Efficiency Principles for Phased-array Radars Using Active Antenna Elements
Efficiency design principles for active antenna arrays are presented and discussed. A dual-antenna then is shown to be a design that easily implements the efficiency principles and also offers other advantages for radars.
Jesse C. James
An active array utilizes a transmit-receive (TR) module for each radiating element. The array may contain thousands of elements, so the generated power of each module need not be large to produce a large total radiated power. TR modules at VHF may occupy several cubic meters, but at X-band they may occupy only a few cubic centimeters. It is difficult to generate high power in a single transmitter at super high frequencies and above, but an active phased array solves this problem. Furthermore, line losses are high at these frequencies but lines are short from the TR modules to the elements. The emphasis in this article is on active antenna arrays at X-band frequencies and above, but the principles apply to all frequencies.
TR Module Efficiency
In effect, the TR module consists of a miniature transmitter and low noise receiver plus switches and phasing networks. The efficiency of the modules is important because, for a given antenna aperture, transmitter power and receiver noise figure, TR losses determine the sensitivity of the radar. The losses within the transmitter and between the transmitter and antenna element determine the ratio of radiated power to generated power. Radiated power is directly related to sensitivity. Losses between the antenna element and the receiver increase the system noise figure during receive, and it is this system noise figure that is related directly to sensitivity.
Inefficient TR modules lead to heat losses in the array, which must be removed by a cooling system. It is not unusual for much more energy to be removed as heat than is radiated. Large heat removal systems occupy valuable space in the array and are expensive and noisy. Figure 1 shows a block diagram of a typical TR module.
The system noise figure of the radar receiver is the weighted average of the system noise figures of the TR modules. The system noise figure is just the module noise figure referred to the antenna element, that is, losses between the element and the module receiver are included. These losses occur in lines, connectors, switches, circulators, polarizers, protective devices and lossy radiating elements. A loss of x dB only adds x dB to the noise figure provided the lossy item is at normal temperature.
It is important to keep the system noise figure low because an increase in noise figure by a certain factor requires an increase in radiated power by the same factor to maintain the same radar sensitivity. For this reason, the polarizing device, if used at all, should be placed after the first amplifier when possible and not before (as is often the case). Ideally, the antenna element should be soldered directly to the first amplifier input via a short lead, or connected by a low loss fuzzy button. Micro-electromechanical system (MEMS) solid-state switches that operate at 1 ms are also reported to have very low loss and thus may be preferred to circulator protectors.
The tiny transmitters in X-band TR modules may produce between 0.25 and 15 W with power-added efficiencies (PAE) of 15 to 60 percent. At present, the higher power units produce the power by combining the outputs of several solid-state units. Losses in the combining circuits are quite large and decrease efficiency. Small-power units have greater efficiency.
Although improvements are being made in the design of X-band power amplifiers, it appears that greater PAEs occur for the smaller output power units. At X-band, a 10 W amplifier may have a PAE of 15 to 20 percent, but a 0.25 W amplifier with a PAE of 60 percent has been reported.6 The gain and phase across the frequency band of each amplifier are also better controlled for a single small-power unit.
When the transmitters consist of amplifiers in tandem, an intermodulation problem exists. Intermodulation results when two signals separated in frequency by f are input simultaneously to a nonlinear amplifier. The output of that amplifier will be the amplified signals at the two frequencies plus intermodulation products. These products are spurious signals and are separated in frequency from the two input signals by the difference f in their frequencies. There may be several sets of these products both above and below the frequency of the input signals (all separated by f). When the output of the first amplifier with many frequency pairs enters a second nonlinear amplifier, the output will have many spurious components above and below the two original signals in frequency. This condition appears as a big smear above and below the desired signals as viewed on a spectrum analyzer. It occurs in a TR module when several stages are used to generate the output power, even when the drive power is clean. A filter could be used, but adds loss. When only one amplifier stage is used and the drive power is clean, there will be few spurious signals in the transmitted signal.
TR Module Cost
The cost of TR modules can be 40 percent or more of the total cost of a large array. The cost of one reported 10 W X-band TR module is approximately $400 in large quantities.1 In quantities of 100,000 or less, the cost may be closer to $1000 each. The module typically would have a PAE of 20 percent or less and a noise figure of 3 or 4 dB. The noise figure of the preamplifier alone would be 0.5 dB, and the efficiency of a single power amplifier alone would be approximately 60 percent. The switching and protective devices in the module increase noise figure and decrease efficiency. When the outputs of several power amplifiers are combined to produce greater power, the losses in the combining circuits are large.
By comparison, the retail cost of a single low noise amplifier at 4 GHz for satellite television is $35 to $45. The $35 and $45 models have 90 K and 60 K noise temperatures, respectively. When quantities of radar TR modules approach one million or less, their costs should decrease to these values. (The noise temperature of a device having a noise figure NF is 290(NF - 1) Kelvins.)
