A design procedure for a circular polarized, nearly square patch antenna.
In order to obtain circular polarization, a dual feed can be used to excite a square patch to generate two fundamental modes, T[M.sub.10] and T[M.sub.01], radiating at the same frequency. To meet the necessary conditions for circular polarization, the two modes must be equal in magnitude and [+ or -]90[degrees] out of phase. Hence, an external polarizer in the form of a power splitter or a directional coupler has to be used and, consequently, the board space of the antenna is increased. (1) A more compact form of the antenna can be obtained by using a single probe feed to excite a nearly square patch. (2) The area of the perturbation segment must be carefully determined so that the fundamental mode is split into two degenerate modes (T[M.sub.10] and T[M.sub.01]) radiating at two slightly different frequencies and also satisfy the conditions for circular polarization. The single feed is normally located along one diagonal to produce left-hand (LH) circular polarization or along the other diagonal to produce right-hand (RH) circular polarization. (3) For the diagonal feed, the area of the perturbation segment is small so that the two dimensions (a and b) of the nearly square patch are approximately equal and hence are very sensitive to manufacturing errors. It is shown in this article that, by using a single microstrip feed, offset from the corner and along one edge of the nearly square patch, the area of the perturbation segment is increased. Further increase in the area of the perturbation segment can be obtained by using a thicker substrate. Consequently, the effect of the manufacturing errors on the performance of the antenna is further reduced.
To simplify the design of this antenna, an equivalent circuit is derived. The radiation along the edges of the patch of the two modes is modeled by two parallel tuned circuits, which are connected to the feed point by two transformers. Based on this equivalent circuit the dimensions of the patch are obtained so that the antenna operates at the designed frequency. Finally, to match the complex input impedance of the antenna to [Z.sub.0], a short length of microstrip line is used.
[FIGURE 1 OMITTED]
EQUIVALENT CIRCUIT DERIVATION AND DESIGN OF THE ANTENNA
Figure 1 shows a nearly square patch antenna having physical dimensions a and b with b > a. The patch is normally fed along one of the two diagonals to generate either RH or LH circular polarization. The area of the perturbation segment ([DELTA]S) must be such that the two modes satisfy the conditions for circular polarization as shown. The problem with the diagonal feed is that [DELTA]S is very small.
More generally, it has been shown (2) that circular polarization can also be achieved by a probe feed located at any point on a locus ([x.sub.0], [y.sub.0]), as shown in Figure 2 for RHCP and LHCP when the patch dimensions depend on the probe location. The equivalent circuit of the antenna where the two tuned circuits represent the two radiating modes at the edges of the patch is also shown. The two transformers [T.sub.a] and [T.sub.b] with turns ratio [N.sub.a] and [N.sub.b] transform the two edge impedances to the feed point ([x.sub.0], [y.sub.0]). For the T[M.sub.10] mode, the voltage [V.sub.Fa] along the 'a' edge of the antenna is proportional to [V.sub.a] cos ([pi][x.sub.0]/a), while for the T[M.sub.01] mode, the voltage [V.sub.Fb] along the 'b' edge is proportional to [V.sub.b] cos([pi][y.sub.0]/b). The turns ratio [N.sub.a] is [V.sub.Fa]/[V.sub.a] [proportional] cos ([pi][x.sub.0]/a) and similarly [N.sub.b] is [V.sub.Fb]/[V.sub.b] [proportional] cos ([pi][y.sub.0]/b). Therefore, the ratio [N.sub.b]/[N.sub.a] is given by
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
[N.sub.b]/[N.sub.a] = [cos([[pi][y.sub.0]]/b)]/[cos([[pi][x.sub.0]]/a)] (1)
From the circuit, it can be shown that, for CP, the ratio [V.sub.b]/[V.sub.a] is given by
[V.sub.b]/[V.sub.a] = [[N.sub.b]/[N.sub.a]] * [[[[f.sub.a]/Q + j([f.sub.0] - [f.sub.a.sup.2]/[f.sub.0])]]/[[[f.sub.b]/Q + j([f.sub.0] - [f.sub.b.sup.2]/[f.sub.0])]]] = 1 [angle] [+ or -] 90[degrees] (2)
[f.sub.0] = design frequency
[f.sub.a] and [f.sub.b] = frequencies of the two modes
Q = Q-factor of the patch
The frequencies for the two modes are given by
[f.sub.b] = v/[2[b.sub.e][square root of ([[epsilon].sub.reff])]]
[f.sub.a] = v/[2[a.sub.e][square root of ([[epsilon].sub.reff])]]
[f.sub.a]/[f.sub.b] = [b.sub.e]/[a.sub.e] = [[a.sub.e] + [c.sub.e]]/[a.sub.e] = 1 + [[DELTA][S.sub.e]]/[S.sub.e] (3)
where the physical dimensions a = [a.sub.e] - 2[DELTA]a and b = [b.sub.e] - 2[DELTA]b, [a.sub.e] and [b.sub.e] are the effective dimensions of the patch, v is the velocity of light and [[epsilon].sub.reff] is the effective dielectric constant. To determine accurately [DELTA]a and [DELTA]b due to the fringing effect, it is recommended that the equations given in Reference 4 be used.
