Антенны, СВЧ / OC / Broadband microstrip antennas

of the cancellation of undesired radiation from the probe. The AR remains below 0.01 dB in the entire VSWR BW. However, since the two additional feed points are not at the null positions of the opposite feeds, impedance loading of 50V takes place. This impedance is in parallel with the impedance of the radiating edge, and hence the overall input impedance of the antenna at any feed-point is less than 50V. The input impedance and VSWR at all the four feed points are identical due to the symmetry of the configuration, and hence these plots are given for only one feed in Figure 8.6(b, c). The BW for VSWR ≤ 2 is 456 MHz (14%). It may be noted from the impedance plot that the input impedance is inductive due to large probe inductance and does not cross the real axis on the Smith chart. The probe inductance decreases with an increase in the probe diameter. Input impedance and VSWR plots for two larger probe diameter (d = 0.2 cm and 0.4 cm) are also shown in Figure 8.6(b, c). With an increase in the probe diameter, the impedance plot shifts downward on the Smith chart providing better matching. The BW of the antenna increases significantly to 1.3 GHz (38%) for d = 0.4 cm. The AR remains below 0.1 dB in the entire BW. This is

theoretical BW, which assumes that the inputs at four feeds remain equal with 0°, 90°, 180°, and 270° phase difference over the entire BW, which

is not practically feasible.

8.3.4 CMSA with Multiple Feeds

Instead of a square MSA, a CMSA with multiple feeds could be used to

yield CP. A CMSA with two orthogonal feeds is shown in Figure 8.2(b). A CMSA of radius a = 3.1 cm, er = 1, and h = 0.4 cm fed with 1 0° and 1 90° at x = y = 1.3 cm, respectively, yields LHCP. The VSWR BW is

from 2.521 GHz to 2.661 GHz, and the AR remains below 1.9 dB within the VSWR BW. As in the case of square MSA, when the CMSA is fed at four orthogonal feed points near the edges as shown in Figure 8.7, a wide VSWR BW of 481 MHz is obtained for a probe diameter of 0.12 cm with an AR less than 0.01 dB in the entire BW. The BW further increases to 1.267 GHz when a probe diameter of 0.4 cm is used, which gives better impedance matching.

8.3.5 Integrated MSA with Dual Feeds

Instead of using an external two-way 0° and 90° power divider, it can be integrated along with the MSA. Two different ways of realizing a power divider with a 90° phase difference for square MSAs are shown in Figure

318 Broadband Microstrip Antennas

For the square MSA with L = 3 cm, er = 2.55, h = 0.159 cm, and tan d = 0.001, the edge impedance is 300V. A quarter-wave transformer of Z 0 = 173V is used to transform the impedance to 100V. If the feed point is placed at 1 or 2, then LHCP or RHCP is obtained, respectively. For the feed at 1, VSWR and AR variation with frequency are shown in Figure 8.9. The VSWR BW is 103 MHz (3.4%), but the AR BW is only 23 MHz (0.7%). The VSWR BW of the antenna is much larger in comparison with a square MSA having two orthogonal feeds, whose BW is 54 MHz as described in Section 8.3.1. This is because the reflected waves from the two edges of the patch are out of phase at the feed-point due to an additional l/4 length in one side, and hence are cancelled. However, the reflected waves excite the opposite polarization, so AR BW decreases. Also, AR degrades due to the change in the phase of the feed line with frequency.

In Figure 8.8(b), a 3-dB two-branch line coupler with Z 1 = 35V and Z 2 = 50V is used to provide equal amplitude with a 90° phase difference at the center of the two adjacent edges of the square MSA. The coupler also provides isolation between the two feed points (i.e., the signal can be transmitted and received simultaneously without interference). For the square MSA with L = 3 cm, er = 2.55, h = 0.159 cm, and tan d = 0.001, the input impedance at the two adjacent edges is transformed to 50V by using quarterwave transformers of Z 0 = 122.5V. These are then connected to the two outputs of the coupler. By locating the feed point at either 1 or 2, LHCP or RHCP is obtained, respectively. The VSWR and AR variations with frequency for the feed at port 1 are shown in Figure 8.9. In this case, the

Figure 8.9 (a) VSWR and (b) AR variation with frequency for a square MSA fed by ( —— ) an offset feed and ( - - - ) a 3-dB two-branch line coupler.

reflected power is absorbed in the matched load connected at the port 2 of the hybrid coupler. A BW of 155 MHz for AR ≤ 3 dB is obtained with VSWR ≤ 1.7. This configuration yields better AR and VSWR performance as compared to that of the offset feed at the expense of a decrease in the gain and an increase in the real estate.