The Required Number of TR Modules
Normally, one TR module serves one antenna element. When one module serves several elements, the additional required power-splitting devices between the element and the TR module decrease efficiency. The number of modules required usually depends on the number of elements, which, in turn, depends on the desired total aperture and element spacing.
The spacing of elements is critical. An antenna element has an inherent effective area that is directly related to element maximum gain. When the physical spacing allows an area for each element that is comparable or larger than the element effective area, very little mutual coupling among elements takes place. On the other hand, large spacings lead to grating lobes of the array pattern. These lobes can have the same gain as the main lobe and radiate as much energy.
The gain or magnitude of grating lobes is often decreased by the element pattern because the overall antenna array pattern is the product of the array and element patterns. The element pattern is affected by nearby elements, but this effect is not large unless the spacing is very small.
For an array having a uniform element spacing larger than one-half wavelength, at least one scan angle will produce a grating-lobe beam in a direction other than the intended scan angle Q0. However, a spacing of one-half wavelength produces large mutual couplings for elements that have effective areas larger than 0.25 square wavelength. A half-wave dipole one-quarter wavelength above a ground plane has an effective area of 0.52 square wavelength, so the mutual coupling at half-wavelength spacing is large for such a dipole because the allotted area is only 0.25 square wavelength. A spacing of 0.7 wavelength would have very little mutual coupling, but grating lobes would be a problem. In this case, a compromise of 0.63 wavelength spacing should be considered.
For evenly spaced elements, the limiting value of array scan angle that produces no grating lobes is
Theta0 =arc sin((1/d)-1)
where, d = the separation of rows in wavelengths normal to the scan direction.
When an antenna element with a gain larger than a dipole is used, the elements must be placed farther apart on the array plane. As a result, fewer TR modules will be required. This configuration causes other problems, including the presence of array grating lobes when the array is phased to look at angles not near broadside. The larger the effective area of the antenna elements, the smaller the solid angle of space to which the array can be phased without grating lobes (assuming the elements are placed so that the effective area of each is approximately the physical area allotted). Also, elements with larger effective areas have smaller element beamwidths. This fact also limits the solid angle of space over which the array will radiate or receive signals. A lossless antenna element with an effective area of 0.25 square wavelength when alone above a ground plane would be highly desired, but has not yet been found. A good compromise for element spacing is often one that allows a physical area equal to 65 to 80 percent of the effective area.
Phasing and Amplitude Accuracies
An increase in phasing accuracy causes an increase in array gain and a decrease in sidelobe level. The integral of normalized antenna gain over all space is unity, which means that when the main beam gain goes up, the average sidelobe level usually goes down, and vice versa.
The 38 MHz MIT El Campo solar radar array comprised 1024 dipole elements covering nine acres. In the 1960s, the array was phased manually by changing lengths of RG-8 cable with type N connectors at each dipole. Four lengths of phasing cable were available at each dipole. The cables had lengths of 1/2, 1/4, 1/8 and 1/16 wavelength, resulting in four-bit phasing. This phasing process required six man-hours. Today, modern defense radars using six bits can phase adjust in 6 ms or less. The smallest phasing length for a six-bit phaser is 1/64 wavelength.
Phased arrays have been built that use as few as three and as many as seven bits in the phasing network. The phase-shift network may be in the TR module. A three-bit accuracy means the phasing is correct within ±1/16 wavelength. A seven-bit accuracy means the phasing is correct to within 1/256 wavelength. The increased antenna gain is insignificant when the number of bits is increased above four, but the change in sidelobe level may be significant.
For any phasing bit increase to be effective, the tolerances in such things as element placements, line lengths and phase shifters must be less than the phase of the smallest bit. These unwanted tolerance errors can be accounted for by the phasing computer provided they are known and change little with time. For example, to be consistent with a six-bit accuracy at X-band, the line lengths and antenna element placements must be accurate to ±0.00925". This accuracy is not practical, unless the errors are stable, and can be measured and accounted for during phasing. One way to measure such errors is to provide an external radiating source of sufficient magnitude and phase stability so that each element alone receives measurable power. Each element then can be calibrated individually.
Pointing accuracies and antenna gains are not appreciably improved by using phasing accuracies larger than four bits. In addition, phase coherence between pulses of successive beams is very high for a phasing accuracy of just three bits, provided the phasing reference is fixed to some point on the array face and the array is not mechanically rotated.
During receive, signals from all elements of the array are combined at a sum point after passing through lines, protective devices, preamplifiers, attenuators and phase shifters. The lowest sidelobes are produced when the phases and amplitudes of all these useful signals are equal. Unaccounted errors - or discrepancies in amplitude and phase from the ideal - cause a decrease in array gain. When phase errors are dominant and the smallest phase increment is 2I, the power-gain factor is ((sin I)/I)2.
