Антенны, СВЧ / OC / Broadband microstrip antennas

36 Broadband Microstrip Antennas

In general, the resonance frequency of the RMSA excited at any TMmn mode is obtained using the following expression [4]:

where m and n are the modes along the L and W, respectively.

To calculate ee , the value of W should be known. For an RMSA to be an efficient radiator, W should be taken equal to a half wavelength corresponding to the average of the two dielectric mediums (i.e., substrate and air) [1].

The width W of the patch can be taken smaller or larger than the value obtained using (2.11). If W is smaller, then the BW and gain will decrease. If W is larger, then the BW increases due to the increase in the radiated fields. The directivity also increases due to the increase in the aperture area as given in (1.7). However, if W is too large, then the higher order modes could get excited. For example, the RMSA shown in Figure 2.1 is fed with a coaxial feed, and the feed is placed in the middle of the width to avoid the excitation of the orthogonal TM01 mode (i.e., where W may become l/2). However, it will excite the TM02 mode, when W is equal to l . In this case, the resonance frequency corresponding to the TM02 mode will be close to that of the TM10 mode, thereby causing interference leading to radiation pattern impurity.

The radiation pattern of the RMSA for the TM10 mode could be calculated by combining the radiation pattern of the two slots of length We and width DL on the infinite ground plane, which are spaced at a distance L + DL . The normalized patterns in the E-plane (Eu in f = 0° plane) and the H-plane (Ef in f = 90° plane) are given by

where u is the angle measured from the broadside as shown in Figure 2.1. For thin substrates, the normalized expression for Eu reduces to

The radiated power is obtained by integrating the radiated fields, from where the radiation resistance can be obtained as described in Appendix C. Another way of finding the total radiation resistance is by first calculating the radiation resistance R r of the slot, which is approximately given by

where we = k 0 We and k 0 = free-space wave propagation constant = 2p/l 0 .

For the fundamental TM10 mode, since the voltage is maximum and the current is minimum at the edges, the input impedance of the RMSA varies from a zero value at its center to the maximum value at the radiating edges. To obtain impedance matching with the coaxial probe (generally a 50-V feed line), the feed point should be placed at the location where the input impedance of the antenna matches the characteristic impedance of the feed.

For the coaxial feed at a distance x from the center, the input impedance of the RMSA at resonance can be approximately calculated as:

where

where Gr =1/R r is the slot conductance and Gm is the mutual conductance, which accounts for the mutual coupling between the two slots and is given by

where l = k (L + DL ), p = k DL, J0(l ) and J2(l ) are zeroand second-order Bessel functions, respectively.

This formulation for input resistance neglects the conductor loss corresponding to the radiating patch and the ground plane and the dielectric loss due to the substrate. Hence, it always predicts the higher value of the input resistance. A detailed analysis procedure based on MNM is given in Appendix C, which accounts for all these losses.

Instead of coaxial feed, a microstrip line feed could also be used to excite the antenna. The RMSA can be fed by a microstrip line along its nonradiating edge at a distance x from the center, which is same as that of the coaxial feed (because the impedance remains uniform along the width) as shown in Figure 2.5(a). However, if the value of W is comparable to L ,

Figure 2.5 RMSA with microstrip line feed along its (a) nonradiating edge, (b) radiating edge with inset feed, and (c) radiating edge with quarter-wave transformer.

then the orthogonal TM01 mode may get excited. If the microstrip feed is placed along its radiating edge, then either an inset microstrip feed—as shown in Figure 2.5(b)—or a quarter-wave transformer could be used to transform the large input impedance at the edge to that of the 50V, as shown in Figure 2.5(c). The characteristic impedance Z 0 of the quarterwave transformer is given by √50R e , where R e is the edge input resistance at the resonance.

The width of the quarter-wave microstrip line is calculated from its Z 0 using the expressions given in Appendix B. The variation of Z 0 of the microstrip line with W /h for various values of er is given in Figure 2.6(a). With an increase in W /h or er , Z 0 decreases. The variation of Z 0 with f.h for various values of W /h and er = 10 is plotted in Figure 2.6(b). As the frequency increases, the fields are more confined to the substrate, which decreases We and hence Z 0 increases.

