# Phase Center Computation of a Corrugated Horn

Phase center computations are a very sensitive subject and difficult to measure. The location of the phase center depends upon a couple of parameters such as polarization direction, scan angle direction and aperture width. The device modeled in this application is a cylindrical corrugated horn with a linear vertical polarization, depicted in Figure 1.

Figure 1: The CST MWS model showing the excitation direction and the definition of H- and E-Plane

Correct settings are crucial in order to obtain meaningful results. The polarization of the E-field is along the E-plane (vertically orientated). Figure 2 shows the E-phi component in a three-dimensional view. It can be seen that this field component is very well defined along a horizontal scan direction, which is the H-Plane in this case. The phase center settings in CST MICROWAVE STUDIO® (CST MWS) are thus applied accordingly as shown on the left hand side of the Figure 2. Alternatively, if the E-Plane scan is selected, the E-theta component has to be selected. Note, that the phase centers for E-plane and H-plane scan generally differ....

Figure 2: Field and H-plane scan direction settings

In the farfield postprocessing of CST MWS the phase can be plotted either in 3D or along a certain path. The power of the phase-center computation is based on the fact that the origin of the farfield computation can be modified. This feature is used to adjust and/or position the center of the farfield at the location of the computed phase center. In this case, the phase variation shows a rather flat phase regime for a certain aperture angle. In Figure 3 the farfield center is repositioned for three different locations, first, at the phase center and second, +/-5% of the total horn length repositioned on the propagation z-axis.

Figure 3: Three locations are defined for further recording of the phase variation

Figure 4 shows the 3D phase plot of the E-field for the various positions according to the positions given in Figure 3. The center plot of Figure 4 shows the least phase variation along the horizontal scan direction. A better representation of the phase variation is shown in Figure 5 in which the phase is recorded along the H-Plane. The slope of the phase is used as an indicator regarding the repositioning of the phase-center in the simulation and/or repositioning of the antenna itself in the real measurement setup.

Figure 4: From left to right: Phase center shifted by +5%, at center and -5% away from the optimal phase center

Figure 5: Phase variation along the H-Plane

The position of the phase center varies according to the aperture angle considered. For smaller apertures the variation is rather small as shown in Figure 6. Note, that in general, the phase center for H-plane and E-plane evaluations differ. The standard deviation is another criteria to estimate the accuracy of the phase center computation, depicted in Figure 7.

Figure 6: Movement of the phase center as a function of the considered aperture angle

Figure 7: Smaller aperture angle result in smaller standard deviations

Comparison to measurement: The measurements were carried out by Kathrein KG, Rosenheim, Germany. At two different frequencies, +/-2% offset from center frequency, the phase center was measured; polarization was in the E-plane. The antenna is rotated in the H-plane (azimutal) thereby recording magnitude and phase of the fields. Depending on the phase-slope versus scan angle the antenna is slightly repositioned along its propagation axis and measured again until a flat phase was found. Figure 8 shows the actual position of the phase center and figure 9 a close-up look at deviation between measurement and simulation in terms of center frequency wavelengths. (Measurement data with courtesy and permission of Kathrein KG, Rosenheim, Germany). The results are in very good agreement with measurements.

Figure 8: Actual phase center postion of the corrugated horn

Figure 9: The deviation is shown for two different frequencies. Note that the phase center varies with frequency.

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