Chapter 3 Broadside Twin Elements 3.1 Introduction

Transcription

1 Chapter 3 Broadside Twin Elements 3. Introduction The focus of this chapter is on the use of planar, electrically thick grounded substrates for printed antennas. A serious problem with these substrates is losses to the guided waves in the dielectric substrate. We will show that through the use of properly spaced twin element antennas such losses can be reduced. We will treat only uniform substrates in this chapter so that the effect of the twin elements can clearly be seen. An additional constraint for imaging applications is a structure which couples radiation to only one side of the antenna. For dipoles on grounded substrates this condition is automatically satisfied. Slot antennas, however, are apertures in the substrate ground-plane and therefore couple to both sides. Through the appropriate choice of substrate thicknesses, however, a slot can be made to radiate mainly through the dielectric substrate. The emphasis of the following discussion is on the use of practical structures and materials, which will make the fabrication of an efficient millimeter wave printed antenna structure as simple as possible. We will find that if the dielectric constant of the substrate is not too high (i.e. ε r = 4 or less), a reasonably efficient antenna structure can be fabricated on a single uniform substrate that is between 0.25 and.25 wavelengths thick. To simplify the discussion, all of the calculations presented in this chapter, as well as in chapter 4, employ infinitesimal elements for the slots and the dipoles. It was found that the results using resonant length elements differed only slightly from the elemental sources, so only the elemental sources were used 34

2 Electrically Thick Substrates The efficiency, as defined by equations 2.9 and 2.0, of single slot and single dipole elements on grounded substrates as a function of substrate thickness is shown in Figure 3.. Note that the dipole antenna has an upper limit efficiency of 00% when the substrate is very thin while the slot antenna has a peak efficiency of only 50% at zero thickness, since it radiates into both half spaces. Also if Figures 3.a and 3.b are compared we can see that as dielectric constant is increased, the efficiency decreases for substrate thicknesses greater than zero. Since our focus is on electrically thick substrates we will shift our attention to the peaks in efficiency at substrate thicknesses greater than zero. These peaks occur near the points where the substrate is odd multiples of a quarter dielectric wavelength thick. We will also restrict most of our discussion to quartz substrates (ε r = 4) which is the most likely material for a substrate. Figure 3.2 shows how the power radiated by a single elemental slot and dipole on a ε r = 4 grounded substrate are distributed between the guided modes in the substrate and the power radiated to air. This plot shows that near odd integral multiples of a quarter wavelength thickness, the power radiated to air peaks for both the slot and dipole, corresponding to the peaks in efficiency in Figure 3.2. The behavior of the radiated-to-air power illustrated by Figures 3. and 3.2 can be understood if we examine the transmission line model shown in Figure 2.2 For the slot antenna, which appears as a voltage source in the model, maximum power would be delivered to a minimum impedance load. If the transmission line equivalent circuit for the substrate is an odd integral number of quarter wavelengths

3 36 Efficiency Dipole Slot Thickness in Dielectric Wavelengths a) A quartz substrate ε r = 4.0 Efficiency Dipole Slot b) A GaAs substrate ε r = 3 Thickness in Dielectric Wavelengths Figure 3.: Efficiency (as defined by eqs. 2.9 and 2.0) of single elements. (a) Element fabricated on an εr=4 (quartz) substrate, and (b) element fabricated on an ε r =3 (GaAs) substrate. Efficiency is plotted as a function of substrate thickness in units of a dielectric wavelength; (λd) = λo/ ε r.

4 37 Normalized Power TM o TE o Radiated-to-air TM TE TM 2 TE 2 TM Thickness in Dielectric Wavelengths a) Power distribution for single slot Normalized Power 2 TMo Radiated-to-air TE o TE TM TM 2 TE 2 TM Thickness in Dielectric Wavelengths b) distribution for a single dipole Figure 3.2: Radiated power distribution of a single dipole and a single slot as a function of substrate thickness. Power for the slot is normalized to the power a slot radiates in free space, similarly the power for a dipole is normalized to the power a dipole radiates into free space.

