As a partial differential equation (PDE)-based time-domain algorithm, the discontinuous Galerkin time-domain (DGTD) method has to deal with a perfectly matched layer (PML) to mimic the infinitely large boundary condition. However, time-domain PML is notorious for its late-time instability, which often appears in an accidental and abrupt manner. This can be attributed to two underlying aspects: first, unlike in the physical region, the mathematical property of the governing equation is not guaranteed in the PML; second, the late-time instability indicates a treacherous manner in the numerical discretization system, since it often appears in a case-dependent way. To resolve these two issues in a consecutive procedure: 1) a Riemann-inspired PML formulation is derived that preserves the exact Riemann solver—the core of DGTD—and recasts the PML effects into a local source term; and 2) based on this structure, a locally implicit deferred correction (DeC) strategy is introduced into the computational electromagnetics (CEM) community for the first time, with only the PML-induced source terms treated implicitly. As a result, our DGTD solver becomes amenable to a variety of extremely long-time stable simulations for complex structures, including a point-source radiation case verified with analytical solution, a 10 000-period resonant cavity case where the benchmark commercial software fails at 700 periods, another two cases—almond and camera box with deep-cavity—verified with experimental radar cross section (RCS) measurement, and finally a large-scale aircraft case with over 100 billion unknowns.
Near-field radio frequency (RF) power distribution requires transmitting apertures that tolerate changes in position and receiver number. This article presents a double-layer orthogonally stacked magnetoinductive metasurface resonator near 6.78 MHz. Two capacitively loaded wire arrays form one collectively resonant aperture whose modal currents synthesize the vertical magnetic field. Over the ${\mathrm {335~mm}}~\times ~{\mathrm {335~mm}}$ footprint, the fabricated transmitter achieves 91.4% effective $\lvert H_{z}\rvert $ coverage at $z= {\mathrm {10~mm}}$ ; a nine-position scan gives 57.27% average peak port-to-port efficiency. The matched one-to-one link reaches 79.02% at 6.780 MHz. Three simultaneous-receiver layouts yield 77.89%–80.30% total efficiency and 14.88–24.71-percentage-point branch imbalance. At their efficiency maxima, the strongest receiver coupling is −8.55 to −7.67 dB. Applying the instrument’s port-2 reference-impedance conversion from 25 to $\mathrm {100~\Omega }$ gives 66.47%–79.02% maxima of the converted $\lvert S_{21}\rvert ^{2}$ metric; this conversion does not physically change the receiver termination. A collective-resonance model, a transmitter-only notch quality-factor descriptor of 150.89, and current-based modal reconstruction explain the aperture resonance, field synthesis, and receiver-coupling perturbation.
This article provides a novel design methodology for a substrate-integrated waveguide (SIW) dual-band bandpass filter (DBBPF) and a diplexer with large frequency ratios (FRs). First, an aperture-coupling topology is employed to route the low-frequency (LF) and high-frequency (HF) signals into dedicated LF and HF SIW elements, respectively. This enables each passband or channel to be independently controlled with good impedance matching. Second, to suppress undesired harmonics between interbands or interchannels, a novel miniaturized SIW bandpass filter (BPF) with an out-of-band rejection exceeding $17\boldsymbol {f}_{\mathbf {0}}$ ( $\boldsymbol {f}_{\mathbf {0}}$ is the operating frequency of the BPF) is proposed based on quarter-mode SIW (QMSIW) resonant cavities. Underlying the proposed design methodology, SIW DBBPFs with an FR exceeding 5 as well as diplexers with an arbitrary FR in the range of (0, 17] can be readily realized. Generally, typical design strategies for large-FR devices are limited by narrow operating frequency ranges. By contrast, SIW components based on the proposed method can realize a dramatically wider frequency span, capable of spanning the microwave and millimeter-wave bands. Finally, three large-FR SIW components are designed, fabricated, and measured to validate the proposed method.