2.2.1 Parametric Study of RMSAs

A coaxial-fed RMSA of L = 3 cm and W = 4 cm is considered to study the effects of various parameters on its performance. The probe diameter is taken as 0.12 cm for the 50-V coaxial probe feed using an SMA connector. The substrate parameters are er = 2.55, h = 0.159 cm, and tan d = 0.001. The antenna has been analyzed using commercially available IE3D software based on MoM [7]. The theoretical results obtained using this software are in good agreement with the reported measured and theoretical results [1–6]. The size of the ground plane is considered to be infinite unless finite ground plane size is specified.

Figure 2.6 Variation of Z 0 with (a) W /h for various values of er , and (b) f.h for various values of W /h and er = 10.

2.2.1.1 Effect of Feed-Point Location

For three different feed-point locations from the center of the patch (i.e., x = 0.55, 0.6, and 0.65 cm), the variations of the input impedance Z in and VSWR with frequency are shown in Figure 2.7(a, b). With an increase in frequency, the input impedance moves in the clockwise direction in the Smith chart. As x increases from 0.55 cm to 0.65 cm (i.e., the feed point is shifted toward the edge), the input impedance loci shifts in the right

Figure 2.7 (a) Input impedance and (b) VSWR plots of the RMSA for three different values of x , ( - - - ) 0.55, ( – - – ) 0.60, and ( —— ) 0.65 cm, and (c) its radiation pattern at 2.975 GHz for x = 0.65 cm; ( —— ) E-plane copolar and cross-polar and ( - - - ) H-plane copolar.

direction on the Smith chart implying that the impedance is increasing. Looking at only the VSWR plots, the impedance variation with change in the feed point is not apparent but is obvious from the impedance plots. The resonance frequency of the RMSA obtained using IE3D is 2.974 GHz. The resonance frequency calculated using (2.9), (2.1), (2.4), and (2.6) is 3.003 GHz, which is within 1% of the above value, thereby validating the simplified expressions.

A perfect match with a 50-V feed line is obtained for x = 0.59 cm, which gives a BW of 60 MHz for VSWR ≤ 2; however, it is not the maximum BW. A larger BW of 64 MHz for x = 0.65 cm is obtained for which Z in

at the resonance is 62V. The reason will be obvious if one sees the impedance variation on the Smith chart. For x = 0.65 cm, the input impedance plot crosses the VSWR = 2 circle at the points, which are closer to diameter of the circle, implying larger frequency range within the circle, and hence larger BW. However, the maximum BW of 65 MHz is obtained for x = 0.67 cm, for which R in = 66V. In this case, the impedance plot crosses the VSWR = 2 circle exactly along the diameter.

The radiation pattern in the E-plane (Eu in the f = 0° and 90° planes) and H-plane (Ef in the f = 90° plane) of the RMSA at 2.975 GHz for x = 0.65 cm is shown in Figure 2.7(c). The copolar components in the E and H planes are Eu in f = 0° and Ef in f = 90° planes, respectively. The

radiation is in the broadside direction, and HPBW in the E and H planes are 105° and 76°, respectively. The directivity D and efficiency h are 7.4

dB and 87%, respectively, which gives a gain G (= hD ) of the antenna as 6.8 dB. The cross-polar components in the E and H planes are Eu in f = 90° and Ef in f = 0° planes, respectively. Since Ef in the f = 0° plane is less than 40 dB, it is not shown in the figure. The magnitude of Eu in the f = 90° plane is less than 40 dB in the broadside direction, and its maximum level is below 27 dB as compared to the maximum copolar level.

2.2.1.2 Effect of W

The width W of the RMSA has significant effect on the input impedance, BW, and gain of the antenna. For four different values of W (2, 3, 4, and 5 cm), the input impedance and VSWR plots for x = 0.65 cm are given in Figure 2.8.

With an increase in W from 2 cm to 5 cm, the following effects are observed:

•The resonance frequency decreases from 3.034 GHz to 2.962 GHz due to the increase in DL and ee .

•The input impedance at resonance decreases from 180V to 36V, because the radiation from the radiating edge increases, which decreases the radiation resistance as can be seen from (2.16).

•The BW of the antenna increases; however, it is not very evident from these plots, because the feed point is not optimum for the different widths. Accordingly, a better comparison will be obtained when the feed point is optimized for the individual widths.

