phased array antennas || reflectarrays and retrodirective arrays

CHAPTER THIRTEEN

Reflectarrays andRetrodirective Arrays

Reflectarrays are sometimes a replacement for phased arrays and small reflectorantennas; they offer a more compact envelope, and simpler circuitry. This chapterprovides a brief overview of reflectarrays; more detailed data are in Huang andEncinar (2008) and Bhattacharyya (2006). Retrodirective arrays, both passive andactive, have recently become of interest, and are also covered.

13.1 REFLECTARRAYS

13.1.1 History of Reflectarrays

The reflectarray was invented by Malech et al. (1962, 1963), although a patent onarray lenses makes a brief mention of a mirror array (Jones et al., 1961). The firstreflectarray consisted of a closely packed planar array of open-ended waveguidesfed by a horn in front of the waveguide array. Each guide was shorted and the guidelengths were chosen to compensate for the feed-to-guide path; the reflected wavewas then a plane wave. Figure 13.1 shows one of their experimental reflectarrays.The next step occurred in the early 1970s with the invention of the spiraphase reflec-tarray by Phelan. This work is described in a four part series of papers in MicrowaveJournal (Phelan, 1974, 1977). Here the array of open-end waveguides is replacedby an array of four-arm spiral antennas. By controlling the spiral feed points bydiodes, the phase of the reflected field can be rotated. This system is inherently wide-band, but diode performance restricts spiraphase capabilities. The jump from wave-guides to patches was made by Malagisi (1977) in 1976; patch reflection phaseswere controlled by diodes on the patch edges; the diodes allowed electronic scanning.

Phased Array Antennas, Second Edition. By R. C. HansenCopyright # 2009 John Wiley & Sons, Inc.

479

This work was continued by Montgomery (1978). The next step occurred �1987when Munson (1987) devised a fixed-beam patch reflectarray, where each elementhad a shorted feed line, with the feed line lengths adjusted to collimate the reradiatedbeam. Work continued on patch reflectarrays, but little was published until themid-1990s. The most useful of these are discussed in the following sections.

13.1.2 Geometric Design

For flat reflectarray with a feed subtended angle of 2u0, the f/D is

f=D ¼ 0:5tan u0

(13:1)

Feeds are usually horns and the electric field pattern is commonly approximated bycosnu. Spillover efficiency is given by

hs ¼ 1� cos2nþ1 u0 (13:2)

Aperture taper efficiency is (Pozar et al., 1997):

ht ¼4n[1� cosn�1 u0]2

(n� 1)2 tan2 u0[1� cos2n u0](13:3)

FIGURE 13.1 Waveguide reflectarray.

480 REFLECTARRAYS AND RETRODIRECTIVE ARRAYS

Finally, the overall optical efficiency is

h ¼ hs �ht (13:4)

Figure 13.2 shows the peak overall efficiency h, and the feed pattern exponent N, allversus f/D. It is apparent that for a wide range of f/D, from 0.5 to 1.5, the efficiencyvaries only slightly, from 0.78 to 0.81. This allows the reflectarray designer to choosef/D on the basis of feed choice (cosn u0) and mechanical convenience. Probably smallf/D and low h are the best choices.

13.1.3 Elements

The original reflectarray elements were, of course, open-ended waveguides. Printedcircuit elements have largely superceded them. Concentric circular ring elementswere developed for FSS (Huang et al., 1994). It required many years for ring elementsto transition to reflectarrays. Chaharmir et al. (2006a,b) use double square ringelements, and double cross loops. Printed strip dipoles are also used (Chaharmiret al., 2006c). Patches and strip dipoles have been combined for dual band operation(Shaker et al., 2000).

FIGURE 13.2 Efficiency and feed pattern exponent.

13.1 REFLECTARRAYS 481

13.1.4 Phasing of Elements

The direct way of phasing a patch reflectarray starts with calculating the excess pathlength of an edge element compared with an element at radial distance, r. An edgepatch would have feed line length ¼ 0; a center patch would have feed line length of

1=2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

D2=4þ f 2p

� fh i

(13:5)

while a patch at radial distance r from the reflectarray center needs a feed line length of

1=2ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r2 þ f 2p

� fh i

(13:6)

The factor of 1/2 occurs as the feed line and is shorted, while the wave is reflected. Inthe simplest implementation, all feed line lengths are decreased by multiples of l untilline length is ,l. This produces a phasing bandwidth, as shown in Figure 13.3.Figure 13.4 sketches a patch reflectarray phased by shorted feed lines.