This article presents the first generalized joined coupler (GJC) matrix-based architecture capable of simultaneously generating multiple independently steerable beams in 2-D. Built upon a conventional single-layer GJC matrix, the proposed dual-phase-controlled (DPC) GJC matrix introduces two independently tunable phase-control sets to realize decoupled beam steering in the azimuth and elevation planes. Unlike existing matrix-based beamforming networks (BFNs) that rely on stacked multilayer structures for 2-D beam scanning, the proposed architecture achieves 2-D multibeam scanning within a single-layer topology, significantly reducing hardware complexity and implementation cost. An inverse coupler synthesis (ICS) method is developed to optimize the coupling coefficients of the matrix. Numerical results demonstrate that the proposed matrix can generate multiple independently steerable beams and can be flexibly mapped to different antenna array configurations without modifying the hardware structure. To validate the concept, a fully integrated $4\times 8$ prototype is implemented using a folded multilayer PCB incorporating phase shifters, gain-compensation amplifiers, and an FPGA-based control module. Experimental results demonstrate simultaneous multibeam generation with independent steering in both azimuth and elevation, with a maximum gain variation of 2.6 dB and sidelobe levels below −8 dB.
Gradient-based inverse design is standard in computational photonics but rare in radio frequency (RF) and microwave engineering, where optimization still relies on derivative-free metaheuristics. We present rfx, a GPU-accelerated 3-D finite-difference time-domain (FDTD) simulator, written in JAX, in which the entire simulation—from time stepping and absorbing boundaries to port extraction and the near-to-far-field (NTFF) transform—forms a single differentiable graph. One reverse-mode automatic-differentiation (AD) pass returns the gradient of RF observables— $S$ -parameters, directivity—with respect to all design variables at a few times the cost of a forward solve, independent of their number; this backward pass is the discrete adjoint of the FDTD recursion, assembled automatically rather than hand-derived per objective. Forward accuracy is validated against closed-form References and a four-solver patch cross-validation including CST; the AD gradient is verified against central finite differences for every smooth observable class. Three examples of increasing dimensionality (one to 2883 design cells)—a microstrip notch filter, a waveguide taper, and a beam-steering superstrate—drive $S$ -parameter and far-field objectives directly; openEMS corroborates the optimized notch and steered beam. On the 30-variable taper, particle-swarm and genetic search at an equal-or-larger solve budget trail the gradient by at least 11.6 dB, and one backward pass returns all 2883 beam-steering cell sensitivities. Reoptimized at fabrication resolution, the taper matches—does not beat—a discretized Klopfenstein design. The designs exercise continuous permittivity and relaxed metal; free-form metal topology and conformal PEC remain open. The contribution is a differentiable formulation of RF observables, realized as an open-source simulator; sensitivity analysis and model calibration follow from the same gradient.
A radial power combining frequency doubler architecture based on circularly polarized TE11 and TE21 modes is presented in this article. In the proposed architecture, the input divider operates with the circularly polarized TE11 mode and generates $N$ fundamental signals with a progressive phase shift of $2\pi $ / $N$ . After frequency doubling, the phase progression of the generated second-harmonic signals is doubled to $4\pi $ / $N$ , which matches the phase condition required by a circularly polarized TE21-mode radial combiner. Therefore, the desired second-harmonic signals can be coherently combined by the TE21-mode radial combiner. Furthermore, the operating principle of the circularly polarized TE21-mode septum polarizer is analyzed, and the minimum number of combining paths required for the proposed architecture is derived from the modal excitation condition. It is shown that at least five paths are required to uniquely excite the desired single-handed circularly polarized TE21 mode. To verify the proposed topology, a 170-GHz five-way radial power combining frequency doubler was designed, fabricated, and measured. The measured results show an output power of 100–203 mW over 163–178 GHz. An average power combining efficiency (PCE) of 69% is achieved at an input power of 750 mW.
