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Low-profile, low-cost antennas support the operation of many modern communication systems. Microstrip patch antennas represent one family of compact antennas that offers the benefits of a conformal nature and the capability of ready integration with a communication system's printed circuitry. By using a straightforward transmission-line model, it is possible to accurately model and analyze microstrip-line inset-fed patch antenna designs. In addition, by applying a curve-fit formula, it is possible to locate the exact inset length needed for a 50-Ω input impedance.

The feed mechanism plays an important role in the design of microstrip patch antennas. A microstrip patch antenna can be fed either by coaxial probe or by an inset microstrip line. Coaxial probe feeding is sometimes advantageous for applications like active antennas, while microstrip line feeding is suitable for developing high-gain microstrip array antennas. In both cases, the probe position or the inset length determines the input impedance.

The input impedance behavior for a coaxial probe-fed patch antenna has been studied analytically by means of various models, including the transmission-line model and the cavity model, and by means of full-wave analysis.^{1-3} Experimentally and theoretically, it has been found that a coaxial-probe fed-patch antenna's input impedance exhibits behavior that follows the trigonometric function:

cos^{2}0/L)>

where:

L = the length of the patch and

y_{0} = the position of the feed from the edge along the direction of the patch length L.

On the other hand, it has been found experimentally^{4} that on low-dielectric-constant materials, the input impedance of an inset-fed probe antenna exhibits fourth-order behavior following the function:

cos^{4}0/L)>

Fortunately, a simple analytical approach has been developed using the transmission-line model to find the input impedance of an inset-fed microstrip patch antenna. Using this approach, a curve-fit formula can be derived to find the inset length to achieve a 50-Ω input impedance when using modern thin dielectric circuit-board materials.

Figure 1 is a graphical depiction of an inset-fed microstrip patch antenna. The parameters ε_{r}, h, L, W, w_{f}, and y_{0}, respectively, are used to denote substrate dielectric constant, thickness, patch length, patch width, feed-line width, and feed-line inset distance. The input impedance of an inset-fed microstrip patch antenna depends mainly on the inset distance, y_{0}, and to some extent on the inset width (the spacing between the feed line and the patch conductor). Variations in the inset length do not produce any change in resonant frequency, but a variation in the inset width will result in a change in resonant frequency. Hence, in the following discussion, the spacing between the patch conductor and feed line is kept constant, equal to the feed line's width; variations in the input impedance at resonant frequency with respect to inset length will studied as a function of various parameters.

Assuming the patch antenna is divided into four regions, it can be modeled as a series of transmission lines loaded by radiating slots of different length (Fig. 2). The table lists the parameters (width and length) of the three transmission lines as well as the width and lengths of the three radiating slots. Radiating slots A, B, and C can be modeled according to the guidelines presented in ref. 5.

Following the strategy outlined earlier, a patch antenna with the parameters ε_{r} = 2.42, h = 0.127 cm, W = 5.94 cm, L = 4.04 cm, and y_{0} = 0.99 cm was analyzed. Figure 3 shows a comparison between the results obtained using the transmission-line-model method presented here and data obtained using a commercial computer-aided-engineering (CAE) electromagnetic (EM) simulator. Even though there is a shift in the resonant frequency, the transmission-line model tracks the return loss profile predicted by the EM simulator very closely. The small shift in the resonant frequency can be attributed to a failure to consider the discontinuity between the inset feed line and the patch.

The transmission-line model was used to perform parametric studies of the patch for various values of ε_{r} (2 ≤ ε_{r }≤ 10). Figure 4 shows that a rectangular microstrip patch antenna fed by a microstrip line at the edge (y_{0} = 0) will have a higher input resistance varying from approximately 150 to 450 Ω for varying ε_{r}. Also, it was observed that the input impedance falls rapidly as the inset position is moved from the edge of the patch toward the center compared to the coaxially probe fed patch antennas. These parametric studies have been used to derive the curve-fit formula (Eq. 1) to find the exact inset length to achieve 50-Ω input impedance for commonly used thin dielectric substrates:

The accuracy of this formula has been checked for a patch with ε_{r} = 5.0, h = 0.127 cm, W = 4.1325 cm, L = 2.8106 cm, and y_{0} = 0.9009 cm. To confirm the validity of the formula, the patch was analyzed using an EM simulator; Fig. 5 offers a comparison between results generated by the transmission-line model and predictions from the EM simulation. Even though there is a one-percent shift in the resonant frequency between the two sets of data, close agreement is apparent between the return-loss profiles predicted by the two approaches.

ACKNOWLEDGMENTS

The authors greatly appreciate the comments of Motorola iDEN group members.

REFERENCES

- K.A. Carver and J.A. Mink, "Microstrip antenna technology,"
*IEEE Transactions on Antennas & Propagation*, Vol. 29, January 1981, pp. 2-24. - H. Pues and A. Van De Capelle, "Accurate transmission line model for the rectangular microstrip antenna,"
*IEEE Proceedings on Microwaves, Optics & Antennas*, Vol. 134, 1984, pp. 334−340. - David M. Pozar, "Input impedance and mutual coupling of rectangular microstrip antennas,"
*IEEE Transactions on Antennas & Propagation*, Vol. AP-30, November 1982, pp. 1191-1196. - Lorena I. Basilio, Michael A.Khayat, Jeffery Williams, and Stuart A. Long, "The Dependence of the Input Impedance on Feed Position of Probe and Microstrip Line − Fed patch Antennas,"
*IEEE Transactions on Antennas & Propagation*, Vol. 49, January 2001, pp. 45-47. - Daniel H. Schaubert, Frederick G. Farrar, Arthur Sindoris, and Scott T. Hayes, "Microstrip antennas with frequency agility and polarization diversity,"
*IEEE Transactions on Antennas & Propagation*, Vol. 29, January 1981, pp. 118-123.