By following these basic guidelines, this compact, low-cost, lightweight patch antenna can be matched to applications operating at both 1.9 and 2.4 GHz.

Patch antennas offer effective low-profile designs for a wide range of wireless applications. They are inexpensive to fabricate, light in weight, and can be made conformable with planar and nonplanar surfaces. The antennas are compact and compatible with microwave integrated circuits (MICs) for high-frequency applications. Unfortunately, they have some shortcomings, including relatively low gain, narrow bandwidth, and sensitivity to fabrication errors.1,2 But because of rising demands for multiple frequencies in wireless designs, patch antennas support multiple-function circuits that must be made light, inexpensively, and compact.

This report presents design graphs that can be used to obtain the dimensions, the input impedance, and the quality factor (Q) for a single-feed microstrip rectangular patch antenna based on FR4 substrate material. The design graphs are then used to compute the dimensions of a rectangular patch and feed network for a dual-frequency antenna for use at 1.9 and 2.4 GHz. For the feed network, two transmission lines are used to connect the two edge feeds to an open circuit stub to match the antenna at the two frequencies.

Experimental results will be shown for a prototype antenna built according to the design graphs, with return loss of 20 dB at both 1.9 and 2.4 GHz. Good agreement was obtained between measurements on the prototype and simulated results obtained with equivalent- circuit simulation software from Advanced Wave Research (www.apwave.com) and the electromagnetic (EM) simulation tools contained in the Advanced Design System (ADS) suite of high-frequency simulation tools from Agilent Technologies (www.agilent.com).

Several different analytical methods have been proposed for designing patch antennas. The most popular models include full-wave analysis,3,4 cavity model,5,6 and transmission-line model.7-9 The transmission-line model is by far the most commonly used method as it gives a good physical and engineering insight into the design of a rectangular-shaped antenna. Equations for the length and width are given in references 1 and 2. However, without suitable simulation software, it can be difficult to determine the input impedance. To ease this part of the process, graphs obtained using Agilent ADS software are used in the design of a dual-frequency patch antenna operating at 1.9 GHz for Global Positioning System (GPS) and at 2.4 GHz for Bluetooth applications.

The antenna was designed for FR4 printed-circuit-board (PCB) material with dielectric constant of 4.3. The height of the substrate is 1.575 mm, the loss tangent of the substrate is 0.019, and the copper patch is 0.035 mm thick.

A rectangular patch as used in such an antenna is shown in Fig. 1, where L is the physical length and the two radiating slots of length xL model the electrical fringing fields. Figure 2 shows a graph that allows the length, L, for a given frequency to be found. The width, W, is normally determined using Eq. 1^{2} where f is the design frequency:

Figure 3 shows the antenna modeled by an equivalent transmission line circuit, and, also by a parallel tuned circuit. The parameters of the tuned circuit can be conveniently obtained from the graphs shown in Fig. 4 and Fig. 5.

The rectangular patch and the dualfrequency feed network are shown in Fig 6a. The transmission-line equivalent circuit of the feed network and the parallel tuned circuit of the patch are shown in Fig 6b. For the patch to operate at both 1.9 and 2.4 GHz, the two patch dimensions obtained from Fig. 2 are L1 = 38 mm and L2 = 29 mm, respectively. The first step in the feednetwork design is to find the characteristic impedances (Z1 and Z2) of quarter-wavelength transformers M1 and M2 to match the edge impedances to 50 ohms.

The two edge impedances obtained from the curve in Fig. 5 are R1 = 195 ohms at 1.9 GHz and R2 = 138 ohms at 2.4 GHz. To match these impedances to 50 ohms, the characteristic impedances of M1 and M2 are Z1 = 98 ohms and Z2= 83 ohms. The lengths of the two lines M3 (L3) and M4 (L4) and the length Ls of the open circuit stub Ms need to be determined so that matching is obtained at both frequencies.

In this design, the line of Ms is chosen so that the input impedance is capacitive at the two frequencies and hence the length Ls needs to be one-quarter wavelength long at a frequency which is higher than 2.4 GHz.To ensure the lengths of the two feed lines are long enough, length Ls was chosen to be one-quarter wavelength long at 9.5 GHz. The capacitive reactance of this line is 155 ohms at 1.9 GHz and 122 ohms at 2.4 GHz.

The two lengths L3 and L4 can be obtained as shown below to produce inductive reactance so that they resonate with the open circuit stub at the two frequencies.

