In this article, we provide a comprehensive review of past and present efforts in the field of microwave nonreciprocity with an emphasis on the most commonly used nonreciprocal devices, namely gyrators, isolators, and circulators. After discussing the origin and history of such efforts, we elaborate on the pros and cons of four distinct approaches to break reciprocity which include magnetic biasing of ferrite materials, intrinsic nonreciprocity of solid-state devices, nonlinearities with geometric asymmetries, and finally, periodic spatiotemporal variation. We subsequently pay due attention to the spatiotemporal approach and show that the recently emerging proposals to achieve magnet-free nonreciprocity with linear, periodically time-varying circuits can compete with traditional ferrite devices and even outperform them in several metrics, thus opening the door to exciting venues for miniaturized low-cost and high-performance nonreciprocal devices with numerous applications ranging from full-duplex communications and quantum computing to biomedical imaging and radar systems.

Microwave Nonreciprocity

The concept of microstrip radiators, introduced by Deschamps in 1953, remained dormant until the 1970s when low-profile antennas were required for an emerging generation of missiles (James & Hall, 1989; Garg et al., 2001; Volakis, 2007). Since then, but mainly over the last three decades, the international antenna community has devoted much effort to theoretical and experimental research on this kind of radiator (Lee & Chen, 1997). Currently, low-loss RF laminates are used in their fabrication and many of their inherent limitations have been overcome (Garg et al., 2001). On the other hand, low-cost solutions are in demand now that both market and technology are ready for mass production (Gardelli et al., 2004). Recently, the design of single-fed circularly-polarized (CP) microstrip antennas manufactured with FR4 substrate was reported (Niroojazi & Azarmanesh, 2004). Unfortunately, the use of low-cost FR4 as the substrate introduces some additional complexity on the antenna design. This is due to the inaccuracy of the FR4 relative permittivity and its high loss tangent (around 0.02). Variations in the FR4 electrical permittivity can shift the operating frequency and the high loss tangent dramatically affects the antenna axial ratio and gain, resulting in poor radiation efficiency. To increase the efficiency, microstrip antenna on moderately thick substrate must be designed. However, the technique used to compensate for the probe inductance, when the patch is fed by a coaxial probe (a known practical way to feed microstrip antennas), still relies on the designer’s expertise. For instance, a series capacitor, which may be constructed in several ways, has been utilized to neutralize this inductance (Hall, 1987; Alexander, 1989; Dahele et al., 1989; Vandenbosch & Van de Capelle, 1994; Nascimento et al., 2006), or the probe geometry has been modified (Haskins & Dahele, 1998; Teng et al., 2001; Chang & Wong, 2001; Tzeng et al., 2005). Unfortunately, due to their complexity, many such techniques are not suitable when the antennas are series-produced in an assembly line. To overcome some of the abovementioned issues, two efficient techniques for designing low-cost probe-fed microstrip antennas are proposed. Using only their intrinsic characteristics, linearlyand circularly-polarized microstrip antennas can now be designed without the need for any external matching network. Limitations of the proposed approach will also be discussed. The chapter is organized as follows: Section 2 covers the design of linearly-polarized microstrip antennas; results obtained with the new approach are compared with those using the standard design technique. Circularly-polarized antennas

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Design of Low-Cost Probe-Fed Microstrip Antennas

A new strategy for designing probe-fed electrically equivalent microstrip radiators based on their electrical dimensions is discussed in this article. Radiators on a Flame Retardant 4 (FR4) substrate are synthesized for equivalent performance, aiming at lower H-plane cross polarization over the bandwidth and resistive input impedance at the operating frequency. The effect of mutual coupling is analyzed for two classical arrangements: side-by-side and collinear configurations. With the proposed strategy, a broadside collinear array of linearly polarized rectangular patches is designed to operate at the center frequency of the industrial, scientific, and medical (ISM) band (2.45 GHz) on a moderately thick FR4 substrate. The array is designed for low cross polarization in the H-plane and to comply with the specified directivity and side lobe level (SLL). Special attention to the beamforming circuit design leads to a radiation efficiency near 70%.

/pdf/design-of-arrays-of-linearly-polarized-patch-antennas-on-an-1wqbd9wh6k.pdf

Design of Arrays of Linearly Polarized Patch Antennas on an FR4 Substrate: Design of a probe-fed electrically equivalent microstrip radiator.

We report a self-biased, low-profile circulator operating in the Ka-band fabricated by an entirely low-temperature (70 °C) screen-printing approach on printed circuit board (PCB). The magnetic material for the circulator is a barium hexaferrite BaFe12O19 (BaM)/polydimethylsiloxane (PDMS) nanocomposite that exhibits a zero-bias ferromagnetic resonance frequency ( $f_{\mathrm {FMR}}$ ) at 46.6 GHz. Using this material, a microstrip-based circulator operating at 35 GHz is designed, fabricated, and characterized. A combination of mechanical milling, screen printing, photolithography, and electroplating is used for fabricating the circulator, in which the circulator disk (diameter of 2 mm and thickness of $250~\mu \text{m}$ ) is completely embedded in the PCB, realizing a packaging compatible low-profile architecture with the total device area of 33 mm2. The measured isolation (IS) and insertion loss (IL) of the fabricated circulator at 35 GHz is 3.9 and 8.7 dB, respectively. When the additional magnetic bias is applied to the circulator using external permanent magnets, the IS and IL performance is improved to be 7.4 and 8.4 dB, respectively. The impact of the loss factors associated with dielectric loss and surface roughness on the device performance is analyzed using High Frequency Structural Simulator (HFSS).

