A major strength of the transient solver of CST MICROWAVE STUDIO® (CST MWS) is the capability to simulate even complex structures with several millions mesh-cells. Therefore, typically complete antenna arrays can be simulated including all edge effects. However, for large arrays a quicker and more efficient simulation can be obtained by assuming an infinite array of antennas. In that case the unit-cell feature of the frequency domain solver offers a very powerful and user-friendly functionality.
Phased-array antennas are planar double-periodic structures that find many applications in electronic systems. This article describes the application of a single periodic open-ended waveguide phased-array antenna with a dielectric radome at its aperture of variable thickness. The absorbing boundary (a so-called Floquet-Port) is placed at some distance away from the aperture and absorbs the generated plane waves of the periodic structure. Complex periodic boundary conditions sustain the propagation of the plane waves at the model’s side walls. In particular, the case of phase-shift angles where two plane waves exists is of interest here. As a verification it is shown that the superposition of two independent plane waves shows the same field pattern as the one created by the unit cell model....
The analyzed structure is shown in Figure 1. Parts of the waveguide are cut away to allow the view of the field distribution inside the structure. In front of the waveguide the dielectric radome is visible.
A primary result from any CST MWS simulation is the S-Parameters. Figure 2 shows the reflection coefficient |S11| of the waveguide port for a fixed frequency of 3 GHz depending on the phase shift between the periodic boundaries. The measured results are shown on the left (taken from ) and the CST MWS simulated results on the right. Both curves show excellent agreement.
The S-Parameters already contain important information about the behavior of the device. The curve for the dielectric sheet with e.g. 1/2*lambda displays a 45° phase shift at the point where maximum radiation is possible (minimum of |S11|). At around 70° the antenna shows a "blind spot" at which almost all energy is reflected (|S11| = 1). A grating lobe appears above a phase shift of 150° and the resulting wave pattern is an overlay of two plane waves. The physical effects can be pointed out even better by visualizing them with the help of field monitors.
As a verification the same result as in Figure 3c can be synthesized from the overlay of two pure plane waves. All necessary information such as direction and amplitude of the two waves can easily be extracted from the previous CST MWS simulation. The next figure shows the two individual plane waves.
Finally, the two waves are combined in figure 5. Both the unit-cell simulation and the plane wave superposition show excellent agreement proving the consistency of both
Figure 5: The original wavguide antenna with periodic boundaries show very good agreement to the overlay of two ideal plane waves
CST MWS offers an extremely user-friendly and intuitive treatment of periodic and unit-cell structures of arbitrary grid angles. Excitation is typically achieved by waveguide ports which correctly takes into account the periodic nature of the mode pattern. These so-called Floquet modes are also used for the absorbtion of the the higher-order wavepatterns in the solution domain and are proven to be more reliable than classic open boundaries. Proper handling of the Floquet modes is imperative for efficient and accurate analysis of periodic structures.
 N. Amitay, V. Galindo and C.P. Wu, " Theory and Analysis of Phased Array Antennas", New York: Wiley Interscience, 1972, p 238
 J. P. Montgomery, "Scattering by an Infinite Periodic Array of thin Conductors on a Dielectric Sheet", IEEE Trans on Ant+Prop, Vol Ap - 23, No. 1, Jan 1975