPBW for the U3DMAs versus bend angle, Lf = 10 mm, Lg = 85, 100, and 120 mm, εr = 2.2, 4.2, and 10 the near-horizon gain roll off is-3.7 dB.*

larger bend angles on small flat tops enhance coverage due to diffraction to the extent that the main lobe appears 180° from broadside when *ϕ* = 90°.

Among the three flat tops considered, results are displayed for the gain and HPBW for the case of *L*f = 10 mm since it provided the best performance in terms of low-elevation angle coverage. **Figure 12** shows the results for the three ground planes

**Figure 13.** *Measured and simulated HPBW of an adjustable upward DMA.*

*Three-Dimensional Microstrip Antennas for Uniform Phase Response or Wide-Angular Coverage… DOI: http://dx.doi.org/10.5772/intechopen.108338*

and substrates under consideration. For bend angles up to 30°, the pattern coverage is found to be not significantly different from the equivalent FMA, particularly for the larger ground planes and substrates with low *ε*r. It is interesting to note that an increase of 40% is observed in the HPBW with respect to the equivalent FMA for the *ε*r = 4.2 substrate with *L*f = 10 mm, *ϕ* = 45°, and *L*g = 85 mm where the bore sight gain is 3.4 dB, and the near-horizon gain roll-off is −3.7 dB.

Next, the bore sight gain and HPBW are considered for the upward DMA. Simulations conducted for three bend locations: *L*f = 10, 30, 50 mm; three substrates with *ε*r = 2.2, 4.2, 10; and three ground planes, *L*g = 85, 100, 120 mm. Compared to the equivalent flat case, the U3DMA geometries considered provided a noticeable beam broadening at bend angles greater than 60° with up to a 60% increase in the HPBW as compared to the equivalent FMA.

To verify the simulation results, a U3DMA prototype with adjustable bend plates is constructed and tested to experimentally verify the results provided by our simulation model. No additional modifications to the topology of the antenna are made as *ϕ*

**Figure 14.** *Polarization ratio for two different substrates, Lg = 100 mm, and five downward bend angles: (a) εr = 4.2, (b) εr = 2.2.*

**Figure 15.** *Axial ratio for different upward bend angles, Lg = 100 mm, εr = 2.2.*

changes. As can be observed from **Figure 13**, a good agreement is observed between simulated and measured HPBWs.

#### **4.3 Circular polarization purity**

In this subsection, the polarization performance of the proposed antenna structures is investigated. The polarization performance near the horizon as shown in **Figure 14** is degraded with reference to the flat microstrip structure. As is the case for traditional flat microstrip antennas, the proposed antennas are not capable of rejecting multipath signals arising from reflection, diffraction, and scattering.

Similarly, the polarization ratio for the upward structures is shown in **Figure 15**. It is clear that the AR is better near the horizon when compared to downward bending. Below the horizon, the downward bending shows better performance. It can be concluded that in both cases, drooping the antenna increases the cross-polarization level near the horizon.
