RL 800 TUNABLE-CIRCULAR PATCH ANTENNAS Guey-Liou Lan* and Dipak L. Sengupta Radiation Laboratory Department of Electrical Engineering and Computer Science The University of Michigan Ann Arbor, MI 48109 U.S.A. Abstract A method to control the resonant or operating frequencies of circular patch antennas has been investigated experimentally and theoretically. It consists of the placement of passive metallic or tuning posts at approximate locations within the input region of the antenna. Comparison of measured and analytical results seems to establish the validity of a theoretical model proposed to determine the input performance of such circular patch antennas. T.he tunable circular patch antenna is considered as an asymmetrically excited radial waveguide loaded internally with axially directed tuning posts and terminated by an equivalent admittance appropriate for the radiating aperture. Figure 1 shows an untuned circular patch antenna excited from the back by a coaxial probe located at p = po, f = 0 degrees. It can be shown' that the normalized mth mode admittance (m = 0,1,2,...) in the two regions, (Fig. 1) are given by the following non-uniform transmission line equations: J'(x) Y (p) = j Jm"( 9 O <P <o 1 m J + Yt (y)ctr(xy)kr(xy) m ( = Ctr xY) + JYt (Y)k (xy) ' a (2) Now with RCA Laboratories, David Sarnoff Research Center, Princeton, NJ 08540, USA. RL-800 = RL-800

-2 - where yt is the normalized boundary admittance appropriate for the m radiating aperture and N'(x)J (y) - J'(x)N (y) ctr(x,y) - (x)-j (3) m m m m Ctr (xY) = J (x)N (y) - Nm(x)J (y) r rJ'(x)N) y) - NNx)'( m m m m J (x)N'(y) - N (x)J'(y) k (x,y) = J(x)N (y) - Nm(x) 5m(y) m m m m r J (x)N (y) - N (x)JO(y) with x = kp, y = ka, k = ko v (1 - j tan 6)1/2, = / (6) ko being the free space propagation constant and Er, tan 6 are the relative permittivity and loss tangent of the substrate material; J 0,1 are the mth order Bessel and Neumann functions, respectively, and the prime represents differentiation with respect to the total argument. The normalized boundary admittance yt can be formally expressed as m t = 9m ibm (7) Explicit expressions for gm and bm are obtained1'2 from the considerations of total power loss (i.e., radiation, conductor and dielectric losses) and the reactive power stored in the fringing fields at the aperture. The input impedance of the antenna, in the absence of the exciting probe effects, can now be written as co Zin(p~) = Zm(Po ) Y ( o) (8) o 2 1 where

-3 - qd Z(p d (9) Zm(P) (1 + 6 )7p n =, p,E being the permeability and permittivity of the ~ ~ substrate material, 6 = 1,0 for m = 0 and f 0, respectively. The resonant frequency of the antenna is determined from the resonant propagation constant obtained numerically from the following: Im Zin(Po) = 0, (10) where Zin(P ) is given by Eq. (8). For a tuned circular patch antenna, the above non-uniform transmission line model is modified by inserting equivalent post impedances (admittances) at the locations of the tuning posts. Equivalent impedances of metallic posts in a radial waveguide have been discussed elsewhere.3 It can be shownl'3 that in the present case the effective inductive impedance of a tuning post of radius r located at p = p, 0 = 0 degrees, may be approximated by kd ln 2 + J (kp)N (kp, (11) P 1 20 1 0 1 where y = 1.78107. For a tunable circular patch antenna, it is now clear that multiple application of Eq. (2) would be required to obtain Ym (p ) before Eq. (10) can be solved to determine the required 2 propagation constant. Measurements and theoretical computations were performed for a 3.8 cm radius circular patch antenna. The antenna was fabricated on a 1/16 inch, double-clad Rexolite 1422 printed circuit board; the dielectric constant and loss tangent in the frequency range considered

-4 - (1.0 - 2.0 GHz) was approximately 2.54 and 0.001, respectively. Figure 2 shows the measured impedance locus (solid line) for the lowest resonant mode of an untuned antenna. The calculated input impedances obtained with m = 1 and m = 10 - c are also shown in Fig. 2 for comparison. The same antenna configuration was then tuned with metallic posts having r = 0.045 cm. Theoretical and experimental resonant frequency vs post location for antennas with one, and two diametrically opposed similar tuning posts are shown in Fig. 3. To maintain the polarization similar to that of the untuned configuration, the tuning posts must be placed along the lines = 0 degrees of 180 degrees; and to minimize the cross-polarized fields the posts be used in pairs and disposed symmetrically in a diametrically opposed fashion.' References 1. Lan, G-L.: "Investigation of a class of tunable circular patch antennas," Ph.D. Dissertation, Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI 48109, U.S.A., 1984. 2. Bahl, I. J., and Bhartia, P.: "Microstrip Antennas" (Artech House, 1980). 3. Sengupta, D. L., and Martins-Camelo, L. F.: "Theory of dielectric filled edge-slot antennas," IEEE Trans., 1980, AP-28, pp. 481-490.

l ) Fig. 1: A circular patch antenna showing the coaxial feed location and two source-free regions.

IMPEDANCE OR ADMITTANCE COORDINATES INCREMENT: 5 MHz a = 3.8 cm PO= 1.2 cm — * MEASURED o ---o CALCULATED (RESONANT MODE, m=I) o ---o CALCULATED (INFINITE MODES) Fig. 2: First-mode input impedance of a circular patch antenna (without tuning posts).

CIRCULAR PATCH ANTENNA WITH ONE OR TWO POSTS fo 1900 - Calculated (double) o Measured (double) - - A <> Calculated (single) Measured(single, near feed) Measured(single, opposite feed) N r 2: LL) z w w cr LL. 0 1800 - 1700 - 1600 - 0 DOUBLE 1500 - 1400 V I opposite feed I e near feed SINGLE POST i.. -. 0 I I I I 2 3 4 P (cm) DISTANCE Fig. 3: The variation of resonant frequency with distance p. (p is the distance between 1 1 the post and the center line.)