The objective of this research topic is to develop a fast algorithm for electromagnetic simulation of microstrip integrated circuits, microstrip antennas, etc.

Full-wave analyses become more and more crucial to design microstrip antennas and microwave integrated circuits. Among them, the integral equation-based approach is the most popular method. Most of the commercially available software packages, such as Sonnet, Zeland IE3D, Ansoft Ensemble etc, make use of this method. The basic principle of this method is to expand the current distribution on the metallization of microstrip antennas or circuits using a set of basis functions with unknown coefficients. The method of moments (MoM) is then employed to discretize the integral equation into a matrix equation. Solving the matrix equation yields the current distribution. All the parameters, such as far fields for antennas and scattering parameters for circuits, can be extracted from the current distribution. In this method, the evaluation of Green's functions and the choice of basis functions are two important ingredients to obtain an accurate solution. The efficiency depends, in part, on how fast the matrix fill and matrix solve processes are.

The algorithm we developed is based on the integral equation method. The induced currents on the metallization are expanded by the RWG triangular basis functions, which are more flexible to model the arbitrary shape. The Green's functions for the layered medium is achieved using the discrete complex image method, which substantially accelerates the calculation of the Sommerfeld integrals. The method of moments (MoM) is applied to discretize the integral equation, which yields a matrix equation. For the small problems, the matrix equation can be solved by the direct method, such as Gaussian elimination or LU decomposition. For the large-scale problems, the iterative solver is prefered. However, the memory requirement and operation count per iteration are of O(N^2), which is still too high for an efficent simulation, where N is the number of unknowns. To overcome this drawback of the iterative solvers, we develope an adaptive integral method, which reduces the memory requirement to O(N) and the operation count to O(NlogN). You will see that this fast algorithm combined with the techniques mentioned above results in a really promising EM solver of microstrip structures.

Parallel-Coupled Bandpass Filter

The following Figures show the module of the electric field and the S parameters on a microstrip of the following type: substrate Er=10.0, thickness h=0.635 mm. (for more information refer to Foundation for Microstrip Circuit Design , T. Edwards, Chichester, UK: Wiley, 1991).

Module of the electric field at f=9.0 GHz

Module of the electric field at f=11.0 GHz

S-parameters

Cascaded Radial Stub

The following Figures show the module of the electric field and the S parameters on a cascaded radial stub of the following dimensions: radius=5.0 mm, line width=0.6 mm, substrate Er=10.0, thickness h=0.635 mm.

Module of the electric field at f=9.0 GHz

Module of the electric field at f=11.0 GHz

S-parameters

Microstrip Antenna Array

The following Figure shows the module of the electric field for a 32 element microstrip antenna array. The number of unknowns is 8,688, the memory requirement 26.7 Mb, and the CPU time 1.5 hr.

Module of the electric field

RCS of Microstrip Antennas

The two following examples are metallic microstrip plates. The first one is a triangle-circle combined plate with a narrow slot with a incident wave coming at 80deg.

Triangle-circle combined plate with narrow slot

RCS of the triangle-circle combined plate

The second example is an airplane-like plate, under the same incident angle. The number of unknown in this case is 13,359, the memory requirement 34.7 Mb, and the CPU time per iteration 4.5 secs.

Airplane-like plate

RCS of the airplane-like plate

The next two Figures show a branch line coupler and its RCS.

Airplane-like plate

RCS of the airplane-like plate

We now consider a microstrip antenna array, with element size L=36.6 mm, W=26.0 mm, and element spacing 55.517 mm, with incident angles theta=0 deg, phi=45 deg, on a substrate of relative permittivity Er=2.17 and thickness h=1.58 mm. The biggest array (31X31 elements) has 141,267 unknowns. The standard method of moments would require around 160 Gb of memory, which is beyond the capability of most currently available computers. Our method requires only 402 Mb of memory. The CPU time per iteration is 35.8 seconds on a single SGI Power Challenge processor (R8000). The following Figure shows the backscatter RCS for various size of arrays as a function of frequency.

Backscatter RCS as a function of frequency

Module of the electric field at f=2.7 GHz

Module of the electric field at f=3.7 GHz

From these Figures, we can see that the RCS peaks at approximately 2.7 and 3.7 GHz, which corresponds to the (1,0) and (0,1) resonant modes of the single microstrip antenna element, respectively.

The above work is a collaboration between Feng Ling, Chao-Fu Wang, and Prof. Jianming Jin. Please send suggestions, comments, and inquiries to: j-jin1@uiuc.edu.