5 38 thick, the substrate will act as an impedance invertor. Since air has a higher characteristic impedance than the dielectric substrate, this inversion will produce the desired low impedance load for the slot. Thus the radiated power is maximum near odd multiples of quarter wavelength thickness. We can also understand the behavior of the dipole with this simple model. The dipole on a grounded substrate (the microstrip dipole) appears as a current source on a transmission line stub terminated in a short (e.g. the ground plane). The quarter wavelength thick substrate transforms the short circuit into an open circuit on boresight, and, consequently, the power delivered to the load by the current source (radiated to air by the dipole) is maximized. If we define the front-to-back ratio for the slot as the ratio of power density on boresight of the front side (dielectric side) beam to the back side (radiated directly to air) beam we find from our transmission line model that at the 0.25λ d thickness the front-to-back ratio of power density is simply ε r. Thus the use of odd quarter wavelength thicknesses is beneficial for both total efficiency and front-to-back ratio, which is desirable for imaging applications. The difference in the behavior of the slot and dipole coupling to the guided waves can be understood if we realize that a dipole over a ground plane in free space has a null in radiated power in the direction parallel to the ground plane. The guided mode can be thought of as a plane wave bouncing back and forth between the ground plane and the interface between the dielectric and air. As the thickness of the dielectric is increased, the angle of incidence in the dielectric at the ground plane and the interface with air approaches grazing incidence. Thus, as the electrical thickness of the substrate is increased, the lower order propagating modes in the dielectric have a k-vector that points more parallel to the ground plane and hence are less strongly

6 39 coupled to the dipole than the higher order modes. Hence, as the substrate thickness is increased, the power delivered to any given mode will drop to zero. The slot, however, will always have power delivered broadside to the TM modes. Thus, as shown in Figure 3.2, the power delivered to the TM modes drops off to an asymptotic value greater than zero for the TM modes. The power a slot delivers to the TE modes, however, does drop to zero as the thickness of the substrate becomes large because the TE wave cannot propagate exactly parallel to the ground plane. In experimental situations frequency is usually an easier parameter to vary than is thickness. Thus, it is useful to investigate the behavior of these antenna structures as a function of frequency. We will focus on the behavior near the first peak in radiated power, which is at 0.25λ d. It is convenient to introduce a normalized frequency, f N, which is chosen so that the frequency will have a value of one when the substrate is 0.25λ d thick. Figure 3.3 shows the efficiency of a single slot and dipole on a 0.25λ d substrate as a function of normalized frequency. This is the same data plotted on Figure 3.a only magnified at the interval around the first quarter wavelength thickness. The slot and dipole are compared directly here; note that the dipole seems to be a better choice for total efficiency than the slot for single elements. Figure 3.4 shows the power distribution of a single slot and a single dipole. This is the same data presented in Figure 3.2 with the focus on the interval around the thickness 0.25λ d. Note that while the power radiated-to-air and the TE surface wave power have "kinks" the total power radiated by the antenna is a smooth function of frequency; i.e. the sum of the power radiated by the element to both air and surface waves does not change abruptly. The apparent abrupt behavior in the radiated-to-air power is due to the way in which we keep track of the power radiated by the element.

7 Efficiency Dipole Slot Normalized Frequency Figure 3.3: Efficiency of a single slot and dipole as a function of normalized frequency, fn, where fn = f/fo and fo is the frequency at which the substrate is 0.25λd thick..4

8 4 Normalized Power a) Single slot Total Power TM o Radiated-to-air TE o Normalized Frequency.4 4 Normalized Power 3 2 Total Power Radiated-to-air TM o TE o b) Single dipole Normalized Frequency.4 Figure 3.4: Power distribution of a single slot and a single dipole as a function of normalized frequency.

