From the magnitude of the current and the voltage, we can determine that the impedance is minimum (theoretically zero ) in the center of the patch and maximum (typically a couple hundred ) near the edges. This means that there are two points where the impedance is 50 somewhere along the resonant length (x) axis of the element and this is where you would typically connect to the antenna.
The possibility to connect to the patch at other impedance points is quite useful and impedances up to 200 Ω are common. For example, a two element array can be fed with a simple parallel feed by matching the individual patch elements to 100 Ω and connecting them in parallel results in 50 Ω end impedance without the need for impedance transformers. The same woks for a 4 element array with the elements connected at their 200 Ω point.
If you wanted to connect to the edge of the patch and were looking for a specific impedance, you could modify the width of the patch to yield the impedance your are looking for. Increasing the width decreases the impedance.
Fundamental Specifications Of Patch Antennas
Radiation Pattern
A patch antenna radiates power in certain directions and we say that the antenna has directivity (usually expressed in dBi). If the antenna had a 100% radiation efficiency, all directivity would be converted to gain. Typical half wave patches have efficiencies well above 90%.
The directivity of a patch can be estimated quite easily:
The radiating edges of a patch can be seen as two radiating slots placed above a ground- plane and, assuming all radiation occurs in one half of the hemisphere (on the patch side of the ground), we get a 3 dB directivity increase. This would be an antenna with a perfect front-to-back ratio where all radiation occurs towards the front and no radiation towards the back. This front-to-back ratio is highly dependent on ground-plane size and shape in real life.
Another 3 dB can be added because there are 2 slots. The length of these slots typically equals the impedance width (length in the y-axis) of the patch and the width of these slots equals the substrate height. These slots typically have a directivity of 2 to 3 dB compared to an isotropic radiator and behave like a dipole.
All of this results in a total maximum directivity of 8 to 9 dBi.
The rectangular patch excited in its fundamental mode has a maximum directivity in the direction perpendicular to the patch (z-axis or broadside). The directivity decreases when moving away from broadside towards lower elevations. The 3 dB beamwidth is the width
at which the gain of the beam decreases by 3 dB relative to the gain in broadside to either side of the main beam.
Figure 4 shows a typical radiation pattern for a square, half wave patch.