Instead of placing the branch line coupler in the same plane, it can be fabricated on the bottom layer and the patch can be placed in the top layer to reduce the planar area. Alternatively, a coupler can be fabricated on a high dielectric constant substrate located on one side of the ground plane, and the antenna on a low dielectric constant substrate located on the other side to realize wideband CP MSA. The coupling between the patch and the coupler is accomplished by passing shorting posts through the ground plane [1].

8.4 Single-Feed Circularly Polarized MSAs

In the case of a dual-feed CP MSA, an external power divider with quadrature phase difference is required to generate the two orthogonal modes. Alternatively, an offset feed line or a 3-dB branch line coupler can be used, but it increases the overall size of the antenna. Instead of dual feed, various singlefeed MSA configurations can be used to generate CP [6–14]. Some of the single-feed CP configurations that are obtained by modifying the square MSA are shown in Figure 8.10. These are diagonally fed nearly square, square with stubs and notches along the two opposite edges, corner-chopped squares, squares with a diagonal slot, among others. Similar single-feed CP MSA configurations are also obtained by modifying CMSAs and TMSAs. In all these configurations, the principle of obtaining the CP is same as described below.

The dimensions of the MSA are modified such that the resonance frequencies f 1 and f 2 of the two orthogonal modes are close to each other as shown in Figure 8.11(a). The antenna is excited at a frequency f 0 in between the resonance frequencies of these two modes, such that the magnitude of the two excited modes are equal. Also, the feed-point location is selected in such a way that it excites the two orthogonal modes with phase difference of +45° and −45° with respect to the feed point, which results in phase quadrature between the two modes. These two conditions are sufficient to yield CP. For a thicker substrate with a low dielectric constant, the BW of the MSA is large, and hence larger separation between f 1 and f 2 (slightly greater than the BW of the individual mode) should be taken as shown in

Figure 8.10 Various single-feed modified square MSA configurations: (a) diagonally fed nearly square and square with (b) two stubs, (c) two notches, (d) two corners chopped, (e) square notches at two corners, and (f) diagonal slot.

Figure 8.11 VSWR variation of two orthogonal modes of a single-feed MSA: (a) narrow band and (b) wideband [( - - - ) individual mode and ( —— ) overall response].

Figure 8.11(b). However, the magnitude of the two orthogonal modes is equal only at f 0, and hence the AR BW is generally limited for these singlefeed MSAs, but the VSWR BW is large. The ratio f 2 /f 1 is generally in the range of 1.01 to 1.10 depending upon the VSWR BW of the individual orthogonal mode of the MSA.

Another way to recognize whether the given dimensions are optimum for the best AR is to look at the impedance plot of the antenna. If there is

a kink (extremely small loop) in the impedance plot corresponding to the excitation of the two orthogonal modes, it will yield the best AR at the kink frequency. Instead of a kink, a small loop or the absence of the loop in the impedance plot yields poor AR.

8.4.1 Diagonally Fed Nearly Square MSA

A nearly square patch with a single feed along the diagonal as shown in Figure 8.12(a) is one of the simplest MSA configurations to generate CP. The ratio of the two orthogonal dimensions L 1 /L 2 should be generally in the range of 1.01–1.10 depending upon the substrate parameters as described above. When the patch is fed along the diagonal, then the two resonance modes corresponding to lengths L 1 and L 2 are spatially orthogonal. The CP is obtained at a frequency, which lies between the resonance frequencies of these two modes, where the two orthogonal modes have equal magnitude and are in phase quadrature.

For a nearly square MSA with L 1 = 3 cm, er = 2.55, h = 0.159 cm, tan d = 0.001, and feed along the diagonal at (−0.15L 1, −0.15L 2), the theoretical input impedance, VSWR and AR plots for three values of L 2 (2.90, 2.92, and 2.95 cm) are shown in Figure 8.12(b–d). As L 2 is increased from 2.90 cm to 2.92 cm, the loop in the impedance plot becomes a kink, and then it disappears as L 2 is further increased to 2.95 cm. The criticality of the dimension is to be noted. Even though a larger VSWR BW of 128 MHz is obtained for L 2 = 2.90 cm due to the loop in the impedance plot, the minimum AR is 2 dB at f 0 = 3.04 GHz. For L 2 = 2.92 cm, the VSWR BW is slightly reduced to 106 MHz, but the minimum AR at f 0 = 3.027 GHz is improved to 0.07 dB. In this case, the BW for AR ≤ 3 dB is 25 MHz (0.8%). The value of L 1 /L 2 = 3.0/2.92 = 1.027 implies separation of 2.7% between the two resonant lengths, which is slightly greater than the VSWR BW (1.8%) of the square patch of length = 3 cm. For this feed, LHCP is obtained, and if the feed is shifted to the other diagonal, then RHCP is obtained.