9 42 As the frequency increases from just below the TE o cutoff frequency the H-plane pattern broadens. As the cutoff frequency is approached, a plane wave component nearly parallel to the interface is excited. At the cutoff frequency this component becomes parallel to the interface, and shifts out of the radiated-to-air power and becomes the TE o guided mode. Thus, the radiated-to-air power shows an abrupt decrease, while the TE o power shows an abrupt increase at the cutoff frequency. Although the total radiated-to-air power peaks at the cutoff frequency of the TEo mode, this is not necessarily the optimum choice for an operating frequency. The broader H-plane pattern at this point may not be desirable and may actually decrease the over-all efficiency of an imaging system due to spill-over losses as discussed by Zah [8]. In addition, if a finite bandwidth is needed, it will also be a disadvantage to have the efficiency drop off rapidly as the frequency increases above the center frequency; therefore the best operating point will probably be a frequency below the TE o cutoff frequency. For the purposes of our discussion we will always consider f N = to be the operating point. The behavior of the radiated power as a function of normalized frequency also changes with dielectric constant. The overall effect of increasing the dielectric constant of the substrate is to decrease both the cutoff frequency of the TE mode and the efficiency. Both of these effects can generally be considered undesirable. For the case shown in Figures 3.3 and 3.4 the cutoff frequency of the first TE mode is f N =.6, while for an ε r = 3 substrate the cutoff frequency of the first TE mode is f N =.05. The peak efficiencies in Figure 3.4 (ε r = 4) are 32% for the slot and 58% for the dipole, while for an ε r = 3 substrate the peak efficiencies drop to 23% for the

10 43 slot and 32% for the dipole. This is due to the increase in power radiated to the TM o mode as noted in []. 3.3 Twin Elements The direction of the peak TM o power that the slot radiates into the substrate is broadside to the element, as discussed in Section III of []. This suggests that two elements placed broadside to each other driven in-phase and properly spaced could reduce the amount of power delivered to this mode. If two elements were spaced one half of a TM o guide wavelength apart, they would cancel the mode power along the broadside direction. In the case of the dipole element, however, placement of the elements broadside to each other is not expected to have as dramatic an effect, since the direction that the dipoles radiate the TM o mode power is off the ends of the elements. Thus, broadside spacing of dipole elements will not introduce any cancellation of the mode in the endfire direction. Figure 3.5 shows the efficiency of twin elements as a function of element spacing for both slots and dipoles. As expected, the efficiency of the slot antenna is modulated much more strongly than the dipole. In fact, the twin element dipole efficiency varies only from about 52% to about 56%, while the twin slot efficiency varies from 20% to 70%. We will show later that this result changes for thicker substrates where several guided wave modes are propagating. Figure 3.6 shows the efficiency of twin elements as a function of normalized frequency, where the element spacing is chosen from Figure 3.5 for optimum efficiency at f N =.0. Again, the efficiency of the slots shows more improvement than the efficiency of the dipoles, to such an extent that the slot antennas are now

11 44.0 Efficiency Twin Slots Twin Dipoles Separation in Free Space Wavelengths Figure 3.5: Efficiency of in-phase, broadside elements as a function of element separation on a 0.25λd thick substrate..0 Efficiency Twin slots Twin dipoles Normalized Frequency Figure 3.6: Efficiency of in-phase broadside twin elements as a function of normalized frequency with spacing chosen for maximum efficiency from Figure

12 45 actually more efficient than the dipoles. An added benefit is that the frequency range over which the slots are efficient is increased. Figure 3.7 shows the power distribution for the same twin element configurations; compared to Figure 3.4 for the single slot, the power delivered to the TM o mode is dramatically reduced, while the power distribution for the dipoles is not dramatically changed. The reason for this effect can be clearly seen in Figure 3.8, which shows a polar plot of the pattern of the TM o mode in the plane of the substrate (x-y plane) for single and twin slots. The strength of each of the twin elements is 0.5, while the single element has a strength of. This clearly shows that radiation into the TM o mode is significantly reduced when phased twin slots are used. The configuration of two elements driven in-phase is a simple phased array. The surface wave losses for finite dipole and patch antenna phased arrays on grounded substrates have been previously discussed by Pozar [4-42]. He found that the efficiency increased with increasing numbers of elements, except for certain scan angles, and that optimum positioning of a twin dipole array is a collinear placement, as expected from the behavior of the TM o mode. As a practical matter, however, two collinear dipoles are much more difficult to feed properly than are two broadside dipoles. Unfortunately, the broadside configuration does not provide any improvement in efficiency, as shown by Figures 3.5 and 3.6. As we have seen, the presence of a dielectric substrate strongly influences the efficiencies of slots and dipoles. The beam patterns of these antennas are also strongly influenced. Figure 3.9 shows the beam patterns for slots on an ε r = 4, 0.25λ d thick substrate. Note that twin and single slots have identical H-plane patterns, while the E-plane pattern of the twin elements is narrower than that of the

13 46 Normalized Power a) Twin slots Radiated-to-air TMo Total Power TEo Normalized Frequency.4 Normalized Power Total Power Radiated-to-air TM o TE o b) Twin dipoles Normalized Frequency.4 Figure 3.7: Power distribution for twin elements with element spacing chosen for optimum efficiency from Figure 3.5. Note that the TMo mode in the case of the slots is reduced compared to the power radiated-to-air, while the TMo mode in the case of the dipoles has about the same amount of power relative to the power radiated-to-air as the single dipole.