A second technique phases the reflectarray by rotating the patches, analogous tothe spiraphase reflectarray (Huang and Pogorzelski, 1998; Chaharmir et al., 2009).Figure 13.5 sketches this example.

FIGURE 13.3 Bandwidth using phase shift.


FIGURE 13.4 Phasing by line length.

FIGURE 13.5 Phasing by patch rotation.


A third technique uses patch size to control phase (Encinar, 2001). Here the patchesdo not have feed lines; the phase of the reflected field is related to the patch size. Avariable patch size reflectarray is sketched in Figure 13.6. Phase versus patch size isgiven by Pozar and Metzler (1993). A Floquet unit cell analysis has been given byTsai and Bialkowski (2003). Phase characteristics were investigated by Bialkowskiand Sayidmarie (2008).

A novel technique uses patches of equal size, with each patch fed by a slot in theground plane (Chaharmir et al., 2003). Varying the slot lengths varies the phase ofthe coupling.

All of these involve phase; if the bandwidth of Figure 13.3 is not comfortably largerthan the patch bandwidth, time delay can be used. Here each patch has a shorted feedline of length equal to one-half of Eq. (13.6). This equation provides beam collimationindependent of frequency.

Cross-polarization can be significantly reduced by placing the feed lines and shortssymmetrically (Chang and Huang, 1995).

Polarization may be changed by rotating the feed of the array (Wu et al., 2006).

13.1.5 Bandwidth

Two factors control reflectarray bandwidth (BW): element and path length BW. With aflat reflectarray, the path length from the feed phase center to each element varies (for

FIGURE 13.6 Phasing by patch size.


broadside radiation). The phase error is (k 2 k0)(R 2 f ), where the wave number is k.Allowing the phase error to be p at both upper and lower frequencies gives(Pozar, 2003):

p ¼ k � k0ð Þ r � fð Þ ¼ k0 � k1ð Þ r � fð Þ (13:7)

Here, r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

D2=4þ f 2p

. The bandwidth is then:

BW ¼ 1D

l

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

f 2=D2 þ 1=4p

� f =Dh i

(13:8)

Figure 13.3 shows bandwidth versus f/D for D/l ¼ 25, 50, and 100. For example,with f/D ¼ 0.5 for D/l ¼ 25 the bandwidth is 19%. Clearly, this exceeds mostpatch bandwidths. Large reflectarrays (large D/l) may not allow sufficient bandwidthusing phase; the simple solution is to use lengths of transmission line to terminate thepatches. This, just as in a phased array, eliminates path length bandwidth restrictions.

Patch reflectarray bandwidth is usually limited by the element (patch) bandwidth.For a resonant patch over a dielectric slab of thickness t and dielectric constant 1r, thebandwidth is approximately:

BW ’ 4t

l0ffiffiffiffiffiffiffi

21rp (13:9)

Several methods exist for BW improvement. The simplest uses a low-loss magneticsubstrate instead of the dielectric slab. Hansen and Burke (2000) showed that a sub-strate with modest m and low 1 would provide a significant BW increase over thepatch with dielectric substrate. For example, a patch with 1 ¼ 1, m ¼ 20 providesmore than three times the BW of a patch with 1 ¼ 1, m ¼ 1. A low-loss magneticmaterial is Metaferrite, which consists of a stack of very thin laminated sheets, eachwith a pattern of magnetic materials (proprietary product of Metamaterials LLC,Austin, TX).

Another technique for increasing BW uses patches with one or two parasiticpatches above the primary patches (Bhattacharyya, 1999). This reference appears tobe the first two-layer patch reflectarray work. Of course, two-layer patches for directradiating arrays have been known for years. Books that discuss parasitic patchdesign include James and Hall (1989), Zurcher and Gardiol (1995), Sainati (1996),Lee and Chen (1997), Wong (2003), and Kumar and Ray (2003). Related papersare Encinar (2001), Tsai and Bialkowski (2003), and Encinar and Zornoza (2003).

