An Empirical Equation for Predicting the Resonant ... - IEEE Xplore

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 8, 2009

An Empirical Equation for Predicting the Resonant Frequency of Planar Inverted-F Antennas Hassan Tariq Chattha, Yi Huang, Senior Member, IEEE, Xu Zhu, and Yang Lu

Abstract—The planar inverted-F antenna (PIFA) is widely used in mobile systems due to its excellent performance. This letter introduces a new empirical equation for predicting the resonant frequency of PIFA, taking into account all the important parameters that significantly affect the resonant frequency. The comparisons between the new and the previously used empirical equations are provided to show the comparative accuracy of the new equation. The average % error found between the predicted and the actual operational frequencies is less than 3%. This proposed equation should be very useful to aid the PIFA design. Index Terms—Empirical equation, planar antennas, planar inverted-F antenna (PIFA).

I. INTRODUCTION HE planar inverted-F antenna (PIFA) is evolved from a quarter-wavelength monopole antenna and is now widely used in mobile and portable radio applications due to its simple design, light weight, low cost, conformal nature, attractive radiation pattern, and reliable performance [1]–[3]. It is well known that, for a monopole antenna, the desired length is quarter-wavelength since it is resonant in this case. Using the same analogy, the following empirical equation was proposed for finding the resonant frequency of a PIFA [4]–[6]:

T

(1) are the length and width where is the speed of light, and of the top plate of the PIFA, and is the resonant/operating frequency. This equation means that the sum of the length and width of the top plate should be quarter-wavelength. However, it is actually a very rough approximation and does not cover all the parameters that significantly affect the resonant frequency of a PIFA. It can hardly be used to guide the design in practice; thus, a more accurate and comprehensive design equation is required. This study is part of a further parametric study of the PIFA in which all the parameters linked to the characteristics of the PIFA are investigated. It is found that the characteristics of the PIFA are affected by a number of parameters.

Manuscript received July 02, 2009; revised July 04, 2009. First published July 21, 2009; current version published August 04, 2009. The authors are with the Department of Electrical Engineering and Electronics, University of Liverpool. Liverpool L69 3GJ, U.K. (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LAWP.2009.2027822

Fig. 1. The configuration of the PIFA under study.

In this letter, we will present both numerical and measured results on the resonant frequency as a function of the major parameters of the antenna. Based on these results, a new empirical equation will be introduced, which will be very useful for practical design. II. ANTENNA CONFIGURATION The configuration of the PIFA under study is shown in Fig. 1. The radiating top plate has dimensions , and the ground plane dimensions are . The dielectric material used above the rectangular ground plane is FR-4 having a thickness mm and a relative permittivity ; this is meant for the application when the antenna is integrated with the printed circuit board (PCB). The antenna height is , and the space between the top plate and the substrate is filled with air (free space). The shorting plate has dimensions of , and the feed plate has dimensions of . The distance

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CHATTHA et al.: EMPIRICAL EQUATION FOR PREDICTING RESONANT FREQUENCY OF PIFAs

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Fig. 2. Some PIFAs used for experiments.

L

Fig. 3. Changes of the resonance frequency (GHz) versus changes of (mm).

W

and Fig. 4. (a) Changes of the resonance frequency (GHz) versus changes of (mm); (b) changes of the resonance frequency (GHz) versus changes of (mm).

between the shorting plate and the edge of top plate is , the horizontal distance between shorting and feed plates is , and the distance between feed plate and the vertical edge of top plate is . The vertical and horizontal distances of the PIFA structure from the ground plane edges are and , respectively, as shown in Fig. 1. III. SIMULATED AND EXPERIMENTAL RESULTS To obtain a more accurate design equation, we need to identify the effects of each of the antenna parameters on the resonant frequency. The procedure adopted for this study is that only one parameter is changed at a time to observe its effects on the characteristics of the PIFA while all other parameters are held constant. Different sets of parameters are taken for study to cover a wide range of values and also at different resonant frequencies. Since there are so many variables, an analytical solution is impossible to obtain. Thus, experimental and numerical approaches are adopted. Some PIFAs used for experiments are shown in Fig. 2. The software used for simulation is High Frequency Structure Simulator (HFSS) based on the finite element method. For convenience, a reference PIFA is chosen with the folmm, mm, lowing parameters (13 in total): mm, mm, mm, mm, , , , mm, mm, mm, and . A. Changes in Dimensions of Ground Plane The width of ground plane and the length of ground plane

