波导缝隙天线英文版waveguide slot antena-part9

9-1 Waveguide Slot Antenna Arrays Roland A. Gilbert BAE Systems, Inc. CONTENTS 9.1 INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-2 9.2 WAVEGUIDE SLOT RADIATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-2 9.3 SLOTTED WAVEGUIDE ARRAY DESIGNS . . . . . . . . . . . . . . . . . . . . . 9-5 9.4 COMPUTATION METHODS FOR SLOT CHARACTERIZATION . . . . 9-18 9.5 DESIGN PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-22 9.6 POWER-HANDLING CAPABILITIES OF SLOTTED-WAVEGUIDE ARRAYS. . . . . . . . . . . . . . . . . . . . . . . . . 9-32 9.7 TOLERANCE AND FABRICATION TECHNIQUES . . . . . . . . . . . . . . . 9-34 Chapter 9 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Source: ANTENNA ENGINEERING HANDBOOK 9-2 CHAPTER NINE 9.1 INTRODUCTION Geometric simplicity, efficiency, polarization purity, conformal installation, and ability to radi- ate broadside beams and vertically polarized E-plane beams at very near grazing angle above a ground plane make slot-antenna arrays ideal solutions for many radar, communications, and navigation applications. Especially today with the desire to make antennas for aircraft as low profile as possible to reduce drag and conserve fuel, slot antenna arrays can be positioned above wings and on top of the fuselage while having the capability to look toward the horizon. Classical slot arrays are depicted as narrow nonconductive slits etched or milled into the host metallic ground plane. They are characterized by the methods used to feed or excite the slots. Without what is behind the slot opening being seen, slot radiators appear similar on the surface of the ground plane. Narrow conformal slots tend to be narrowband (< 5 percent f0) and have high cross-polarization isolation when operating near their resonant frequency. Wider slots can exceed an octave bandwidth given a well-matched feed. However, polarization purity is usually not as good as with the narrower slots. Conformal slot arrays are generally limited in bandwidth because the array lattice spacing has to be large enough to accommodate the waveguide and feed structures behind the slots without creating grating lobes. Conformal slot elements can be fed in a variety of ways: (1) tapping into a transmission line such as a waveguide, (2) coupling to a resonant cavity, and (3) feeding them directly with voltage sources across the slots. Each method has some impact on the radiation per- formance and operating bandwidth of the slot radiators and hence the array. This chapter focuses on the first approach, which is the transmission-line method whereby slots are cut along a waveguide to couple energy in a controlled manner to slots that radiate. Waveguide- fed array systems are either traveling-wave or standing-wave approaches. Because wave- guides are dispersive transmission lines, the array excitation along the waveguide has a differential phase relationship between elements that changes with frequency, causing the array beam to scan. For fixed beam (nonscanning) arrays, the waveguide is converted into a resonant, standing-wave structure. Before the advent of broadband MMIC T/R module technology, waveguide-fed slot arrays were most common in microwave radar applica- tions. Today corporate feed networks offer a greater flexibility to excite slot arrays over a broader bandwidth. They are most effective when T/R modules, comprised of amplifiers, attenuators, and phase shifters or time delay devices, are connected in series with each array element. The slot elements can be phased independently to scan a beam anywhere in a hemisphere above their host ground plane. However, such large phased arrays that have independent control of every radiator are still prohibitively expensive. Therefore array architectures are employed that utilize hybrid scan approaches where electronic scanning is used in one plane, and either mechanical or frequency scanning is used in the other plane. Thus waveguide slot arrays can still provide a very cost-effective solution to fulfilling many high performance array needs. 