14 Single slot Twin slots Slot orientation Figure 3.8: TMo mode patterns of single and twin in-phase broadside twin slots on an εr=4, 0.25λd thick substrate. The total magnetic current strength is the same for both patterns. The twin elements are spaced for optimum efficiency. The scale is linear power with the peak of the single element pattern normalized to one.

15 48 Power Density. Twin slots Single slot.0-90 a) E-plane pattern Angle Power Density b) H-plane pattern Angle Figure 3.9: Beam patterns for slots on an εr=4, 0.25λd thick substrate. The spacing for the twin element pattern is the same as in Figure 3.6 and 3.7. Note that the H-plane patterns of single and twin slots are identical.

16 49 single slot. Thus, although the overall efficiency of the twin slots is better than a single element, the asymmetry between E- and H-plane patterns is worse. Figure 3.0 shows the beam patterns for dipoles, also on an ε r = 4, 0.25λ d thick substrate. In contrast to slots, it is the E-plane pattern which is identical for both single and twin dipoles, while the twin element H-plane pattern is narrowed compared to the single element. Here, although the twin dipole efficiency was not significantly improved compared to the single element, the narrower H-plane pattern actually helps symmetrize the E- and H-plane patterns for twin dipoles. 3.4 Thicker Substrates At very high frequencies, even a quarter wavelength thick substrate may be too thin to handle easily. In such cases, it would be convenient to use a thicker substrate. From inspection of Figures 3. and 3.2 we see that there are also efficiency peaks for both slots and dipoles at thicknesses of 0.75λ d and.25λ d. For example, at 500GHz, a 0.75λ d substrate made of quartz would be about 8.85 mils thick, or about the thickness of a microscope coverslip. The efficiency of both twin slots and twin dipoles versus element separation for 0.75λ d and.25λ d thick substrates is shown in Figure 3.. As with a 0.25λ d thick substrate, the use of twin slots can improve the efficiency; the use of twin dipoles also improves efficiency for these thicker substrates, unlike the 0.25λ d case. Here the efficiency of the dipoles is always better than the efficiencies of the slots. This behavior can be understood if we again examine Figure 3.2. The radiated-to-air power for a single dipole on a substrate of thickness 0.75λ d is larger than the total power coupled to all of the guided modes, so the efficiency is already fairly high (about 50%). For the case of a

17 50 Power Density a) E-plane pattern Angle Single dipole Power Density. Twin dipoles.0-90 b) H-plane pattern Angle Figure 3.0: Beam patterns for dipoles on an εr=4, 0.25λd thick substrate. The spacing for the twin element pattern is the same as in Figure 3.6 and 3.7. Note that the E-plane patterns of single and twin dipoles are identical.

18 5.0 Efficiency Twin dipoles Twin slots a) 0.75λ d thickness Separation in Free Space Wavelengths Twin dipoles Efficiency Twin slots b).25λ d thickness Separation in Free Space Wavelengths Figure 3.: Efficiency for broadside twin elements as a function of elements separation on εr=4, 0.75λd, and.25λd thick substrates.