is varied from 45 to 85 mm, is varied from 45 to 105 mm,

X L

while all other parameters are held the same as that of the reference PIFA. The simulated and measured results are shown in Fig. 3, which shows that the greater the value of or , the lower the resonant frequency. However, changes in the resonant frequency ( 20%) are small as compared to the changes in the length or width of the ground plane ( 100%), i.e., the resonant frequency is not sensitive to the dimensions of the ground plane—this could be due to the fact that the antenna dimension is the dominant factor for radiation. B. Changes in Position of PIFA on Ground Plane The value of is changed from 0 to 20 mm, and the value of is changed from 0 mm to 50 mm, while all other parameters are the same as that of the reference PIFA. The simulated and measured results are shown in Fig. 4, which shows that the increase in either or increases the resonant frequency. Again, the resonant frequency change is not very sensitive to the position on the ground plane. C. Change in Length, Width, and Height of Top Plate The width of top plate is varied from 38 to 50 mm, the length of top plate is varied from 5 to 25 mm, mm, mm, and the height of top plate is varied from 12 to 20 mm, while all other parameters are again the same as the reference PIFA. The simulated and measured results are shown in Figs. 5 and 6. As expected, the increase of the length, width, and height of top plate decreases the resonant frequency since the current path length is increased.

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L


Fig. 6. Changes of the resonance frequency (GHz) versus changes of

8. Changes of the resonance frequency (GHz) versus changes of L W and Fig. L (mm).

h (mm).

W


W

and

and

F. Changes in Widths of Shorting and Feed Plates The final investigation is to change the width of shorting plate from 5 to 20 mm and the feed plate width from 6 to 14 mm while keeping the other parameters unchanged. The simulated and measured results are shown in Fig. 9. It can be concluded that the variations in the widths of shorting and feed plate changes the resonant frequency. The increase in width of shorting or feed plate increases the resonant frequency. Fig. 7. Changes of the resonance frequency (GHz) versus changes of

L

(mm).

D. Changes in the Distance of Shorting Plate From Edge of Top Plate The horizontal distance of the shorting plate from the edge of the top plate is varied from 0 to 15 mm, and mm, while other are parameters are unchanged. The simulated and measured results are shown in Fig. 7. The results show that inincreases the resonant frequency. crease in E. Position of Feeding Configuration Under the Top Plate Now, the position of feeding configuration is changed by altering the values of horizontal distance from 5 to 15 mm and vertical distance from 0 to 18 mm while all other parameters are the same as the reference antenna. The obtained simulated and measured results are shown in Fig. 8. It is apparent that the increase of or increases the resonant frequency. However, the effects of are not very significant.

IV. EMPIRICAL EQUATION FOR PIFA Based on our comprehensive parametric study, a large database of different sets of parameters using different ground plane dimensions is created, and a new empirical equation is derived to find the center frequency by using the function “nlinfit” (nonlinear least-squares data fitting by the Gauss-Newton method) of MATLAB, taking into account all those parameters that significantly affect the value of the resonant frequency as seen in Figs. 3–9. These parameters are length, width and height of the top plate, widths of shorting and feed plates, and locations of shorting plate and feeding configuration under the top plate. Only horizontal distances of locations of shorting and feed plates are chosen. The vertical distances of feed and shorting plates from the edge of top plate are neglected to make the equation simple and also because their role is found to be not as significant as compared to the horizontal distances. The new proposed equation is therefore obtained as follows:

CHATTHA et al.: EMPIRICAL EQUATION FOR PREDICTING RESONANT FREQUENCY OF PIFAs

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Fig. 12. Comparison between old and new equations for different values of height of top plate. Fig. 10. Comparison between old and new equations for different values of length of top plate.

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Fig. 13. Comparison between old and new equations for different values of . width of feed plate Fig. 11. Comparison between old and new equations for different values of width of top plate.

