Figure 1: Triangular waveguide with slot and a wire feed
The National Science Foundation's (NSF) Tokyo Office periodically receives and disseminates reports on research developments in Japan that are related to the Foundation's mission. NSF-sponsored researchers currently working in Japan prepare many of these reports. These reports present information for use by NSF program managers and policy makers; they are not statements of NSF policy.
Special Scientific Report #00-11 (October 23, 2000)
Mr. John Calvin Young, a graduate student in Electrical and Computer Engineering, Clemson University, prepared the following report. Mr. Young is a participant in the 2000 Monbusho Summer Program sponsored by NSF and the Ministry of Education, Science, Sports and Culture (Monbusho). Dr. Makoto Ando of The Department of Electrical and Electronic Engineering at The Tokyo Institute of Technology in Tokyo, hosted Mr. Young. Mr. Young can be reached via email at: johny@ces.clemson.edu
A triangular waveguide of infinite extent containing a slot with a wire feed interior to the waveguide (Fig. 1) may be used as a directional antenna. An important parameter of any antenna is the input impedance, which is defined as the ratio of the voltage at the input of the antenna to the current at the input of the antenna. Knowledge of the input impedance of the antenna allows one, among other things, to design matching networks, determine power consumption, and determine the bandwidth of the antenna. To calculate the input impedance of the wire feed, the current on the wire is needed. Computing the current on the wire, although conceptually simple, can be a complex process in practice. For this reason care must be taken to formulate the problem in such a way that is amenable to calculation on a computer.
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Figure 1: Triangular waveguide with slot and a wire feed |
The current on the wire can be determined by the following procedure. First, an approximation is made by replacing the wall of the triangular waveguide without the slot with a cylindrical wall. Hence, the triangular waveguide becomes a sectoral waveguide. This approximation greatly simplifies the problem and the new structure is a good approximation of the original structure for the physical dimensions of interest. The benefit of using the sectoral waveguide approximation is that the dyadic Green’s functions for current inside a sectoral waveguide are known analytically but the dyadic Green’s functions for current inside a triangular waveguide are not known. Next, one shorts the aperture and places a magnetic current on the shorted aperture. The wire is then removed and replaced by an electric current. If these currents are adjusted so that the tangential electromagnetic fields on the slot and wire are identical to those of the original problem, then the electromagnetic field produced by the equivalent currents are also identical to those of the original problem. This condition allows one to formulate a set of coupled integral equations by enforcing the original boundary conditions on both the wire and the aperture that can be solved for these unknown currents.
Unfortunately, the dyadic Green’s function for the magnetic current in region II is not known, so another method for calculating the magnetic field due to the equivalent magnetic current on the shorted aperture in region II is needed. To calculate the magnetic field in region II, another equivalent problem is formed using the same technique described above. The cylindrical surface of the sectoral cylinder is extended to form a complete cylinder. Magnetic currents are placed on the interior and exterior, respectively, of this new cylindrical surface. The new interior region III is a sectoral waveguide similar to region I and hence the dyadic Green’s function for the magnetic current is known. Furthermore, the obstacle in the new exterior region IV is a complete cylinder and the dyadic Green’s function for the magnetic current in this region is also known. By enforcing the continuity of the tangential electromagnetic fields across the new cylindrical surface, an auxiliary integral equation can be written from which the magnetic current on the cylindrical surface can be determined. Because the cylindrical surface is infinite in extent, the equivalent magnetic current on this surface is difficult to calculate in the spatial domain. A more efficient method for solving the auxiliary integral equation in the spectral domain is described in [1].
The procedure described above is a method for determining the currents on the wire feed that is amenable to solution on a computer. Once the current is known, several important antenna properties, including input impedance, may be computed. Knowledge of these antenna characteristics allows one to effectively design antennas and to study the effects of changing various physical parameters.
[1] J. Hirokawa, et.al., “Calculation of External Aperture Admittance and Radiation Pattern of a Narrow Slot Cut Across an Edge of a Sectoral Cylinder in Terms of a Spectrum of Two-Dimensional Solutions,” IEEE Trans. Antennas Propagat., Vol. AP-42, pp. 1243-1249, September 1994.