•The aperture area of the antenna increases resulting in an increase in the directivity, efficiency, and, hence, gain. The HPBW in the

Figure 2.8 (a) Input impedance and (b) VSWR plots of the RMSA for four different W : ( ? ? ? ) 2, ( —— ) 3, ( - - - ) 4, ( – - – ), 5 cm.

H-plane decreases, whereas it remains almost the same in the E-plane, because the increase in the width is in the H-plane.

With an increase in W, the input impedance decreases, so the feed point is shifted toward the edge to obtain input resistance R in in the range of 50V to 65V; the results are summarized in Table 2.1. As W increases from 2 cm to 5 cm, the value of x is increased from 0.35 cm to 0.75 cm, and the BW increases from 42 MHz to 73 MHz. The HPBW in the E-plane remains around 105°, but in the H-plane, it decreases from 86° to 70°. The gain of the RMSA increases from 6.2 dB to 7.0 dB.

Table 2.1

Effect of W on the Performance of RMSA

(L = 3 cm, er = 2.55, h = 0.159 cm, and tan d = 0.001)

2.2.1.3 Effect of h

The input impedance and VSWR plots for two different values of h (0.159 cm and 0.318 cm) are shown in Figure 2.9 for L = 3 cm, W = 4 cm, er = 2.55, and x = 0.7 cm. With an increase in h from 0.159 cm to 0.318 cm, the following effects are observed:

•With the increase in h, the fringing fields from the edges increase, which increases the extension in length DL and hence the effective length, thereby decreasing the resonance frequency. On the other hand with the increase in h, the W /h ratio reduces, which decreases

ee and hence increases the resonance frequency. However, the effect of the increase in DL is dominant over the decrease in ee . Therefore, the net effect is to decrease the resonance frequency.

•The input impedance plot moves clockwise (i.e., an inductive shift occurs) due to the increase in the probe inductance of the coaxial feed.

•The BW of the antenna increases from 64 MHz to 124 MHz. However, for the thicker substrate, this BW is not the maximum. It increases further to 135 MHz, when the feed point is optimized to x = 0.85 cm.

The directivity of the antenna increases marginally because the effective aperture area is increased marginally due to increase in DL . However, h

Figure 2.9 (a) Input impedance and (b) VSWR plots of the RMSA for two different values of h : ( - - - ) 0.159 and ( —— ) 0.318 cm.

decreases from 87% to 81%, due to an increase in the cross-polar level from 28 dB to 22 dB and surface-wave propagation. Generally, h increases with an increase in the substrate thickness initially due to the increase in the radiated power, but thereafter, it starts decreasing because of the higher crosspolar level and excitation of the surface wave [8].

The surface waves get excited and travel along the dielectric substrate (i.e., between the ground plane and the dielectric-to-air interface due to total internal reflection). When these waves reach the edges of the substrate, they are reflected, scattered, and diffracted causing a reduction in gain and an increase in end-fire radiation and cross-polar levels. This also increases the cross coupling between the array elements. The excitation of surface waves is a function of er and h. The power loss in the surface waves increases with an increase in the normalized thickness h /l0 of the substrate. The loss due to surface waves can be neglected when h satisfies the following criterion [9]:

The value of h = 0.318 cm is very close to the above criterion. When h is further increased to 0.5 cm, the BW increases to 256 MHz for x = 1.4 cm, but the surface waves increase considerably, thereby reducing h to 67%. Also, the cross-polar level increases to 17 dB because of the increase in the probe length. The probe acts as a top-loaded monopole antenna, whose radiation increases with the increase in its length. Since the monopole has only the Eu component, it gets added vectorially to Eu in the f = 0° plane of RMSA, but it appears as cross-polar component in the f = 90° plane.

2.2.1.4 Effect of er

For RMSA with L = 3 cm, W = 4 cm, and h = 0.159 cm, when er is decreased to 1, the resonance frequency increases to 4.541 GHz. The BW of the antenna is 167 MHz for the feed at x = 0.7 cm. This increase in BW is due to a decrease in er and an increase in h /l 0, because the resonance frequency has increased.

A better comparison of effect of er is obtained when the antenna is designed to operate in the same frequency range for different values of er . Therefore, with change in the dielectric constant from er 1 to er 2, the L and W dimensions of the RMSA are scaled with a factor of √ee 1 /√ee 2. For operation around 3 GHz, the dimensions of the patch for four different