9.2 WAVEGUIDE SLOT RADIATORS The radiating elements of a waveguide slot array are an integral part of the feed system, which is the waveguide itself. This simplifies the design since baluns or matching networks are not required. A familiarization with the modal fields within a waveguide is necessary to understand where to place slots so that they are properly excited. Narrow slots that are parallel to waveguide wall currents do not radiate. However, when a slot is cut into a waveguide wall and it interrupts the flow of current, forcing it to go around the slot, power is coupled from the waveguide modal field through the opening to free space. To have good control of the excitation of a linear slot array, it is recommended that the waveguide Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Waveguide Slot Antenna Arrays WAVEGUIDE SLOT ANTENNA ARRAYS 9-3 only operate in a single mode, preferably the lowest mode. When a waveguide as shown in Figure 9-1 is excited with a TE10 mode and the ends are terminated in a matched impedance, the fields are given by Eq. 9-1. H E x e E E x e x z o x j z y o x j z z z = − = − − β ωµ β β β β sin( ) sin( ) HH j E x ez x o x j zz= βωµ β βcos( ) − (9-1) where β π β β πλ π λ ω λ λ λ λ λ x z x g g c c a k k c a = / = − = = = = − = 2 2 2 2 2 2 2 (9-2) FIGURE 9-1 Slots cut in the walls of a rectangular waveguide. Slot g does not radiate because the slot is lined up with the direction of the sidewall current. Slot h does not radiate because the transverse current is zero there. Slots a, b, c, i, and j are shunt slots because they interrupt the transverse currents (Jx , Jy) and can be represented by two-terminal shunt admittances. Slots e, k, and d interrupt Jz and are represented by series impedance. Slot d interrupts Jx, but the excita- tion polarity is opposite on either side of the waveguide centerline, thus prevent- ing radiation from that current component. Both Jx and Jz excite slot f. A Pi- or T-impedance network can represent it. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Waveguide Slot Antenna Arrays 9-4 CHAPTER NINE The currents J along the inner waveguide wall surfaces are proportional to H.   J n H= ׈ (9-3) The currents along the top and side walls are shown in Figure 9-2. At the top inner wall surface ( y = b), J j E x e J E x x x o x j z z z o x z= − = − −β ωµ β β ωµ β βcos( ) sin( )ee j zz− β (9-4) On the bottom inner wall surface ( y = 0),  J Jbottom top= − (9-5) On the inner sidewalls (x = 0, x = a), there is only a yˆ -directed current with the same phase. J j E ey x o j zz= − −βωµ β (9-6) Rotating the slot with respect to a peak current direction can control the power coupled to a slot. For example, slot e couples maximum power, while the power is proportional to sin2f for slots d and c. Another way to control coupled power is to take advantage of the natural field intensities within the waveguide by locating the slots accordingly. For exam- ple, Jx is a null at the center of the surface wall and varies sinusoidally as you approach the edge. Therefore, by offsetting longitudinal slots such as slot a from the center of the wave- guide, the power coupled to the slots can be adjusted. The ability to control the excitation of slots in a linear waveguide is important in order to design arrays with tapered sidelobes. Moreover, depending on how the array is fed, the coupling of the waveguide to the slots must vary progressively down the length of the waveguide if the first elements are not to radiate all the power, with little power left for the remaining elements. FIGURE 9-2 Surface-current distribution for rectangular wave- guide propagating TE10 mode: (a) Cross-sectional view shows E- and H-fields. (b) Longitudinal view shows polarity of E-field along wave- guide. (c) Surface views show top and sidewall currents and H-field. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Waveguide Slot Antenna Arrays WAVEGUIDE SLOT ANTENNA ARRAYS 9-5 Slots are classified by their shapes, locations in the rectangular waveguide, and how they are arrayed. Slots are usually about l/2 long at the center frequency of their operating bandwidths. For slots located on the wider waveguide surfaces (a = lc /2), there is plenty of room for offset and rotated slots. For slots cut into the side walls, where the rotation angle f cannot be large and b < a/2, there is usually not enough room for l /2 slots. The slots are either extended or “wrapped around” into the adjoining surfaces (e.g., slot b in Figure 9-1) or the slots are end loaded (e.g., C and I slots) to resonate them. Wrapped-around slots are not as desirable in conformal planar array configurations because the elements have to be slightly elevated above the ground plane or gaps or spacers provided between waveguides. Complicated slot designs are also more costly to manufacture. Slots are usually represented as rectangular shapes, which simplifies analysis. Unless they are etched on a metallized substrate, narrow slots on the broad wall of a waveguide are usually fabricated by a milling process in which rounded ends are a natural output of the process. Wider slots can be manufactured with straight ends but with rounded corners. The impact of rounded ends is small but does change the impedance of the slot and hence its resonant frequency. 