In the above cases, even though the VSWR BW is larger than the AR BW, it is not useful for many applications. At the lower frequency, the radiation pattern is linearly polarized in the f = 0° plane. As the frequency increases, it becomes elliptically polarized and then circularly polarized at the kink frequency followed by elliptical and linear polarization in the f = 90° plane.

The AR and VSWR BWs are improved by doubling the substrate thickness to h = 0.318 cm. For L 1 = 3 cm, L 2 = 2.83 cm and feed along

Figure 8.12 (a) Diagonally fed nearly square MSA and its (b) input impedance, (c) VSWR, and (d) AR plots for three values of L 2: ( - - - ) 2.9, ( —— ) 2.92, and ( – - – ) 2.95 cm.

the diagonal at (−0.16L 1, −0.16L 2), the input impedance and AR variations with frequency are given in Figure 8.13. A larger ratio of L 1 /L 2 = 1.06 is taken in this case, because BW increases with an increase in the substrate thickness. For the SMA connector (probe diameter d = 0.12 cm), the kink in the input impedance plot is formed in the inductive region of the Smith chart, which is because of the larger probe inductance due to the increased substrate thickness. The probe inductance is reduced by increasing its diameter to 0.2 cm (BNC/TNC connector), which shifts the kink toward the

Figure 8.13 (a) Input impedance and (b) AR variation with frequency of single-feed nearly square MSA for h = 0.318 cm and two values of probe diameter d : ( —— ) 0.12 cm and ( - - - ) 0.2 cm.

center of the Smith chart as shown in Figure 8.13, thereby improving the VSWR at the kink. The increase in the probe diameter increases the resonance frequency slightly because of a decrease in the probe inductance, which decreases the total inductance of the antenna. For the thicker probe, the BW for VSWR ≤ 2 is 220 MHz (7.4%) and the BW for AR ≤ 3 dB is 49 MHz (1.7%). The measured results are in agreement with these theoretical results [6, 7].

The AR BW is further improved when a thicker substrate with a low dielectric constant is used. A thicker probe diameter of 0.4 cm is taken to reduce the probe inductance, so that the kink in the impedance plot is within the VSWR = 2 circle. For L 1 = 4.5 cm, L 2 = 4.1 cm, er = 1.0, h = 0.5 cm, and a feed along the diagonal at (−0.16L 1, −0.16L 2), the VSWR and AR variations with frequency are given in Figure 8.14. The BWs for VSWR ≤ 2 and AR ≤ 3 dB are 425 MHz (14%) and 82 MHz (2.8%). The BW of the antenna is limited by its AR and not by its VSWR.

8.4.2 Square MSA with Modified Edges

Instead of using a nearly square MSA to generate CP, the edges of the square MSA can be modified by adding stubs or by cutting notches as shown in Figure 8.15. By adding only one stub or by cutting one notch, CP can also be obtained, but then the configuration is not symmetrical. However, as long as the total effective areas of these perturbations are of the same order,

Figure 8.14 (a) VSWR and (b) AR variations with frequency of single-feed nearly square MSA for er = 1.0, h = 0.5 cm.

Figure 8.15 Diagonally fed square MSA with (a) two stubs and (b) two notches along its opposite edges.

the performance of one edge modified is similar to that of a two-edge- modified square MSA. The area of the stub or the notch is very critical to yield a lower AR value, just as in the case of a nearly square MSA, where L 1 /L 2 ratio is very critical to yield CP.

A square MSA of length L = 3 cm and two square stubs of length l = 0.25 cm with er = 2.55, h = 0.159 cm, and tan d = 0.001, yields LHCP when fed at (x , y ) = (−0.15L , −0.15L ). The BW for AR ≤ 3 dB and VSWR ≤ 2 are 22 MHz and 95 MHz, respectively, at f 0 = 2.970 GHz. Similarly, when a square notch of length l = 0.2 cm is cut, then the RHCP is obtained when fed at (x , y ) = (−0.15L , −0.15L ). The AR and VSWR BWs are 23 MHz and 95 MHz, respectively, at f 0 = 2.975 GHz. These values of AR