19 52 single dipole the majority of the power coupled to guided modes is in the TE o mode at this thickness. The use of broadside twin dipoles will cancel most of the power radiated into this mode. Hence, the efficiency for twin dipoles properly spaced can be as high as 70%. In contrast to the dipole, a single slot antenna on a 0.75λ d substrate has more power in the guided modes than is radiated to air. There are two TM modes that carry substantial power, as well as the TE o mode. The use of twin broadside slots will allow the cancellation of at most one TM mode at a particular element separation; thus, even though the TM o mode may be cancelled, there will still be a substantial amount of power coupled to the TM and TE o guided modes. Consequently, the efficiency for twin slots on substrates thicker than 0.25λ d remains low. In addition, the efficiencies for both types of antennas drop as the dielectric constant of the substrate increases, as has been noted by previous workers [-3]. For a substrate 0.75λ d thick, the peak efficiency of twin slots drops from 55% for ε r = 4 to about 34% for ε r = 3, while the efficiency of twin dipoles drops from 70% for ε r = 4 to 4% for ε r = 3. The.25λ d thick substrate is very similar to the 0.75λ d case. The overall efficiencies are a little lower because there are more guided modes propagating, as can be seen from Figure 3.2. The total power coupled to the modes by either a single slot or a single dipole is about the same as in the 0.75λ d case, but the power is divided between more modes. This case shows that a trend for thicker substrates is to have nearly the same total power coupled into guided modes, but with the power distributed more evenly among many modes. In fact, for a very thick substrate all the power radiated outside of the critical angle in the dielectric will be trapped in guided modes [2]. This suggests that the twin element antenna configuration (which allows

20 53 coupling to only one mode to be eliminated) will probably not provide a great increase in efficiency for substrates thicker than.25λ d. The beam patterns for a substrate 0.75λ d thick are shown in Figure 3.2. The patterns for a.25λ d thick substrate are very similar to the 0.75λ d case. In addition, for fairly thick substrates the patterns for twin elements are very similar to those of single elements. One apparent improvement in beam patterns of both types of elements is that the E- and H- plane patterns are fairly symmetric. These patterns are narrower than those for the 0.25λ d case. This suggests that it is the dielectric which determines the pattern, rather than the type of antenna, since the patterns for the two types of elements are now very similar. 3.5 Conclusions In this chapter we have shown that, even though substrate guided mode losses are a significant problem for planar antennas on finite thickness dielectric slabs, the efficiency of slot and dipole antennas can be improved through the use of properly spaced, broadside twin elements. For the case of a 0.25λ d thick substrate, the only guided mode that propagates (and thus contributes to losses) is the TM o mode. Broadside-spaced twin slots effectively cancel this mode and consequently show a substantial improvement in efficiency over a single slot. Broadside-spaced twin dipoles, however, show almost no improvement over a single dipole, because the TM o mode is radiated off of the ends of the elements, rather than the sides. The thicker (0.75λd and.25λd) substrates show a different behavior than the 0.25λd case. The twin dipoles have the highest peak efficiencies because most of the guided wave power is now concentrated in a single TE mode, which can be effectively

21 54 Slot Power Density. Dipole a) E-plane Angle Slot Dipole Power Density. b) H-plane Angle Figure 3.2: Beam patterns for single elements on an εr=4, 0.75λd thick grounded substrate.

22 55 cancelled by the broadside-spaced elements. The slots, in contrast, have more power radiated into the TM guided modes than radiated to air. Since there are several propagating modes, which all carry a significant amount of power, the cancellation of a single guided mode by employing twin slots provides only limited improvement in efficiency. Consequently, on thick substrates, the peak efficiency for slots is lower than for dipoles, for either single or twin elements. In addition to the integrated antenna efficiencies (as defined in Chapter 2), the overall efficiency of an FIR imaging system is also very dependent on the match between the feed element beam patterns and the primary objective pattern. We have seen here that the beam patterns of both slots and dipoles on a 0.25λ d thick substrate have several undesirable features in this respect. The beam patterns are asymmetric between the E- and H-planes for both single slots and dipoles. In the case of slots, the use of twin elements makes the beam patterns more asymmetric; in contrast, the use of twin dipoles makes the patterns more symmetric. For this thickness substrate, the patterns are broad and are probably only suitable for coupling to low f-number systems. On thicker dielectric slabs (0.75λd and.25λd), the beam patterns are dominated by the substrate; thus there is very little difference between slot and dipole radiation-to-air patterns. This suggests that modifications to the dielectric substrate, rather than modifications to the antenna element itself, will probably have a greater impact on beam patterns and efficiencies. Thus, further improvements in overall system efficiency for planar antenna arrays on dielectric substrates should focus on restructuring of the substrate, as we will show in the next chapter, to allow both suppression of guided wave losses and feed pattern optimization.