9.3 SLOTTED WAVEGUIDE ARRAY DESIGNS A slotted waveguide array is, by its very nature, a linear or stick array. Planar slotted waveguide arrays are comprised of multiple stick arrays placed side by side, as shown in Figure 9-3. The mutual coupling between slots in a planar array is high, especially between slots along the E-plane, such that dimensional and positional modifications to the slots are needed to compensate for resonant frequency changes. Most slot array designs are for fixed beam or mechanically scanned applications where the array is mounted on a gimbaled pedestal to steer the beam. Low loss beamforming networks to feed the arrays can also be constructed out of waveguides. Sum/difference waveguide components, such as magic-Ts, Waveguides machined into common aperture plate FIGURE 9-3 Planar longitudinal shunt-slot array. Adjacent waveguides are indicated at right. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Waveguide Slot Antenna Arrays 9-6 CHAPTER NINE simplify the implementation of monopulse networks in planar arrays for use in radar or sat- ellite tracking applications. Electronic scanning is possible along the axis transverse to the waveguide stick subarrays. Phase shifters and attenuators are included in the network that feeds signals to each stick subarray. However, the active impedance of the array is highly affected with scan angle, especially in the case of longitudinal slots where the polarization is such that the E-plane is the scan plane. Hence the array design must be optimized with scanning requirements in mind. If a TEM transmission line fed slot elements, the beam would radiate at a fixed angle as a function of the delay between elements, independent of changes in frequency. Waveguides are dispersive and the group velocity or delay between slots varies with frequency. Therefore the beam radiated by a slot array scans along the longitudinal axis of the waveguide as the frequency changes. The group delay is not a linear function of frequency, and it increases rapidly as the frequency decreases to near cutoff frequency. For a fixed beam array, this is a feature, or a problem as the case might be, that limits the bandwidth over which the array can be used. Frequency scanned radars make use of this feature to scan a pencil beam in a plane by “chirping” the signal. The array is either mechanically scanned in the other plane or electronically scanned through a network with phase shifters. Waveguide slot arrays are classified into two groups: (1) standing-wave arrays and (2) traveling-wave arrays. The standing-wave arrays have elements spaced lg /2 and radiate a beam broadside to the waveguide. The fields repeat in a waveguide every lg /2 but are of opposite phase. Therefore the slots are placed in a +/− configuration so that they are all fed in phase. Because of dispersion in a waveguide, the bandwidth around the center operating frequency cannot deviate by more than a few percent without causing rapid deterioration of the beam pattern and sidelobe levels, especially for the standing-wave array. Standing- wave arrays can be fed either at one end of the waveguide with the other end terminated in a matched load or short circuit, or at the center of the waveguide with matched load or short circuit terminations at the waveguide ends. Short circuit terminations provide for a more efficient array since the reflected wave from the waveguide ends can be phased with the incident wave. This allows for a higher power handling capability. If a slightly larger band- width is desired, matched terminations minimize reflected waves that potentially could cause the array to radiate another beam in the opposite direction. Traveling-wave arrays are used in applications where the direction of the main beam is pointed at angles that are not broadside to the waveguide wall or where frequency scanning is desired. Inter-element spacing does not have to be the same between the elements, and lg /2 spacing is particularly avoided. In designing these arrays it is important to have wide- band terminations with a very low VSWR to prevent the formation of reflected or backward waves. Backward waves appear to originate from the opposite end of the waveguide and excite the slots to produce unwanted beams in the backward direction. Traveling-wave arrays can only be fed from the ends of the waveguide. To maximize the impedance band- width of the array, the