Scaling Non-Foster NGD-Based Squint-Free Series-Fed Antenna Arrays: Large-Array Gain, Noise, and Stability Accumulation, Mutual-Coupling-Accurate Beam Pointing, and Continuous Beam Steering

Series-fed antenna arrays are compact and low-loss but inherently squint: the beam direction drifts with frequency because the feedline phase progression is frequency-dependent. Mirzaei and Eleftheriades (IEEE Trans. Antennas Propag., 2015) removed this limitation for arbitrary design angles by inserting, between adjacent radiating elements, loss-compensated negative-group-delay (NGD) networks that synthesize stable non-Foster fast-wave sections with amplifiers providing loss compensation and power distribution, and demonstrated a squint-free four-element array at 30 degrees over 1--1.5 GHz. The paper itself identified the unresolved obstacles to making this architecture practical: cascading many NGD-amplifier sections accumulates excessive out-of-band gain (risking amplifier saturation and intermodulation), accumulates in-band noise (degrading signal-to-noise ratio toward the end of the array), scales DC power consumption, and raises stability concerns because high out-of-band gain combined with mutual coupling between antenna elements can close unintended feedback paths through free space; in addition, mutual coupling between the radiating elements shifts the measured beam angle (about 1 degree at a 30 degree design angle, worse toward endfire) without an available characterization or mitigation, and the demonstrated steering was limited to switched, discrete angles. This problem asks for the extension of the architecture to large-scale arrays with quantified signal-integrity, power, and stability budgets, a full characterization and mitigation of mutual-coupling effects on beam-pointing accuracy, and tunable NGD networks enabling continuous squint-free beam steering beyond existing two-element, narrow-band proofs of concept.

Background

A series-fed linear antenna array feeds its radiating elements sequentially from a single transmission line, in contrast to a corporate (parallel) feed that splits power through a tree of dividers; the series feed is more compact and lower loss but suffers from beam squint, an unwanted change of the beam direction and pattern shape with frequency. For a linear array with inter-element spacing $d_E$ measured along the feed axis, squint-free beamforming at a fixed angle $\theta_m$ from broadside (broadside is the direction perpendicular to the array axis; $\theta_m=90^\circ$ corresponds to endfire, radiation along the array axis) requires the phase progression between adjacent elements to satisfy $\Delta\phi=-k d_E \sin\theta_m$ (with $k$ the free-space wavenumber) at every frequency in the band. If the feedline section between two adjacent elements fills the spacing $d_E$, this condition translates into a required dispersionless feedline phase velocity $v_p=c/\sin\theta_m$: for any angle other than endfire this is superluminal ($v_p \geq c$), which passive transmission lines cannot provide, and passive fast-wave structures such as hollow waveguides are dispersive, meaning their phase velocity varies with frequency. Non-Foster reactive elements (negative capacitors and negative inductors, so called because they violate Foster's reactance theorem, which states that the reactance of any passive lossless one-port increases with frequency) can, when used to periodically load a host line, reduce the effective propagation constant and raise the phase velocity; however, ideal non-Foster loaded unit cells have poles in the right half of the complex frequency plane and are unstable when cascaded. Mirzaei and Eleftheriades had earlier shown (IEEE Trans. Microw. Theory Techn., 2013) that loss-compensated negative-group-delay (NGD) networks — active circuits whose transmission phase increases with frequency over a band, so that the group delay, defined as the negative derivative of phase with respect to angular frequency, is negative — can realize equivalent non-Foster behavior, and that using unilateral (one-directional) amplifiers for loss compensation yields inherently stable, cascadable 'unilateral non-Foster' sections. Sievenpiper (IEEE Antennas Wireless Propag. Lett., 2011) had likewise proposed non-Foster superluminal waveguides for broadband squint-free leaky-wave radiation (a leaky-wave antenna radiates power continuously along a guiding structure, so its beam angle is set by the guide's propagation constant and therefore also squints when that constant is dispersive). Building on this, the 2015 source paper derived the required NGD value $\tau_{NGD}=-(d_E/c)[\sqrt{\varepsilon_{r,eff}}(1-(d_{NGD}+d_{AMP})/d_E)-\sin\theta_m]-\tau_{AMP}$ for an arbitrary design angle (accounting for the physical footprints of the NGD network and amplifier and the amplifier's own group delay), introduced a distributed NGD network topology, and demonstrated a four-element array on RO4003C laminate (a low-loss commercial microwave circuit-board material) at 1--1.5 GHz with squint-free beamforming at 30 degrees, switched steering to $-30$ degrees, 0 degrees, and 60 degrees, an active +3 dB-per-section power distribution scheme, and time-domain pulse fidelity across the band. Two physical effects central to the open problem are: mutual coupling, the electromagnetic interaction between neighboring radiating elements by which signal from one antenna re-enters the feed through another, perturbing the designed amplitude and phase progression; and the fundamental NGD loss-bandwidth tradeoff, quantified by Kandic and Bridges (IEEE Trans. Circuits Syst. I, 2011), whose asymptotic bound on the negative-group-delay-bandwidth product of active distributed circuits limits how much dispersion compensation a given active network can deliver. Related stability analysis tools for multi-element non-Foster networks (implemented with negative-impedance converters, active circuits whose input impedance is a scaled negative of their load) were later developed by Suarez and Ramirez (IEEE Trans. Microw. Theory Techn., 2018).

Problem Statement

Extend the NGD-synthesized non-Foster series-feed architecture of Mirzaei and Eleftheriades (2015) into a scalable, steerable, squint-free series-fed array, resolving the three coupled obstacles the source paper left open. (1) Large-scale arrays: analyze and experimentally demonstrate the method for arrays with a large number of cascaded NGD-amplifier feedline sections, quantifying and controlling (i) the accumulation of the NGD networks' excessive out-of-band gain along the feedline, which can drive downstream amplifiers into saturation and intermodulation from low-level out-of-band signals or amplified noise (an input filter mitigates this only partially); (ii) in-band noise accumulation from the successive amplifiers and NGD networks (whose noise figure equals their attenuation), which degrades the signal-to-noise ratio toward the end of the array; (iii) the DC power consumption and efficiency trade-off among NGD network loss, bandwidth, and required amplifier gain; and (iv) stability, since the high out-of-band gain combined with mutual coupling between antenna elements can establish unintended feedback paths through the surrounding space. (2) Mutual coupling: fully characterize the effect of mutual coupling between the radiating elements on the beam-pointing accuracy of such feeds (the four-element prototype pointed about 1 degree off its 30-degree design angle, with larger errors toward endfire) and incorporate the characterization into the feed design so that the pointing error is corrected or bounded. (3) Continuous steering: extend tunable NGD networks beyond the demonstrated two-element, plus/minus 15 degree, approximately 5%-bandwidth proof of concept so that continuous squint-free beam steering is achieved at arbitrary design angles in arrays of many elements. The single overarching objective is a quantitatively characterized series-feed design methodology that delivers squint-free arbitrary-angle beamforming with specified noise, linearity, DC-power, and stability budgets at array scales of practical interest — concretely, an array of at least sixteen cascaded NGD-amplifier feedline sections; the three obstacles in (1)–(3) are coupled.

References

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