13.1.6 Reflectarray Extensions

Reflectarrays can be configured for beam scanning and amplification. Just as a phasedarray is scanned, the reflectarray is scanned by insertion of phasers (phase shifters) ordelayers (time delay) in the element feed lines. Typically, diode switches (Martynyuk


et al., 2003) or MEMS (Legay et al., 2003) are used to select one of several lengths ofline to provide the requisite phase shift. This complexity and loss removes much of theadvantage of the reflectarray. Another configuration uses varactor diodes to connect asplit patch thereby controlling the phase (Hum et al., 2005). An exotic scheme uses ahigh-resistivity silicon slab under the patch elements; optical excitation of the slabcontrols a photoinduced plasma and thus controls the phase (Chaharmir et al.,2006d). Still another scheme uses a hybrid and diode mixers to steer the beam(Cabria et al., 2006).

Another configuration uses patch elements, each contains a slot that couples todelay lines underneath (Carrasco et al., 2008).

When dual polarized elements with separate feeds are used in the reflectarray,low-power amplifiers may be applied at each element, receiving a signal at one port(polarization), amplifying it, and transmitting it out the second port (cross-polarization) (see Robinson et al., 2000). Amplifier gain must be comfortablyless than the element cross-polarization level in order to prevent instability.Alternatively, the incurring modulation can be removed, and applied to a new carrierfrequency (Cutler et al., 1963).

Cassegrain reflectarrays have also been used (Pozar et al., 1997). A Gregoriansystem can also be used, where the subreflector is hyperboloidal instead of paraboloi-dal. Due to aperture blockage, feeds are sometimes offset using Cassegrain orGregorian subreflectors or even a direct offset feed. For all these geometries, theusual design constraints exist. The direct offset feed exacerbates the phasing band-width problem, but for modest D/l the bandwidth may be limited by the elementbandwidth (see Chapter 5).

Multiple feeds can provide multiple beams, or a shaped-beam for particular earthcoverage (Pozar et al., 1999; Zornoza and Bialkowski, 2003; Encinar and Zornoza,2004; Carrasco et al., 2008).

Shaped-beam coverage can be provided by adjusting the element phases (Encinarand Zornoza, 2004), and then in a second step adjusting element sizes to improve theBW while maintaining the desired phase at each patch.

13.2 RETRODIRECTIVE ARRAYS

13.2.1 History of Retrodirective Arrays

The retrodirective array (Fig. 13.7) was invented by Van Atta (1959). Each arrayelement is connected to another array element by transmission lines of equal lengths.Almost immediately a difficulty arose, when Sharp and Diab (1960) showed that thebackscatter RCS is comparable to the reradiated wave. This difficulty is readily over-come by changing polarization, frequency, or modulation, or by adding amplification.Several of these were explored for communications satellites by Hansen (1961).Steady interest in these arrays resulted in a March 1964 special issue of the IEEEAP Transactions. Van Atta arrays are sometimes called “self-focusing”; a betterterm would be “self-collimating”. Sichelstiel and Waters (1964) discuss an array


with frequency shift. Of course, with any change in frequency the BW must be con-sidered. Andre and Leonard (1964) consider a retrodirective array for satellite use;both frequency offset and polarization change are considered. This requires elementsthat handle both polarizations. A more common technique, which trades element com-plexity for circuit complexity, is phase inversion at each antenna element. This inver-sion allows the retrodirective array to have any shape, although grating lobes mustalways be considered. Gruenberg and Johnson (1964) use a balanced mixer, wherethe LO frequency is close to the signal frequency. The second harmonic of the LOand the signal frequency are mixed; the lower sideband frequency has the invertedphase [see also, Pon (1964)]. A tunnel-diode has also been used instead of themixer (Rutz-Phillipp, 1964). Use of dual mixers (see Section 13.2.2) was pioneeredby Skolnik and King (1964).