slot elements are designed to be resonant at their center operating frequency, hence they are called resonant slots. This should not be confused with resonant arrays discussed earlier which, unlike traveling-wave arrays, have a standing-wave condi- tion within the waveguide. Initial Slot Array Design Considerations One advantage of waveguide slot arrays is that not only the radiating aperture but also the feed network can be made from waveguides. Waveguides can couple energy to other waveguides in a very precise manner. They are also the preferred low loss transport medium to feed arrays at X-band frequencies and above. Several methods can be used to manufacture the radiating aperture. One popular way is to mill waveguide troughs into a solid piece of aluminum and Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Waveguide Slot Antenna Arrays WAVEGUIDE SLOT ANTENNA ARRAYS 9-7 then to machine the slots. Therefore waveguide width can be made to any custom dimension that is not in cutoff at the operating frequency. This allows design flexibility in the selection of standard waveguide sections for the feed network in the rear of the array aperture. However, be careful to keep inter-element spacing less than a free-space wavelength lo to prevent the appearance of grating lobes. For scanning arrays, the spacing between elements should be closer to lo /2 in the plane of scan. For resonant slotted-waveguide arrays, the element spacing along the waveguide must be equal to half the waveguide wavelength (lg /2) since all the ele- ment excitations must be in-phase. For nonresonant slotted-waveguide arrays, inter-element spacing is slightly larger or smaller than lg /2. The waveguide wavelength is larger than the free-space wavelength for the same frequency. Designing slot arrays is similar to designing any other fixed beam or phased arrays. Once the array requirements are determined, such as gain, sidelobe level, beamwidth, bandwidth, polarization, input VSWR, scan impedance, cross-polarization level, power- handling capability, etc., then the array element excitations are calculated. Most array design codes available that consider mutual coupling between array elements utilize the infinite array approach, which is numerically efficient. However, it does not include array edge and truncation effects. These must be computed by low-frequency methods such as MOM or FEM. Because slots will have different excitations although they have the same resonant frequency, they will have different offset positions from the centerline of the waveguide to achieve their resonant conductances and/or resistances, as in the case of longitudinal shunt slots. Series and edge-wall slots are rotated along the waveguide axis. The element layout is not exactly periodic. Hence slot placement and orientation must be approximated. Once an array excitation is obtained that includes compensation for edge and radome effects, then the element coupling can be readjusted. Since the elements have been moved, a last performance prediction is made to verify that performance will be as desired. This design process is outlined in Figure 9-4. To optimize bandwidth performance, the slots are designed to be resonant at midband for either resonant or nonresonant arrays. The power coupled from the waveguide and ARRAY REQUIREMENTS • Beamwidth • Gain • Sidelobe level • bandwidth • Polarization • Scan Angle (if applicable) • Power level • Frequency OPTIMIZING SLOT ARRAY DESIGN • Model mutual coupling between slots external waveguide and within. • Include Array edge effects • Include radome if close to array • Adjust slots dimensions and positions to achieve needed element excitation • Iterate as needed to optimize design Readjust layout to match with feed network FINALIZE FEED NETWORK DESIGN • Power handling analysis CAD FILES FOR AUTOMATED MACHINING • Aperture size • Slot type selection • Slot Layout Use slot resonance & conductance design formulas PRELIMINARY APERTURE DESIGN • Slot Dimensions • Element excitation • Sub arraying/power partitioning layout • Row & column feeds • Coupled slot feeds • Corporate feeds • Monopulse Network • Hybrid scan/ phase shifters PRELIMINARY FEED DESIGN FIGURE 9-4 Slot array design process. Once the slot element excitations are determined to meet the array beamwidth, gain, and sidelobe requirements, the next step is to lay out the slots onto waveguide. Considerations must be given to the beamformer design. One or more design iterations will be needed to optimize the design. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Any use is subject to the T