Introduction

A stable Marching-On-Time (MOT) algorithm based on the time domain Electric (EFIE) and Magnetic (MFIE) Field Integral Equations has been developped to analyze transient radiation characteristics of complex antennas (see Figure 1a). We introduced the modeling of surface-wire junctions in the MOT algorithm, and we included the feed network in the analysis using a one-dimensional finite difference scheme in time with a special treatment for the junctions where the feed is connected to the wire antennas, as shown on Figure 1b.

Figure 1a: Log periodic monopole antenna (LPMA) array on an object and radiation pattern

Figure 1b: Feed network

Previous Contributions
1972: Bennet and Weeks - MFIE, rectangular patches
1981: Bennet and Mieras - EFIE, rectangular patches
1989: Bretones et. al. - EFIE, thin-wires
1991: Rao and Wilton - EFIE, RWG basis f, explicit scheme
1991: Rynne - EFIE, RWG basis f, different B.C.
1992: Tijhuis et. al. - Straight thin wires
1992-1997: Rao, Vechinski, Sadigh, Rynne, Smith, Davies, Manara, ... - Stability issues
1997: Walker, Rao - Implicit schemes (MFIE, EFIE)
1997: Ergin et. al. - Plane Wave Time Domain (PWTD) algorithm

Previous modeling algorithms using averaging and filtering techniques were unstable. Our current algorithm has a 7-point integration over surface patches and wire segments, cubic interpolation function in time with piecewise continuous second derivatives, and an implicit scheme, which all in all makes it stable.

Numerical Results
The following Figures will show some examples of numerical simulations performed by the MOT algorithm. The computations are performed with an input impulse shown in Figure 2.

Figure 2: Unit input impulse

1m x 1m square plate with two monopoles

Figure 3a: 1m x 1m square plate with two monopoles

Figure 3b: Corresponding feed network

Figure 3c: Time dependent induced current

Figure 3d: Time dependent radiated field

Figure 3c: Current at the first surface-wire junction

Figure 3d: Theta directed radiated electric field

The "Sputnik" satellite

Figure 4a: A three element linear antenna array mounted on a 393 unknown sphere (a.k.a. "Sputnik")

Figure 4b: Corresponding feed network

Figure 4c: Magnitude of radiated electric field in the far field at f= 120, 130, 140, 150, 160 and 170MHz. The MoM simulation is in dashed red, the MOT one in solid blue.

Figure 4d: Magnitude of the surface current distribution at f= 240MHz
(scale in dB shown in Figure 4e)

Figure 4e: Magnitude of the surface current distribution at f= 260MHz

Figure 4f: Magnitude of the surface current distribution at f= 280MHz
(scale in dB shown in Figure 4e)

Figure 4g: Magnitude of the surface current distribution at f= 325MHz
(scale in dB shown in Figure 4e)

Four element linear antenna array on a flat plate

Figure 5a: Four element linear antenna array mounted horizontally on the edge of a flat plate (535 unknowns)

Figure 5b: Corresponding feed network

Figure 5c: Magnitude of radiated electric field in the far field at f= 25, 27.5, 30, 32.5, 35 and 37.5MHz. The MoM simulation is in dashed red, the MOT one in solid blue.

Figure 5d: Real part of the input impedance of the antenna as seen by the source as a function of frequency ( *: MoM ; solid line: MOT)

Figure 5e: Imaginary part of the input impedance of the antenna as seen by the source as a function of frequency ( *: MoM ; solid line: MOT)

Figure 5f: Magnitude of the surface current distribution at f= 37.5MHz

Six element LPMA mounted on a cylindrical wing model

Figure 5a: Six element LPMA mounted on a cylindrical wing model (1124 unknowns)

Figure 5b: Corresponding feed network

Figure 5c: Magnitude of the surface current distribution at f= 25MHz
(scale in dB shown in Figure 5g)

Figure 5d: Magnitude of the surface current distribution at f= 31MHz
(scale in dB shown in Figure 5g)

Figure 5e: Magnitude of the surface current distribution at f= 34MHz
(scale in dB shown in Figure 5g)

Figure 5f: Magnitude of the surface current distribution at f= 40MHz
(scale in dB shown in Figure 5g)

Figure 5g: Scale in dB for the previous current distributions
(Figures 5c to 5f)

CPU time requirement comparisons

Figure 6: CPU time requirement comparison for 8 element LPMA mounted on a planar wing model (1030 unknowns, max. frequency 250MHz)

Conclusions and Continuing Work

A novel time domain algorithm for analyzing arrays of thin wire antennas mounted on arbitrarily shaped open or closed conducting bodies has been sucessfully implemented. The antenna feed network with modulated feed lines for LPMAs is consistently included in the analysis. We are presently conducting experiments for larger structures and comparing the MOT-FDTD-PWTD algorithm to FISC.

The above work is a collaboration between K. Aygün, S. E. Fisher, A. A. Ergin, Dr. B. Shanker, and Prof. Eric Michielssen. Please send suggestions, comments, and inquiries to: kaygun@decwa.ece.uiuc.edu.