For example, for a three-bit phase shifter, the smallest phase increment is 1/8 wavelength, I is 22.5° and the power-gain factor is 0.22 dB, representing the decrease in antenna gain from the ideal. As long as phase errors are dominant and the gain loss shows up in sidelobes, the average sidelobe level decreases 6 dB for each bit increase in phase increment (at least within a certain limit).10 A change of one in the number of phasing bits is a factor of two in phasing accuracy and four in the variance of phase error, hence the 6 dB. Sidelobe level is related to the sum of the variances of phase and amplitude errors.
Amplitude errors have an effect similar to that of phase errors. The normalized RMS values of phase and amplitude are of equal importance. For example, an RMS fluctuation of 0.24 V of normalized amplitude among the elements at the sum point causes the same average sidelobe level as a three-bit phase shifter. In other words, when the mean voltage from all elements at the sum point is 1 V but is distributed from approximately 0.7 to 1.3 V, the effect on the average sidelobe level is about the same as a three-bit phase shifter. Normally, attenuators are used to keep element channel gains approximately equal.
Advantages of Dual Antennas for an Active Radar
A two-antenna radar can easily implement the efficiency principles enumerated here. Furthermore, a two-antenna radar has other advantages over a one-antenna radar. One antenna is used for transmit and another antenna, about one mile away, is used for receive. A bistatic radar system often has synchronization problems, but this dual system is not a typical bistatic system. Rather, it is a monostatic system with the transmitter located a mile away rather than a few feet away. The added cost of two antenna frames is expected to be offset by a greater efficiency that results in less required transmit power for the same sensitivity. Most, if not all, defense radars in the US use one antenna for both transmit and receive.
For a dual-antenna radar, the TR module is replaced by a transmit-only and a receive-only unit, and protective and switching devices are not needed because of the physical separation. Additional advantages include an increase in radar sensitivity because of no loss due to switching and protective circuits, decreased power and cost per transmit module, greater flexibility for upgrades and increased efficiency resulting in decreased cooling cost. When one of the antennas was made slightly larger than the other so that the first sidelobe of one fell at the first null of the other, a decreased two-way close-in sidelobe level resulted. This situation occurs when one aperture is approximately twice the size of the other, as shown in Figure 2 . Note that the first sidelobe for the dual system is down 6 dB relative to the single antenna.
The transmit array has one antenna element fed by each low power amplifier, and the power is added in space where combiner losses are zero. Many broad-beam elements are required. These elements are physically small and are manufactured in groups with amplifiers attached.
A two-antenna system with aperture diameters in the ratio of 1.4 will be more power efficient and have greater sensitivity and 6 dB smaller close-in sidelobes than a single antenna system with the same two-way antenna gain. The two-antenna system has greater pulse scheduling flexibility and greater angular resolution during receive. It also is more amenable to upgrades, and spurious transmissions are less. Furthermore, smaller-gain elements minimize the grating lobe problem, and the useful electronic scan region increases.
For a constant range, cross section, waveform and noise figure, radar sensitivity is proportional to PD4 where P is total radiated power and D is the antenna diameter. A larger aperture also increases angular resolution.
Defense radars normally transmit circular polarization and receive both left and right circular polarizations. To accomplish this configuration in the dual system, the transmit array uses a circularly polarized element such as a helix, printed spiral or patch (if a low loss patch can be developed). Then a polarizer is not needed.
The elements may be placed 0.63 wavelength apart and fed by single-stage power amplifiers of 1 W or less. Element groups of 256 or more may be manufactured as individual panels to permit ease of installation and also to decrease costs and RF losses.
A suggested element for the receive array is a pair of crossed dipoles spaced 0.64 wavelength apart on a plate approximately one foot square and slightly larger than the transmit plates. The dipoles are one-quarter wavelength above the plate or ground plane and fed by two coaxial lines. With proper coaxial design, no balun is required because of the quarter-wave spacing above the ground plane. (Baluns are also lossy.) The output of each dipole is fed directly to the input of a low noise preamplifier, which has a gain of at least 15 dB. The outputs of the preamplifiers are combined and fed via another amplifier to a polarizer that converts the two linear polarizations to left and right circular polarizations.
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Jesse C. James received his BS in electrical engineering and BS in physics from Auburn. In addition, he received his MA in physics from Rice, and his PhD in electrical engineering from Georgia Tech. James has published 21 papers in scientific journals and two book chapters: "Radar Studies of the Sun" and "Practical Problems of Antenna Arrays." His experience has been equally divided between astronomical research and defense radar development. In addition, he has 10 patents mostly dealing with antennas, radar and defense procedures.