## Tuesday, January 24, 2012

### Microstrip (Patch) Antennas

Introduction to Patch Antennas

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board. Microstrip antennas are becoming very widespread within the mobile phone market. Patch antennas are low cost, have a low profile and are easily fabricated.
Consider the microstrip antenna shown in Figure 1, fed by a microstrip transmission line. The patch antenna, microstrip transmission line and ground plane are made of high conductivity metal (typically copper). The patch is of length L, width W, and sitting on top of a substrate (some dielectric circuit board) of thickness h with permittivity . The thickness of the ground plane or of the microstrip is not critically important. Typically the height h is much smaller than the wavelength of operation, but not much smaller than 0.05 of a wavelength.

(a) Top View of Patch Antenna

(b) Side View of Microstrip Antenna
Figure 1. Geometry of Microstrip (Patch) Antenna.
The frequency of operation of the patch antenna of Figure 1 is determined by the length L. The center frequency will be approximately given by:

The above equation says that the microstrip antenna should have a length equal to one half of a wavelength within the dielectric (substrate) medium.
The width W of the microstrip antenna controls the input impedance. Larger widths also can increase the bandwidth. For a square patch antenna fed in the manner above, the input impedance will be on the order of 300 Ohms. By increasing the width, the impedance can be reduced. However, to decrease the input impedance to 50 Ohms often requires a very wide patch antenna, which takes up a lot of valuable space. The width further controls the radiation pattern. The normalized radiation pattern is approximately given by:

In the above, k is the free-space wavenumber, given by . The magnitude of the fields, given by:

The fields of the microstrip antenna are plotted in Figure 2 for W=L=0.5.

Figure 2. Normalized Radiation Pattern for Microstrip (Patch) Antenna.
The directivity of patch antennas is approximately 5-7 dB. The fields are linearly polarized, and in the horizontal direction when viewing the microstrip antenna as in Figure 1a (we'll see why in the next section). Next we'll consider more aspects involved in Patch (Microstrip) antennas.

# Fringing Fields for Microstrip Antennas

Consider a square patch antenna fed at the end as before in Figure 1a. Assume the substrate is air (or styrofoam, with a permittivity equal to 1), and that L=W=1.5 meters, so that the patch is to resonate at 100 MHz. The height h is taken to be 3 cm. Note that microstrips are usually made for higher frequencies, so that they are much smaller in practice. When matched to a 200 Ohm load, the magnitude of S11 is shown in Figure 3.

Figure 3. Magnitude of S11 versus Frequency for Square Patch Antenna.
Some noteworthy observations are apparent from Figure 3. First, the bandwidth of the patch antenna is very small. Rectangular patch antennas are notoriously narrowband; the bandwidth of rectangular microstrip antennas are typically 3%. Secondly, the microstrip antenna was designed to operate at 100 MHz, but it is resonant at approximately 96 MHz. This shift is due to fringing fields around the antenna, which makes the patch seem longer. Hence, when designing a patch antenna it is typically trimmed by 2-4% to achieve resonance at the desired frequency. The fringing fields around the antenna can help explain why the microstrip antenna radiates. Consider the side view of a patch antenna, shown in Figure 4. Note that since the current at the end of the patch is zero (open circuit end), the current is maximum at the center of the half-wave patch and (theoretically) zero at the beginning of the patch. This low current value at the feed explains in part why the impedance is high when fed at the end (we'll address this again later).
Since the patch antenna can be viewed as an open circuited transmission line, the voltage reflection coefficient will be -1 (see the transmission line tutorial for more information). When this occurs, the voltage and current are out of phase. Hence, at the end of the patch the voltage is at a maximum (say +V volts). At the start of the patch antenna (a half-wavelength away), the voltage must be at minimum (-V Volts). Hence, the fields underneath the patch will resemble that of Figure 4, which roughly displays the fringing of the fields around the edges.

Figure 4. Side view of patch antenna with E-fields shown underneath.