# `Slotted Waveguide Antennas`

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 The most common slotted waveguide resembles that shown in Figure 1: Figure 1. Geometry of the most common slotted waveguide antenna. The front end (the open face at the y=0 in the x-z plane) is where the antenna is fed. The far end is usually shorted (enclosed in metal). The waveguide may be excited by a short dipole (as seen on the cavity-backed slot antenna) page, or by another waveguide. To begin to analyze the antenna of Figure 1, lets view the circuit model. The waveguide itself acts as a transmission line, and the slots in the waveguide can be viewed as parallel (shunt) admittances. The end of the waveguide is short circuited, so a rough circuit model of Figure 1 is: Figure 2. Circuit model of slotted waveguide antenna. The last slot is a distance d from the end (which is short-circuited, as seen in Figure 2), and the slot elements are spaced a distance L from each other. Before we discuss choosing the sizes, they will be given in terms of the guide-wavelength, which is the wavelength within the waveguide. The guide wavelength () is a function of the width of the waveguide (a) and the free space wavelength. For the dominant TE01 mode, the guide wavelength is given by: The distance between the last slot and the end d is often chosen to be a quarter-wavelength. Transmission line theory states that the impedance of a short circuit a quarter-wavelength down a transmission line is an open circuit. Hence, Figure 2 then reduces to: Figure 3. Circuit model of slotted waveguide using quarter-wavelength transformation. If the parameter L is chosen to be a half-wavelength, then the input impedance of Z Ohms viewed a half-wavelength away is Z Ohms. L is designed to be about a half-wavelength for this reason. If the waveguide slot antenna is designed in this manner, then all of the slots can be viewed as being in parallel. Hence, the input admittance and input impedance for an N element slotted array can be quickly calculated: The input impedance of the waveguide is a function of the slot impedance. Note that the above design parameters are only valid at a single frequency. As the frequency departs from where the waveguide was designed to work, there will be degradation in the performance of the antenna. To give an idea of the frequency characteristics of a slotted waveguide, a sample measurement of S11 as a function of frequency will be shown. The waveguide is designed to operate at 10 GHz. It is fed by a coaxial feed at the bottom as shown in Figure 4. Figure 4. Slotted waveguide antenna fed by a coaxial feed. The resulting S-parameter graph is shown in the following figure. Note that the antenna has a very large drop in S11 around 10 GHz. This indicates that most of the power is radiated away at this frequency. The bandwidth of the antenna (if defined as where S11 is less than -6 dB) extends from about 9.7 GHz to 10.5 GHz, giving a Fractional Bandwidth of 8%. Note that there is also a resonance at about 6.7 and 9.2 GHz. Below 6.5 GHz, the waveguide is below the cutoff frequency and virtually no energy is radiated. The S-parameter graph shown above gives a good idea of what the bandwidth and frequency characteristics of a slotted waveguide will resemble. The 3D radiation pattern for the slotted waveguide is shown in the following figure (it was calculated using a numerical electromagnetics package called FEKO). The antenna gain is approximately 17 dB. Note that in the x-z plane (or h-plane), the beamwidth is very narrow (2-5 degrees). In the y-z plane (or e-plane), the beamwidth is much larger. Obtaining a more pencil-type beam using slotted waveguides is discussed in the next section.

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