There are seven parameters in this proposed equation, although the other five parameters also affect the resonant frequency, but in a less significant way. This new equation clearly shows how the resonant frequency is linked to the various parameters of the PIFA. In the denominator, , , and are positive quantities, as shown in the study that the length, width, and height of top plate changes inversely to the resonant frequency. Conversely, , , , and are negative quantities in the denominator, as these parameters change directly to the resonant frequency of PIFA as indicated. Figs. 10–12 show the comparisons for predicting the operational frequency of PIFA between a previously used equation and the new empirical equation for changes in the values of length, width, and height of the top plate of PIFA with feed at the top edge of top plate, and the simulated resonant frequencies are taken as the actual operational frequencies. The comparisons show that the old equation gives a poor prediction of operational frequency of the PIFA; the error increases as the operational frequency increases, and its prediction is the poorest when changes are made in the parameters other than the length and width of the top plate. It is evident that the new empirical equation gives a much better prediction of the resonant frequency than the old equation. There is not a significant effect on the resonant frequency even if we replace the thin FR4 substrate with air, as shown in Figs. 10 and 11. In some configurations of PIFA, the shorting plate is used at the edge of the top plate and the feeding configuration is vertically downward under the top plate [7]–[10]. In this case, the horizontal distance should be taken between the feed plate

W

Fig. 14. Comparison between old and new equations for different values of width of shorting plate

and one side edge of top plate, and the equation still holds. Figs. 13 and 14 show the comparisons for prediction of the operational frequency of PIFA for changes in the widths of feed [7] and shorting plates [8], [9] when feed is provided in the middle of the top plate. Similarly for [10], the computed value by the new equation is 1.95 GHz and the measured value for resonant frequency given in the paper is 1.89 GHz. On the average, as compared to the old empirical equation, the new proposed equation provides 35% more accuracy in predicting the operational frequency of a PIFA. This new equation can provide much more accurate prediction of the resonant frequency than (1), especially when the whole PIFA structure is placed on the edge of a ground plane and feed is provided at the upper edge of the top plate, i.e. mm. We can have even better accuracy by adding the dimensions of ground

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plane in the above equation, but these dimensions are ignored due to the fact that the resonant frequency is less affected by the variations of these dimensions and it will also make the equation complex. This new equation gives the prediction of the first resonant frequency of the antenna. It has been tested that the new equation can be applied for our normal application where the an. tenna size is smaller than one wavelength, i.e., V. CONCLUSION A new empirical equation for the prediction of the resonant frequency is formulated, which involves all the parameters that significantly affect the resonant frequency of the PIFA, and it should be a very useful aid for the PIFA design and fine-tuning of the center frequency. REFERENCES [1] K. L. Virga and Y. R. Samii, “Low-profile enhanced-bandwidth PIFA antennas for wireless communication packaging,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 10, pt. 2, pp. 1879–1888, Oct. 1997.

[2] K.-L. Wong, Planar Antennas for Wireless Communications, ser. Microwave and Optical Engineering. New York: Wiley, 2003. [3] Y. Huang and K. Boyle, Antennas: From Theory to Practice. Hoboken, NJ: Wiley, 2008. [4] H. Haruki and A. Kobayashi, “The inverted-F antenna for portable radio units, in Conv. Rec.,” in IECE Jpn. (in Japanese), Mar. 1982, p. 613. [5] P. S. Hall, E. Lee, and C. T. P. Song, “Planar inverted-F antennas,” in Printed Antennas for Wireless Communications, R. Waterhouse, Ed. Hoboken, NJ: Wiley, 2007, ch. 7. [6] K.-L. Wang, Planar Antennas for Wireless Communications. Hoboken, NJ: Wiley-Interscience, 2003. [7] R. Feick, H. Carrasco, M. Olmos, and H. D. Hristov, “PIFA input bandwidth enhancement by changing feed plate silhouette,” Electron. Lett., vol. 40, no. 15, pp. 921–922, Jul. 11, 2007. [8] P. S. Hall, C. T. P. Song, H. H. Lin, H. M. Chen, Y. F. Lin, and P. S. Cheng, “Parametric study on the characteristics of planar inverted-F antenna,” Proc. Microw., Antennas Propag., vol. 152, no. 6, pp. 534–538, Dec. 2005. [9] H. M. Chen and Y. F. Lin, “Experimental and simulated studies of planar inverted-F antenna,” in Proc. IEEE Int. Workshop on Antenna Technol., 2005, pp. 299–302. [10] M. C. Huynh and W. Stutzman, “Ground plane effects on planar inverted-F antenna (PIFA) performance,” Proc. Microw., Antennas Propag., vol. 150, no. 4, pp. 209–213, Aug. 2003.