13.2.2 Recent Progress

As sometimes happens in science, a large time gap occurred after the 1964 papers.Tausworthe and Chernoff (1979) introduced a chain-phase conjugation circuitwhere one antenna element is used to generate a phase reference, which is thenpassed onto the next element; each element has a phase conjugation circuit using

FIGURE 13.7 Van Atta retrodirective array.

13.2 RETRODIRECTIVE ARRAYS 487

mixers [see also Luxey and Laheurte (1999)]. However, the complexity outweighs anyadvantages. Another variation utilizes an incoming signal plus an incoming pilotcarrier, using mixers (Brennan, 1989). The mixer-phase inverter previously described(see Fig. 13.8) is susceptible to reflection at the antenna terminals due to impedancemismatch, and to leakage from the input port of the mixer to the output port. Theeffect of leakage has been assessed by Toh et al. (2002). Major leakage can be avoidedthru use of two mixers (Chang et al., 1998). Good RF–IF isolation is provided by adual channel-phase conjugator (see Fig. 13.9). The delay line causes RF cancellationat the RF–IF port, and the two channels have a 1808 delay at the RF–IF port, therebyproviding good IF isolation (Miyamoto et al., 2000, 2001, 2003).

Subharmonic mixing avoids the problem of an LO frequency that is too high. In thisarrangement, dual mixers are used with the LO frequency one-half of the signalfrequency (Lim et al., 2005; Lim and Itoh, 2008). As sketched in Figure 13.10, thefirst mixer output is connected to the second mixer input through a low pass filterthat removes the LO leakage and the incoming RF signal.

Another scheme to avoid using an LO twice the signal frequency uses a double-balanced harmonic mixer (Brabetz et al., 2001) (see Fig. 13.11). The LO signal is can-celed in the rat-race hybrid, providing good LO–IF isolation. The LO is at the signalfrequency, easing the LO requirement. The RF leakage thru the two mixers is in phase;this can be remedied thru use of two harmonic mixers in a circuit that cancels both RFand LO signals (see Fig. 13.12).

FIGURE 13.8 Rudimentary mixer-phase inverter.


FIGURE 13.9 Mixer-phase inverter with delay line.

FIGURE 13.10 Subharmonic mixing-phase inversion.

13.2 RETRODIRECTIVE ARRAYS 489

FIGURE 13.11 Subharmonic phase-inverter using ratrace hybrid.

FIGURE 13.12 Phase inversion with RF and LO cancellation.


Still another scheme for obtaining phase inversion utilizes quadrature hybrids ter-minated with loads similar to those used in reflection phasers. With this arrangementthe input and output lines are reversed so crossover circuits are used (Hsieh and Chu,2008). This technique has not yet been fully evaluated. When the hybrid terminationsare reflection amplifiers, a bidirectional amplifier results (Chung et al., 2003).

Returning to the array as a scatterer, the performance of a retrodirective array hasbeen analyzed in terms of the field scattered from the patches, the field scatteredfrom the ground plane, and the reradiation field (Chung and Chang, 1998; Tsenget al., 2000). The scattered field introduces oscillations in the reradiated field, andslightly increases the peak value of the total field.

13.2.3 Advanced Applications

Use of a retrodirective array in a full duplex communications system requires specialdesign to avoid retransmitting the received signal. A PSK signal can be received andthe modulation stripped off. Then the carrier can be phase inverted and remodulatedwith a new PSK signal (DiDomenico and Rebeiz, 2001). Another approach usesorthogonal modulations for receive and transmit (Leong and Itoh, 2005). Frequencyoffset between receive and transmit is another option (Cutler et al., 1963; Karodeand Fusco, 1999).

When a retrodirective array is on a moving platform, the frequency transmitted isrelated to the phase-inversion circuit open-loop gain. The high gains requiredfor good retrodirection may be incompatible with certain platform motions(DiDomenico and Rebeiz, 2000).

An unusual application of a retrodirective array with phase inversion uses noisecorrelation to accelerate the detection of targets. In this system, the LO frequency istwice the carrier frequency. Correlator circuits augment the noise from the target direc-tion (Gupta and Brown, 2007).

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phased array antennas || reflectarrays and retrodirective arrays

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