Last edited: 2024-10-28 12:31:13

**The patch antenna is the component used to connect the Transmit Receive Module's amplifiers to free space, allowing for electromagnetic waves to be transferred with minimal losses. For most antennas to work efficiently, however, the radiated electromagnetic energy not only needs to be transmitted but also directed in order to be able to transmit efficiently and over longer distances.**

A single antenna element usually has a wide radiation pattern but for many applications such as for radars, it is necessary to have antennas with a high directivity that can create beams that focus the radiated power. To do this the most common way is to form an array of antenna elements, known as an antenna array. The total radiated field of such an array is determined by how the individual elements' radiation interfere in different directions which results in constructive interference in some directions while others experience destructive interference.

The smallest antenna array possible is a simple two element linear array as the one shown in the figure above consisting of two infinitesimal horizontal dipoles positioned at $\pm d/2$ along the z-axis. Assuming no coupling between the elements the radiated field is given by adding the field of the two individual antenna elements giving

$\mathbf{E}_t = \mathbf{E_1} + \mathbf{E_2} = \hat{\theta}j\eta\frac{kI_0l}{4\pi}\left( \frac{e^{-j[kr_1-(\beta/2)]}}{r_1}\cos{\theta_1} + \frac{e^{-j[kr_2+(\beta/2)]}}{r_2}\cos{\theta_2}\right).$where $\eta$ is the free space impedance, $k$ is the wavenumber, $I_0$ is the current amplitude, $l$ is the length of the dipoles, and $\beta$ is the phase of the signal. With the assumptions that $\theta\simeq\theta_1\simeq\theta_2$, the phase variations $r_1\simeq r-\frac{d}{2}\cos{\theta}$, $r_2\simeq r+\frac{d}{2}\cos{\theta}$ and the amplitude variation $r_1\simeq r_2 \simeq r$ the equation reduces to

$\mathbf{E_t} = \hat{\theta}j\eta\frac{kI_0le^{-jkr}}{4\pi r}\cos{\theta}\cdot\left\{ 2\cos\left[\frac{1}{2}(kd\cos{\theta}+\beta)\right] \right\}.$The last factor within curly brackets is called the array factor (AF). It can be seen by comparing the first and second equations that the radiated field from the array is the product of the radiated field from a single element multiplied by the AF. By varying the separation $d$ and/or the phase $\beta$ the total field of the array can be controlled. Most antennas however have a fixed separation by design and what is left to control is the phase. When controlling the phase for the antenna array it is then called a phased antenna array.

The same principle as for the two element array still applies for arrays when extending it to higher dimensions and adding more elements. Using more elements can get even better directivity allowing for beams that can reach longer. An illustration of the beam angles $(\theta,\varphi)$ in three dimensions can be seen in the figure above where it can be seen that at $\theta = 0$ and $\varphi = 0$ the antenna array is sending radiation straight ahead. To get more accurate results, however, the interaction between the elements, known as mutual coupling, has to be accounted for.

Mutual coupling in an antenna array is a term that is used to describe the interaction between antenna elements. It occurs mainly as a consequence of nearby elements receiving some of the radiated energy but can also occur because of reflections, reradiation, and scattering of electromagnetic radiation. This phenomenon exists for all types of arrays but becomes even more important to account for when working with large arrays. What happens is that when an element is excited by a current, the surrounding antenna elements will receive some of the energy leading to changes in their own respective excitation. This sums up to a total change in the excitation for all elements which will change the characteristics of the antenna seen from the driving source. One key factor is that the antenna's terminal impedance, as seen by the source, changes which might cause an impedance mismatch resulting in a decrease in radiated energy. While designing an antenna array the coupling is accounted for and the antenna array is typically impedance matched for a beam angle straight ahead. To assess the beamforming capability, however, all angles of interest have to be evaluated since the coupling tends to be worse for large beam angles.

A patch antenna is a type of microstrip antenna that is lightweight, easy to manufacture, and commonly used for a variety of applications. It typically consists of three layers; a ground plane, a substrate, and the patch elements. A patch antenna designed on a printed circuit board (PCB) requires a large grounded plane below the antenna elements with the substrate in between. The signal can be fed to the elements in different ways such as through a microstrip feed line or with a coaxial cable with its feed pin going through the substrate and soldered to the patch, the latter being shown in the figure above.

When designing a patch antenna array, lots of different aspects have to be taken into account. For example, the shape of the patch, the type of material, and the dimensions all have significant effects on the antenna array performance.

While the layout of the patch can take different shapes to better suit a specific application, a rectangular patch antenna with probe feeding is shown in the figure above because of its simplicity. This shape has also proven to have better overall characteristics compared to other simple shapes such as triangular and circular patches.

For a large antenna array, most of the antenna elements will behave similarly with the exception of the elements close to the array edge. Therefore a practical way to design an antenna array is to use a unit cell representing one element within an infinite array. Using a unit cell reduces the simulation time and computational complexity significantly. It is a decomposition-based finite element technique for modeling repetitive antenna arrays and can be used because of the similarities of the electromagnetic fields for elements inside a large array.

The figure above shows a hexagonal unit cell of one of the patch antennas in an infinite array. A hexagonal unit cell can fit more elements within the same amount of area compared to a square cell. The element spacing in all three directions is chosen to be half a wavelength ($\lambda/2$). Using $\lambda/2$ spacing of the elements is chosen since it gives a good trade off between directivity and stearability with low risks of grating lobes. Grating lobes are beams that can be created for larger scan angles if the spacing is higher which would cause a decrease in transmitted power in the desired direction.

Depending on the frequency at which the antenna is designed the remaining parameters such as cell width, patch width, feed pin offset, feed pin radius, and the feed pin's teflon thickness for the antenna element can optimized for this single frequency using a finite element analysis software and common measurements from manufacturers.

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