In Fig. 6b, the 2.4-GHz the tuned circuit has a high Q factor (see Fig. 4) and is effectively a short circuit at 1.9 GHz. The input impedance Zin1 at 1.9 GHz looking into the transmission lines Z4 and Z2 see Fig. 7a> is given by Eq. 2.

Continued on page 2

### Page Title

The parameter x4 = 170 deg. is obtained for Zin1 = j155 ohms. Using Eq. 2 and the AWR simulation software, the frequency response of this network is found to be as shown in Fig. 7b. As can be seen at 1.9 GHz, the two lines behave as a parallel tuned circuit and all the power from the generator is fed to the 1.9-GHz tuned circuit.

At 2.4 GHz, the 1.9-GHz tuned circuit is modelled as a short circuit as shown in Fig. 8a. The input impedance looking into lines Z3 and Z1 is given by Eq. 3 (see below) and the length x3 = 148.5 deg. is obtained to produce an inductive reactance of 122 ohms. These two lines behave as a parallel tuned circuit and matching is now obtained at 2.4 GHz. The frequency response of this network is shown in Fig. 8b. The fabricated prototype dual-frequency patch antenna is shown in Fig. 9 with the dimensions of the feed network summarized in the table.

The return-loss results of the antenna, as obtained from actual measurements, from the eqivalent-circuit module using the AWR software, and from EM simulation using the Agilent ADS software, are shown in Fig. 10. The plots show excellent agreement among the three different means of obtaining the results.

Figure 11 shows the polar patterns of the dual-frequency patch antenna at 1.9 and 2.4 GHz. It is apparent from these patterns that there is excellent isolation between the two radiated modes. Figure 12 shows the gain response with frequency, where gain of 0 dB was obtained at 1.9 GHz and gain of 2 dB was found at 2.4 GHz. The low gains can be traced to the loss tangent of the FR4 substrate, at 0.019. Higher gains are possible if lower-loss substrate materials are used, with gains of more than 5 dB possible.

In short, this article has presented some quick design graphs to determine the dimensons of a rectangular patch antenna for a frequency or frequencies of interest, using the plotted curves to also find the input impedance at a resonant frequency and the circuit Q. The graphs were then applied to a practical example: the design of a dual-frequency patch antenna operating at 1.9 and 2.4 GHz. With the design of a matching network, measurements showed the antenna's return loss to be 20 dB at the two frequencies. Although the gain of the example design was low, this was attributed to the loss tangent of the FR4 substrate material, with higher gain expected from the use of lower-loss substrate materials.

References

- R. Garg, P. Bhartia, I. Bahl, and A. Ittipiboon, Microstrip Antenna Design Handbook, Artech House, London, 2001.
- C.A. Balanis, Antenna Theory: Analysis and Design, 2nd ed., Chap. 14, Wiley, New York, 1997.
- Y.T. Lo, D. Solomon, and W.F. Richards, "Theory and experiment on microstrip antennas," IEEE Transactions on Antennas & Propagation, Vol. AP-27, No. 2, March 1979, pp. 137-145.
- W.F. Richards, Y.T. Lo, and D.D. Harrison, "An improved theory for microstrip antennas and applications," IEEE Transactions on Antennas & Propagation, Vol. AP-29, No. 1, January 1981, pp. 38-46.
- D.M. Pozar, "A reciprocity method of analysis for printed slot and slot-coupled microstrip antennas," IEEE Transactions on Antennas & Propagation, Vol. AP-34, No. 12, December 1986, pp. 1439-1446.
- Z.G. Qian, T.J. Cui, W.B. Lu, X.X. Yin, W. Hong, and W.C. Chew, "An improved MoM model for line-fed patch antennas and printed circuits," IEEE Transactions on Antennas & Propagation, Vol. 53, No. 9, September 2005, pp. 2969-2976.
- K. Moussakhani and A. Ghorbani, "A novel transmission line model for analyzing bowtie patch antennas," in Proceedings of the Progress in Electromagnetics Research Symposium, Cambridge, MA, March 2006, pp. 168-171.
- D. Jaisson, "Transmission line model for the input impedance of a slot-coupled rectangular patch antenna," IEE Proceedings on Microwave Antennas & Propagation, Vol. 153, No. 5, October 2006, pp. 461-468.
- B. Al-Jibouri, T. Vlasits, E. Korolkiewicz, S. Scott, and A. Sambell, "Transmission-line modelling of the cross-aperture- coupled circular polarised microstrip antenna," IEE Proceedings on Microwave Antennas & Propagation, Vol. 147, No. 2, April 2000, pp. 82-86.