Антенны, СВЧ / OC / Broadband microstrip antennas

A schematic representation of the MNM is shown in Figure C.2. The radiation from the RMSA can be taken into account by either

using the two-slot or four-slot model [1, 2]. For the RMSA excited in the fundamental mode, the field distribution is constant along the radiating edges and varies sinusoidally along the nonradiating edges. In the two-slot model, only the radiating edges are loaded by the sum of the self-conductance and the mutual conductance between the radiating edges of the antenna. This loading scheme is similar to the T-line model, because the field varies only along one dimension. The model predicts the results with good accuracy for the linearly polarized fundamental mode.

When the field varies along both the dimensions—for example, the diagonally fed nearly square MSA—the two-slot model is not accurate. Therefore, all the edges of the RMSA should be loaded with their respective radiation conductance, which is known as the four-slot model. The fourslot model is a generalized model that yields an accuracy of ±1% against the accuracy of approximately ±5% for the two-slot model.

C.5 Segmentation Method

The segmented network for the four-slot model of RMSA is shown in Figure C.3. In Figure C.3, p stands for the feed port. The connected peripheral and external ports are represented by c and d , respectively. For a RMSA or any other regularly shaped patches, EAN represents the external network.

The Z -matrix of the patch and the EAN are combined using the segmentation method, which is given by

where Vp , Vc , and Vd , and Ip , Ic , and Id are the port voltages and currents, respectively. The number of c ports are the same as number of d ports, so the boundary conditions at these interconnections are Vc = Vd and Ic = −Id . The input impedance and the voltage distribution around the periphery of the patch are obtained by applying the segmentation method as:

Figure C.3 Segmentation of an RMSA with its EAN.

The matrixes Z pp , Z pc , Z cp , and Z cc are obtained from the Z -matrix of the rectangular patch using Green’s function. The Z pp is an Np × Np matrix, where Np is the number of external ports and for a single feed, Np = 1. Z pc and Z pd are Np × Nc matrixes, where Nc is the total number

400 Broadband Microstrip Antennas

where K ix and K iy are the components of magnetic current vectors along the x - and y -directions, evaluated from (C.24), and j is the angle between the two vectors. Since K has no component in the z -direction, Fz is zero. Also,

where r, u, and f correspond to the spherical coordinate system and f ′ is shown in Figure 2.7. Since the magnetic current K has only x - and y - components, u ′ = 90°, so (C.26) reduces to

The total radiated power Pr is obtained as:

Pn (u, w) d V

Here Pn (u, f) gives the normalized power in the (u, f) direction [8]. The efficiency h of the antenna is given by [1, 6]

where Pr is radiated power and Pd and Pc are the power loss in the dielectric substrate and conductor (patch and ground plane), respectively. The expressions for Pd and Pc are given in Section C.3.

For circularly polarized antennas, AR is obtained from Eu and Ef as described in [9].

References

[1]James, J. R., and P. S. Hall, Handbook of Microstrip Antennas, Vol. 1, London: Peter Peregrinus, Ltd., 1989.

[2]Srinivasan, V., ‘‘MNM for Variations in Rectangular Microstrip Antennas,’’ Ph.D. thesis, Indian Institute of Technology, Bombay, India, 2000.

[3]Ray, K. P., ‘‘Broadband, Dual-Frequency and Compact Microstrip Antennas,’’ Ph.D. thesis, Indian Institute of Technology, Bombay, India, 1999.

[4]Okoshi, T., and T. Miyushi, ‘‘The Planar Circuit—An Approach to Microwave Inte-

grated Circuitry,’’ IEEE Trans. Microwave Theory Tech., Vol. 20, April 1972,

pp. 245–252.

[5]Gupta, K. C., R. Chadha, and R. Garg, Computer-Aided Design of Microwave Circuits,

Dedham, MA: Artech House, 1981.

[6]Bahl, I. J., and P. Bhartia, Microstrip Antennas, Dedham, MA: Artech House, 1980.

[7]Lier, E., and K. R. Jakobsen, ‘‘Rectangular Microstrip Patch Antenna with Infinite and Finite Ground Plane Dimensions,’’ IEEE Trans. Antennas Propagation, Vol. 31, November 1983, pp. 968–974.

[8]Jordan, E. C. and K. C. Balmain, Electromagnetic Waves and Radiating Systems, Englewood Cliffs, NJ: Prentice Hall, 2000.

[9]Sharma, P. C., ‘‘Desegmentation Method and Its Application to Circularly Polarized Microstrip Antenna,’’ Ph.D. thesis, Indian Institute of Technology, Kanpur, India, 1982.

404 Broadband Microstrip Antennas