Conventional electromagnetic (EM) design is typically restricted to predefined frequency ranges. This article presents a language-driven generative framework for high-fidelity EM synthesis at arbitrary frequencies, incorporating physics-scaling-guided surrogate model (PSGSM) with vector to interval line preprocessing (VILP) and variable-controlled data collection (VCDC). The approach is defined by three methodological pillars. First, frequency scaling invariance is leveraged to decouple multiband responses into a normalized domain, enabling robust cross-frequency data/model reuse. Second, the VILP method transforms stochastic user vectors into structured, piecewise linear intervals, allowing the surrogate model to perceive continuous scaling trajectories rather than isolated points. Third, the VCDC strategy stabilizes the low-frequency resonance ( $f_{1}$ ) to isolate high-frequency variations ( $f_{2}$ ), ensuring data alignment with scaling logic and significantly enhancing sampling efficiency. The framework is validated through the design of a bandpass filter (BPF) and dual-passband frequency-selective surfaces (DP-FSSs). Experimental results from a fabricated DP-FSS prototype demonstrate high precision and flexibility in frequency-independent EM synthesis.
This article proposes a dual-polarized millimetre-wave phased array integrated with a compact hole-coupling feedback (FB) structure to support online digital predistortion (DPD) for handset applications. The integrated hole-coupling structure can capture the distortion signals of the power amplifiers (PAs) as the FB signal. Since the FB structure is integrated in the antenna element, the need for an additional coupling structure is eliminated, enhancing the compactness of the array. Using a single-pole four-throw (SP4T) switch (SW), the FB signal can be captured by the time-shared scheme without interruption of the signal transmission, enabling online updating. Measurement results show that the proposed FB structure has negligible impact on the radiation performance of the antenna. The radiation pattern of the phased array can scan from −45° to +45°. The DPD performance is validated using a 100-MHz 256-QAM 5G NR signal at a carrier frequency of 26 GHz. The measurement results show that the error vector magnitude (EVM) is reduced to below 3.5%, while the adjacent channel leakage ratio (ACLR) is improved to below −40 dBc, achieving performance comparable to that of conventional over-the-air (OTA) DPD across various steering angles.
Radio frequency integrated circuit (RFIC) design and optimization often involve exploring a large number of design variations in an invariant background, such as a fixed layer stack and unchanged circuit blocks. Conventional partial-differential-equation (PDE) solvers require simulating the entire domain for every design variation. In this article, we present a fast and accurate method that effectively separates the variant components from the invariant background by algebraically decomposing the field solution into the contributions from the design-dependent variations and the invariant background. Hence, the field solution due to the invariant background can be simulated once and reused for all design variations. Only the variant components need to be simulated for each design, the size of which is small. Moreover, we develop an efficient method for model fusion, allowing individual component models to be reused and fused into a system model while rigorously capturing the coupling between components. The proposed method involves computing the field solutions in the invariant background due to all possible sources located at variant components, the number of which can be large. We develop a fast algorithm to reduce them to a few field solutions, the number of which is only related to the layer number, independent of variant components. The proposed method has been applied to RFIC design space exploration. Its accuracy and efficiency have been demonstrated.
A compact and wideband diplexer with low insertion loss and broad stopband based on substrate integrated coaxial line (SICL) in single-layer printed circuit board (PCB) technology is presented. The proposed diplexer consists of two SICL resonators and matching networks. Multiple evanescent modes (TM01, TM11, and T ${\mathrm{M}}_{21}$ ) are excited in each resonator, which comprises a segment of SICL shorted at one end and loaded with four lumped capacitors. These evanescent modes enable the diplexer to achieve compact size, wide bandwidth, and low insertion loss and broadband out-of-band suppression. Furthermore, the resonant frequencies of the two SICL resonators can be independently determined, offering increased design flexibility. The proposed diplexer is fabricated with low-cost PCB technology and occupies a compact footprint of $43.9\times 30.7$ mm. It achieves a 1-dB fractional bandwidths of 17.0% for Channel I (center frequency $f_{\mathbf {1}}$ @ 1.88 GHz) and 16.7% for Channel II (center frequency $f_{\mathbf {2}}$ @ 3.06 GHz), respectively. The corresponding 3-dB fractional bandwidths are 19.7% for Channel I and 19.5% for Channel II. The in-band isolations are better than 36 and 42dB in Channel I and Channel II, respectively. Additionally, the diplexer features with a rejection level of 27 dB at 8.89GHz (approximately $4.75f_{1}$ ), demonstrating excellent stopband performance.
