Documentation

## Polarization Analysis for an X-band Microstrip Patch Antenna

In it's most basic form, a microstrip patch antenna consists of a radiating patch on one side of a dielectric substrate and a ground plane on the other side. Microstrip patch antennas radiate primarily as wide open-open half-wave microstrip resonators. The length L of the rectangular patch for the fundamental excitation mode is slightly less than $\lambda$/2. For a good antenna performance, a thick dielectric substrate having a low dielectric constant is usually desired since it provides a larger bandwidth and a well-defined beam. A rectangular microstrip patch antenna normally radiates a linearly polarized wave with about 6-7 dBi gain at broadside. Higher gains (up to 10 dBi) can be achieved by using different means including large patch heights and parasitic patches.

### Patch Antenna

This example discusses a microstrip patch antenna using the air substrate. The dimensions are chosen from [1] for the center frequency of 10.35 GHz.

```freq = 10.35e9; patchLength = 12e-3; patchWidth = 17.73e-3; patchHeight = 1.56e-3; lengthgp = 55e-3; widthgp = 55e-3; feedoffset = [2.9e-3 0];```

### Create the Antenna

The parameters defined above are used to create the microstrip patch antenna.

```ant = patchMicrostrip('Length', patchLength, 'Width', patchWidth, ... 'Height', patchHeight, 'GroundPlaneLength', lengthgp, ... 'GroundPlaneWidth', widthgp, 'FeedOffset', feedoffset); figure; show(ant);```

### Co-Polarization Pattern in the H-plane

The plane, which contain the electric-field vector and the direction of maximum radiation, is known as the E-plane [2] for linearly-polarized antennas. The E-plane is the xz-plane in the present case it is determined by the feed shift in the x-direction, but has generally nothing in common with the relative patch dimensions in the figure. The plane, which contains the magnetic-field vector and the direction of maximum radiation, is known as the H-plane for linearly-polarized antennas. The H-plane in the present case is the yz-plane. Co-polarization is the intended antenna polarization. In the H-plane, the intended polarization is the electric-field component in the x- direction (which coincides with azimuthal component). The plot given below shows the directivity of this azimuthal component in the H-plane (the co-polarization radiation pattern). As expected, the co-polarization pattern drops sharply close to the ground plane, which reflects the boundary condition of no tangential field on the metal ground plane.

```pattern(ant, freq, 90, 0:1:180, 'CoordinateSystem', 'rectangular', ... 'Polarization', 'H');```

### Cross-Polarization Pattern in the H-plane

Cross-polarization is the undesired antenna polarization. Cross polarized electric-field component is perpendicular to the co-polarized component. In the H-plane, the cross-polarization is given by the combined electric-field components in the y- and z-directions, which is the elevation electric-field component. The difference between the co- and cross-polarizations is called the polarization isolation. The plot given below shows the directivity of the cross-polarized E-field in the H-plane (cross-polarization radiation pattern). As expected, there is a null at zenith.

```pattern(ant, freq, 90, 0:1:180, 'CoordinateSystem', 'rectangular', ... 'Polarization', 'V');```

### Co-Polarization Pattern in the E-plane

In the E-plane, the intended polarization is given by the combined electric-field components in the x- and z-directions, which is the elevation electric-field component. The plot given below shows the directivity of the co-polarized E-field in the E-plane (co-polarization radiation pattern). As expected, the pattern is not symmetric due to the feed effect.

```pattern(ant, freq, 0, 0:1:180, 'CoordinateSystem', 'rectangular', ... 'Polarization', 'V');```

### Cross-Polarization Pattern in the E-plane

In the E-plane, the cross-polarization is given by the electric-field component in the y-direction, which is the azimuthal electric-field component. The plot given below shows the directivity of the cross-polarized E-field in the E-plane (cross-polarization radiation pattern). As expected, the pattern indicates a very low cross-polarization.

```pattern(ant, freq, 0, 0:1:180, 'CoordinateSystem', 'rectangular', ... 'Polarization', 'H');```

### Comparison with Ref. [1]

The overall behavior of the antenna matches well with the results published in [1].

### Reference

[1] D. Guha, S. Chattopadhya, J. Y. Siddiqui, "Estimation of gain enhancement replacing PTFE by air substrate in a microstrip patch antenna [Antenna Designer's Notebook]," IEEE Antennas and Propagation Magazine, vol.52, no.3, pp.92-95, June 2010.

[2] C. A. Balanis, 'Antenna Theory. Analysis and Design,' p.33, Wiley, New York, 3rd Edition, 2005.

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