Substituting Equation 3 into Equation 2 for [f.sub.a] and applying the CP conditions gives the following results:
For the magnitude condition, it can be shown that
[[alpha].sup.4](r - 1) + [[alpha].sup.2] (r[M.sup.2] - 1) (1/[Q.sup.2] - 2) + r[M.sup.4] - 1 = 0 (4)
r = ([N.sub.b]/[N.sub.a])[.sup.2]
[alpha] = [f.sub.0]/[f.sub.b]
M = 1 + [[DELTA][S.sub.e]]/[S.sub.e]
Similarly for the phase condition:
[[alpha].sup.4] + [[alpha].sup.2](M/[Q.sup.2] - [M.sup.2] - 1) + [M.sup.2] = 0 (5)
Equations 4 and 5 are solved to determine the values of the effective patch dimensions [a.sub.e] and [b.sub.e] for a given feed location ([x.sub.0], [y.sub.0]). The value of Q can be determined for the unperturbed square patch, (5) or by simulation, (6) or by practical measurement at the design frequency [f.sub.0].
An antenna with a microstrip feed is easier to match than one with a probe feed. The design presented here is for a feed position ([x.sub.0], 0) as shown in the figure, so that
[N.sub.b]/[N.sub.a] = 1/[cos([pi][x.sub.0]/a)].
EFFECT OF THE MICROSTRIP OFFSET FEED POSITION AND Q ON THE SIZE OF THE PERTURBATION SEGMENT
Solving Equations 4 and 5, the percentage of the perturbation [DELTA][S.sub.e]/[S.sub.e] as a function of the offset feed position [x.sub.0] with a fixed [y.sub.0] = 0 and Q are shown in Figure 3. As can be seen for the corner-feed position at [x.sub.0] = 0 and [y.sub.0] = 0 the area of the perturbation segment is very small and the condition for circular polarization is very sensitive to manufacturing errors. As the offset feed position [x.sub.0] approaches the center of side a, the percentage of [DELTA][S.sub.e]/[S.sub.e] increases exponentially. By using a thicker substrate, the Q-factor of the patch is reduced, which further increases the relative size of [DELTA][S.sub.e]/[S.sub.e].
INPUT IMPEDANCE AND MATCHING
For a square patch using an FR4 PCB substrate with [[epsilon].sub.r] = 4.3, h = 1.575 mm, tan [delta] = 0.019, and at an operating frequency of 2.45 GHz, the calculated value of Q was 32.7. The input impedance of the antenna at the offset position [x.sub.0], and [y.sub.0] = 0 is given by (5)
[Z.sub.in] = [[j[omega][mu]h]/a][-[1/k]cot(kb) + [[8[a.sup.3]]/[[[pi].sup.3][w.sup.2]]] [[infinity].summation over (m=1)] [[(cos(m[[theta].sub.1]) * sin(m[[theta].sub.2]))[.sup.2]]/[[m.sup.2][square root of ([m.sup.2] - [A.sup.2])]]] coth ([pi]C)] (6)
k = [omega][square root of ([mu][[epsilon].sub.0][[epsilon].sub.r] (1 - j/Q))]
[[theta].sub.1] = [[pi][x.sub.0]]/a
[[theta].sub.2] = [[pi]w]/[2a]
A = [ka]/[pi]
C = b/a[square root of ([m.sup.2] - (ka/[pi])[.sup.2])]
w = width of the feed line
[FIGURE 4 OMITTED]
It is sufficiently accurate, for values of Q < 35, to use only the first five terms of the series to calculate [Z.sub.in].
