Supplement: Aerospace, Military and Defence


Combining the best of both worlds: True time delays and phase shifters


By Bilgin Kiziltas, field applications engineer, Analog Devices P


hased array RADAR applications are a trend mainly in military and defence applications as they have advantages compared to traditional RADAR applications. This is because different beamforming methods could be implemented to ensure a higher performance of the complete system. This article reviews the strengths and weaknesses of two electronic beamforming techniques: phase shifters (PSs) and true time delays (TTDs). It argues that these two methods can be combined in a hybrid beamforming architecture to offer better SWaP-C and a comparatively less complex system design.


Introduction


Electronically scanned arrays (ESAs) utilise PSs or TTDs or a mix of both to point the summed beam toward the desired direction within an array’s steering angle limits. Adjustable attenuators used for tapering can also be considered as beamforming elements. This article discusses where and how a tiered approach between TTDs and PSs in the same ESA can be helpful to mitigate some phased array design challenges.


Leveraging fundamental formulas to explore possible scenarios Instantaneous bandwidth (IBW) can be defined as the frequency band where no tuning is required to stay within the target performance criterion set by the system requirements.


TTDs exhibit constant phase slope over frequency; therefore, ESAs implemented with TTDs instead of PSs do not have beam squint effect. As a result, TTD-based ESAs are more convenient for high IBW applications. PSs exhibit constant phase over their operating frequency range; hence, a particular phase shifter setting throughout the system results in different beam steering angles for different frequencies. As a result, PS-based arrays tend to have narrower IBW compared to TTD-based arrays.


20 October 2023


This phenomena is called beam squint and it can be calculated using Equation


1 where ∆θ is peak squint angle, θ0 is maximum beam angle, f0 is carrier frequency, and f is instantaneous signal frequency.


when 6-bit 5.6° LSB PSs are used behind every antenna element would be approximately ≅ 0.056° by Equation 3.


Using Equation 1, we can calculate


that ∆θ at worst case, that is at the low frequency edge (carrier at 3GHz and instantaneous signal at 2.9GHz), is around 1.15° for ±30° beam steering angle system for a signal at 3GHz with 100MHz IBW. Changing beam steering angle to ±60° and IBW to 200MHz results in around 8.11° beam squint at worst case. It is evident that TTDs can be a better choice even in radar applications. Arguably, phase shifter dominance in ESAs can be explained by the fact that PSs have had wider market availability due to their design simplicity and cost advantage over TTDs. If we had a TTD that meets the system requirements, how could it be reasonable to use PSs in the same signal chain? To investigate, a 32 × 32 square ESA with


d = λ/2 lattice spacing (d) between antenna elements desired to operate between 8GHz and 12GHz with ±60° scanning angle will be examined and EIRP criteria is assumed to be met for all scenarios (Figure 4). In this example, the system beamwidth in both azimuth and elevation would be ≅ 3.17° at boresight (θ = 0°) and ≅ 6.35° at the max scan angle (θ = 60°) by the half power beamwidth approximation formula for a uniform linear array given in Equation 2 where N is the number of elements on one axis and θB is the beamwidth in degrees on the same axis.


Approximately 1.3 ps LSB TTDs would be required to replace 5.6° LSB PSs to have a 0.056° beam angular resolution at 12GHz by Equation 4 that is used for conversion between time and phase shift.


The beamwidth value is considerably greater than the beam angular resolution even at very


small scan angles and placing PSs on the same line with TTDs to compensate for beam angular resolution would introduce additional beam squint and beam angular resolution degradation into the system. In practice, the reason to have finer TTD resolution is to have lower quantization sidelobe levels (QSLL) rather than having finer beam angular resolution. As the frequency goes higher, designing a TTD with a required time resolution to meet the target QSLL criteria gets relatively more difficult than designing a PS with a required phase resolution; hence, PSs can be a companion of TTDs to achieve the target QSLL while still having an acceptable level of beam squint. Another reason to implement PSs and TTDs in the same ESA could be to mitigate


Figure 1. Nonsquint free wideband cross polarisation with phase shifters behind the V and H feeds of antenna elements.


Figure 2. Squint free narrow-band cross polarisation with true time delays behind the V and H feeds of antenna elements.


The maximum beam angle resolution θRES_MAX of this array in one dimension


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