In this article, a 71–76 GHz eight-element isolated LO frequency distribution phased-array transceiver (TRX) using the direct-modulation transmitter (TX) and reflectionless sliding-IF receiver (RX) is proposed. Due to the different modulation and demodulation principles adopted in the TX and RX paths, respectively, the LO generates different frequencies for TX and RX to achieve the proposed TX/RX isolation without extra isolation elements or switching operations. Besides, for the TX path, the $2 \times 8$ -bit quadrature direct-modulator is used to generate the high-data-rate modulation signals. Meanwhile, for the RX path, to suppress the intermodulation (IM) and high-order mixing products, the signal absorption network (SAN) is adopted in a reflectionless RX architecture to reject the out-of-band (OOB) signal reflected back to the mixer. The proposed eight-element phased-array TRX is implemented in a conventional 40-nm CMOS technology. The fabricated phased-array TRX features 16.7–17.3 dBm TX output power and 6.3–6.7 dB RX noise figure within 71–76 GHz. Meanwhile, it shows typical 45.9 dBc isolation for TX and 52.1 dBc rejection for RX. The proposed eight-element TRX array steers a ±30° beam range and supports modulation signals for 4.8 Gb/s 16-QAM and 3 Gb/s 64-QAM.
Wireless sensors are vital for Internet of Things (IoT) applications, but battery dependence limits lifetime and contributes to electronic waste. Radio frequency (RF) backscattering sensors offer a sustainable alternative by reflecting RF signals without re-generating them, thereby achieving ultralow power consumption. However, resistive sensors, the most common type of industrial passive sensors, operate inherently in the DC domain and are generally incompatible with conventional RF backscattering devices. This article presents a passive backscattering device that employs a Schottky-diode-based DC–RF impedance conversion technique to enable direct compatibility with DC resistive sensors. Under −25-dBm excitation at 917 MHz, the device demonstrates a maximum reflection-coefficient variation of 0.342 as the load resistance changes from 1 to 100 k $\Omega $ . Wired modulation tests confirm analog amplitude modulation (AM) operation up to 100 kHz with the sideband signal as high as −8.0 dBc. Wireless image transferring was further demonstrated using a slow-scan television (SSTV) scheme over 2 m, with the transmitted image successfully recovered by a software-defined radio (SDR) receiver. These results confirm the feasibility of analog AM backscattering with DC resistive sensors and highlight potential extensions to amplitude-shift keying (ASK) and frequency-shift keying (FSK) modulation schemes.
Artificial neural network (ANN)-based surrogate models have been widely used to reduce the computational cost of electromagnetic (EM) optimization for microwave filters. However, repeated surrogate reconstruction in iterative optimization may still introduce considerable overhead as the design point moves. To address this issue, an adaptive neuro-coupling matrix (neuro-CM)-based surrogate optimization framework is developed in this article. In the proposed framework, coupling matrix (CM)-related intermediate variables are extracted from full-wave EM responses, predicted by ANNs, and then used for physics-based response reconstruction. The neuro-CM surrogate model is then embedded into a trust-region-based optimization procedure with full-wave EM validation. To further improve the efficiency of multiround surrogate reconstruction, a CM-related sensitivity-guided modeling region update strategy is introduced. Specifically, the design-error sensitivity is transferred from the intermediate-variable space to the geometrical-parameter space, and the modeling radii are allocated anisotropically according to parameter activity. In this way, subsequent surrogate reconstruction can focus on the parameter directions that are more relevant to performance improvement. Two microwave filter examples demonstrate that the proposed method reduces the number of surrogate reconstruction rounds and the total optimization time compared with the considered baseline methods.