For offset feed positions in the interval 0 [less than or equal to] [x.sub.0] [less than or equal to] 0.45a, the dimensions of the nearly square patch were determined using Equations 4 and 5, and [Z.sub.in] obtained from Equation 6.
The predicted input impedance [Z.sub.in] is compared with simulation results, as shown in Figure 4. As [x.sub.0] approaches 0.5a, [Z.sub.in] becomes smaller, making it very difficult to match the antenna. Consequently, in the realization of the matching network, there is a trade-off between the increase in perturbation and the feed location.
[FIGURE 5 OMITTED]
To maintain a compact form of the matched antenna, a short length of a microstrip line is used, as shown in Figure 5. The transmission line model of the matching network is also shown.
The characteristic impedance [Z.sub.0m] of the microstrip line is given by (7)
[Z.sub.0m] = [square root of ([Z.sub.0][[([Z.sub.0]R - [R.sup.2] - [X.sup.2])]/[[Z.sub.0] - R]])] (7)
where [Z.sub.0] = 50 [ohm] and [Z.sub.in] = R + jX is the input impedance of the patch.
The electrical length of the matching line is given by
[[theta].sub.m] = [beta][l.sub.m] = [[2[pi]]/[[lambda].sub.g]][l.sub.m] = [tan.sup.-1] (j[Z.sub.0m] [[[Z.sub.in] - [Z.sub.0]]/[[Z.sub.0m.sup.2] - [Z.sub.in][Z.sub.0]]]) (8)
By this method, only a certain range of [Z.sub.in] can be matched, as shown in Figure 6, and this determines the maximum value of the offset position [x.sub.0].
SIMULATED AND MEASURED RESULTS
A nearly square patch antenna was designed with the offset feed location at 0.3a. The calculated and simulated input impedances of the patch were 97-j35.4 [ohm] and 75.5-j32.2 [ohm], respectively. The design of the matching network was based on the input impedance of 75.5-j32.2 [ohm]. The parameters of the designed antenna operating at 2.45 GHz are summarized in Table 1. The fabricated nearly square patch antenna with a simple matching network is shown in Figure 7.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
Figure 8 shows a comparison of the simulated and measured results for the axial ratio (AR) of the designed antenna. The measured axial ratio was 0.45 dB at 2.458 GHz, which is less than a 0.5 percent shift from the design frequency. The simulated and measured results for the return loss also show good agreement.
Based on the equivalent circuit of the nearly square patch antenna, the conditions for circular polarization were determined. It has been shown that using an offset microstrip line and a thicker substrate increases the size of the perturbing segment. To match the antenna a simple matching network has been designed, consisting of a short length of microstrip line. The measured and simulated results are in good agreement with predicted values.
TABLE I THE PREDICTED AND SIMULATED IMPEDANCE AND DIMENSIONS OF THE PATCH ANTENNA Parameters Predicted Simulated [Z.sub.0m] ([ohm]) 76.2 78 [l.sub.m] (mm) 8.614 8.32 a (mm) 28.824 28.52 b (mm) 29.934 29.75 Q 32.7 30.5
The authors would like to acknowledge the assistance of Peter Gale, Peter Elsdon, Stan Scott and professor Fary Z. Ghassemlooy.
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S.K. LEE, A. SAMBELL, E. KOROLKIEWICZ, S.F. LOH, S.F. OOI AND Y. QIN
University of Northumbria
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|Title Annotation:||TECHNICAL FEATURE|
|Author:||Lee, S.K.; Sambell, A.; Korolkiewicz, E.; Loh, S.F.; Ooi, S.F.; Qin Y.|
|Date:||Jan 1, 2005|
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