**ABSTRACT**

Electromagnetic (EM) simulation of dual-polarized antennas is necessary for precise initial alignments, calibration and performance predictions of multi-function phased array radar systems. To achieve the required flexibility and scalability, a novel Finite-Difference Time-Domain (FDTD) solution is developed for rectangular, cylindrical and non-orthogonal coordinate systems to simulate various types of array antenna manifolds. Scalable array pattern predictions and beam generations are obtained by combining the FDTD simulation solutions with the Near-Field (NF) chamber measurements. The effectiveness and accuracy of this approach are validated by comparing different simulations and comparing simulations with measurements.

**THEORY**

When we apply this assumption, a periodically-arranged patch antenna is modeled as a unit cell. The FDTD model for the unit cell of a planar phased array is depicted as in Figure 1. In Figure 1, the Yee cells in the x and y directions in the mesh only contain the patch antenna without any air gap. By switching among appropriate boundary conditions, this array model can also be used to obtain the AEP of any elements in a semi-infinite array in the x or y directions.

In our solution, the simulation model for a fully-conformal cylindrical phased array antenna has been implemented using absorbing boundaries and periodic boundaries in the cylindrical coordinate system. The PBC implementation utilized in the rectangular grid can be adapted for PBC in the cylindrical grid, as well. The detailed computing procedure is presented in the rest of this section.

**SIMULATION OF ACTIVE ELEMENT PATTERNS**

The material specifications (Section 4) and dimensions (Figure 8) are the same as the specifications and dimensions of the array being measured. One thousand two hundred fifty seven radiating elements with λ/2 spacing can occupy one ring (the circumference of the cylinder) of the 100 λ-diameter cylindrical array.

**MEASUREMENTS OF ACTIVE ELEMENT PATTERNS**

To measure the AEPs, one port of a test patch antenna element is excited while all other ports are terminated with matched load (50 Ω). In near-field measurements, the complex AEP, measured directly as the amplitude and phase of co-polar and cross-polar electrical field sampled at the near-field range, is obtained first, and then, it is transformed to far-field as needed. The planar and faceted-cylindrical array measurement system set up in the near-field chamber is shown in Figure 9.

**GENERATION OF THE ARRAY PATTERN FROM MEASURED AEP**

The azimuth principal plane cut is shown in Figure 15. In the same manner, radiation patterns for V-channels are generated using AEPs for V channels. The azimuth principal plane cut of the measured co-polar and cross-polar magnitude patterns of an eight-by-eight faceted-cylindrical phased array antenna (based on AEPs and software calibration).

**LARGE FINITE ARRAY ANTENNAS**

The frequency domain or time domain current densities can also be collected. For the proposed procedure herein, the frequency domain current values are used for the near-field to far-field transformation calculations. Four separate simulations are performed firstly as the building blocks, and they are illustrated, in Figure 16a–d. The first building block is an active element in an infinite array (infinite-by-infinite array with periodicities in both the x and y directions).

Figure 18 shows both the azimuth principal plane cut (Figure 18a) and elevation principal plane cut (Figure 18b) of a 32-by-32 planar array simulation (1024 elements). Both HFSS and PASim simulations were done only for calculation principal plane cut results, and only one CPU core is used for both. For PASim, this 32-by-32 array simulation used the similar computational resources as that of the eight-by-eight simulation.

**SUMMARY AND CONCLUSIONS**

This work introduces an approach that combines FDTD-EM simulation and chamber-laboratory measurements for the challenges of the precise characterization of dual-polarized array antennas for multi-functional radars. The traditional FDTD for different coordinate systems and domain termination boundary conditions are implemented in a Java language-based, computationally-efficient software. This unique character of the software tool enables full-wave simulation of a wide variety of array configurations from the small laboratory scale to large field system scales, such as planar arrays, fully-conformal cylindrical arrays and faceted-cylindrical arrays.

The fidelity of the EM simulation is validated by using a laboratory array testbed (CPAD) and a near-field chamber measurement. A simple array alignment approach is used to generate dual-polarized, three-dimensional and focused radiation beams from both simulated and measured AEPs. The EM simulation is then extended to large-scale array systems through a new near-field aperture merging technique, and reasonable results are obtained. An interesting contribution of this work is comparing the dual-polarized pattern characteristics for planar and faceted-cylindrical arrays. CPAD allows both configurations with the same aperture size in hardware. The comparison reveals that the far-end sidelobes of cylindrical array radiation patterns are more significant for a smaller cylinder radius, which is consistent with theoretical predictions and EM simulations.

On the other hand, there are no real significant advantages of cross-polarization levels for a particular radiation direction. There is much future work expected related to this study. Since the simulation and measurements are based on AEP, array pattern optimizations are naturally next steps to improve the co-pol and cross-pol pattern performance generated using simple alignments. Computational speed needs to be enhanced through more efficient, C-language implementation and applications on the General-Purpose Graphic Processing Unit (GPGPU). Validations through measurements will be more comprehensive as larger field-scale systems and chambers become available.

Source: The University of Oklahoma

Authors: Sudantha Perera | Yan Zhang | Dusan Zrnic | Richard Doviak