35-GHz Barium Hexaferrite/PDMS Composite-Based Millimeter-Wave Circulators for 5G Applications

This article reports on the design and practical development of RF co-designed MMIC components that exhibit the function of a bandpass filter and an RF isolator. They are based on cascaded non-reciprocal frequency-selective stages (NFSs), one-pole/two-transmission zero (TZ) multi-resonant stages, and impedance inverters. The combination of these components results in a two-port network that exhibits a nonreciprocal quasi-elliptic bandpass filter (NBPF) response in the forward direction and full RF signal cancellation in the reverse one. The operating principles of the NBPF are presented through various circuit-based design examples of low- and high-order configurations. For proof-of-concept demonstration purposes, NBPF prototypes were designed on an MMIC GaAs process and were experimentally validated at $X$ -band. They include a two-pole/two-TZ NBPF and a three-pole/four-TZ NBPF.

X -Band Quasi-Elliptic Non-Reciprocal Bandpass Filters (NBPFs)

This article presents a study of the impact of different external magnetic bias field (MBF) distributions on Y-junction microstrip ferrite circulator performance. By using magnetostatic, full-wave, and circuit commercial simulation tools for a circular ferrite disk, several permanent magnet (PM) configurations are investigated for unsaturated and nonuniform bias conditions. Eigenmode simulations are used to analyze the circulator bandwidth over a range of MBF intensities. We show in simulations and experiments that different bias conditions can result in an operating frequency range from 1.5 to 7GHz using the same 9.7-mm-diameter commercial ferrite disk resonator.

Microstrip Ferrite Circulator Design With Control of Magnetization Distribution

This paper reports on a new class of miniaturized RF circulators with bandpass filtering capabilities. They are based on capacitively-loaded ferrite disk resonators that occupy a 64% smaller area than conventional RF circulator architectures. Frequency selectivity is achieved by introducing four transmission zeros (TZs) below and above the circulator passband. The spectral locations of the TZs are controlled by i) the position of the capacitive load on the ferrite-based disk and by ii) incorporating resonant-type external coupling elements to its input, output and isolated ports. In this manner, non-reciprocal quasi-elliptic type power transmission responses can be obtained, which eliminate the need for additional RF filtering elements in the RF front-end. For proof-of-concept validation, two microstrip prototypes are designed, built and measured at 2.5 GHz, achieving 2.2 and 1.4 dB minimum insertion loss, and 33.4 and 30 dB maximum isolation in the pass-band and are presented in this manuscript for the first time.

Frequency Selective Ferrite Circulators with Quasi-Elliptic Transmission Response

A modeling approach for the design of microstrip ferrite circulators is presented and validated on several examples using the same commercially-available ferrite disk. A baseline narrowband 4.2S-GHz microstrip circulator is first demonstrated with a commercial 4.97-mm radius ferrite disk operated in saturation and below the ferromagnetic resonance. The non-uniform DC magnetic field distributions of a cylindrical permanent magnet is taken into accout by spatial discretization of the ferrite properties in full-wave simulations. Several design parameters are shown to affect the frequency response; the ferrite thickness relative the microstrip substrate thickness shifts the operating frequency, while external matching networks can increase the fractional bandwidth from 10% up 40%. Another degree of freedom is the applied DC magnetic field, which can be reduced to set the ferrite operation below the ferromagnetic resonance with significant miniaturization of the overall device, as demonstrated with a 1.6-GHz circulator designed with the same 4.97-mm radius ferrite disk, resulting in an almost factor of 3 reduction in linear electrical size.

Design-Oriented Modelling of Microstrip Ferrite Circulators

The analysis of XPol suppression techniques in linear arrays reveals that, even though some particular structures can cancel these fields efficiently, the geometrical composition of the entire array affects the side lobe levels. Previous reports have proposed geometries where the Chebyshev SLL control technique is not effective. This work presents a novel geometrical approach, whose radiation pattern response to excitation is similar to that of uniformly spaced arrays, allowing more precise SLL control. Experimental results validate this new approach; mismatches between simulated and measured results can be imputed to variations in the laminates' relative permittivity and BF circuit manufacturing process. In addition, the XPol performance can be further improved by insulating the BF circuit with a metallic cover.

High-performance, low-cross-polarization suspended patch array for WLAN applications

This letter presents the design and characterization of an octave-bandwidth, small-aperture, linearly polarized, high-gain horn antenna operating in the 6–12 GHz band for active arrays. The aperture size is limited by the waveguide feed cutoff at lower frequencies and by grating lobes at higher frequencies. The radiating structure is composed of an E-plane flared horn with an exponential double ridge fed by a low-loss waveguide-to-microstrip transition, eliminating the need for additional connections between the antenna elements and the beamforming and amplification circuits. The horn is loaded with an artificial dielectric with 1  $  2.2, which lowers the cutoff frequency and improves phase distribution over the aperture. The lens and feed loading structure are designed together to improve matching without degrading the radiation pattern. A prototype is fabricated in brass using split-block machining, and the lens is machined from 16 parallel dielectric slabs. The measured performance is in agreement with simulations.

Laila Marzall

Papers

Microstrip Ferrite Circulator Design With Control of Magnetization Distribution

Frequency Selective Ferrite Circulators with Quasi-Elliptic Transmission Response

Design-Oriented Modelling of Microstrip Ferrite Circulators

High-performance, low-cross-polarization suspended patch array for WLAN applications

Broadband Small-Aperture High-Gain Ridge Horn Antenna Array Element