A miniaturized bandpass filter with ultrawide stopband performance is proposed in this article. Based on two eighth-mode folded substrate integrated waveguide (FSIW) cavities, the proposed filter introduces two controllable transmission zeros (TZs) by employing cross couplings, adding a metal pin, and etching a defected ground structure (DGS). The generation principle and controllable characteristics of the two TZs are investigated in detail with an equivalent circuit model (ECM). As a result, it exhibits a 20-dB stopband that extends to $5.07~f_{0}$ ( $f_{0}$ is the center frequency) with a total size of only $0.094~\lambda _{g}^{2}$ ( $\lambda _{g}$ denotes the guided wavelength at $f_{0}$ ). Furthermore, taking the above high-performance filter as the fundamental unit, a balanced filter is achieved through the symmetrical placement of this unit in the vertical direction. By virtue of the fundamental characteristics of a perfect electric conductor (PEC) and a perfect magnetic conductor (PMC), a PEC-PMC-PEC hybrid electromagnetic (EM) boundary structure is formed under common-mode (CM) excitation. This structure prevents CM signal from exciting cavity resonant modes, ensuring effective CM suppression within the differential-mode (DM) passband. Ultimately, the proposed balanced filter reaches a 20-dB stopband up to $5.82~f_{0}$ under DM excitation, and achieves a CM suppression of over 54.7 dB, with a size of only $0.219~\lambda _{g}^{2}$ . To validate the design, both the aforementioned bandpass filter and balanced filter are fabricated. The measured results of each filter exhibit good agreement with their respective simulated results.
This article presents a neural recording probe for brain–machine interfaces (BMIs) using a miniaturized on-chip antenna for wireless communication. The proposed neural microprobe consists of a neural recording integrated circuit and a photovoltaic cell that receives wireless power using near-infrared light from a repeater unit, implanted at the skull. The neural recording circuit performs signal acquisition and processing, feature filtering, and uplink data communication to the repeater unit at a 2-mm distance. The uplink data communication is performed with power-efficient backscatter communication, using a $260{\,}{\,}\times {\,}{\,}274$ - $\mu $ m $\mathbf {^{2}}$ on-chip antenna and consuming 12.41 pJ/bit. To the best of the authors’ knowledge, the proposed neural recording system represents the smallest neural recording unit with radio frequency (RF) wireless communication capabilities. Each microprobe encodes the data with a random chip ID to enable code-division multiplexing to a single receiver. The off-chip receiver consists of a $2 {\,}{\,}\times {\,}{\,}2$ -mm $\mathbf {^{2}}$ antenna with a distributed matching network, a directional coupler, a low-noise amplifier, and a power detector. Concurrent wireless communication at 3 GHz of four units with the same receiver is demonstrated, and accurate motor function prediction results are presented, showing that near-field magnetic induction is a viable technique to communicate with microscale neural probes.
This article presents a highly stable injection-locked digital-phase-locked-loop optoelectronic oscillator (IL-DPLL OEO) employing an infinite-tuning-range microwave phase shifter for phase stabilization. The proposed phase shifter compensates delay variations inside the resonance loop, enabling stable operation over a wide temperature range without any thermal control. An FPGA-based digital feedback loop integrating phase detection and control is implemented to stabilize the oscillation phase. Experimental results demonstrate that, after locking to an external reference (REF), the generated microwave signal at 10GHz achieves an Allan deviation of $4.1 \times 10^{-14}$ at 1 s and $6.06 \times 10^{-15}$ at 10 s. Stable operation is verified over a $20~^{\circ }$ C temperature variation without loss of lock. The results confirm the effectiveness of the proposed stabilization scheme for high-stability optoelectronic oscillators (OEOs) operating under wide temperature variations.
The ladder network is widely considered to be the most effective topology for acoustic wave (AW) filters in wireless communication. It is composed of either surface AW (SAW) or bulk AW (BAW) resonators, which allow for device miniaturization, low insertion loss, and high selectivity. However, with the introduction of increasingly wider bands in new wireless communication standards, AW ladder filters face topological limitations, as they require an electromechanical coupling factor ( $k_{t}^{2}$ ) of approximately twice their fractional bandwidth (FBW). Although the $k_{t}^{2}$ can be increased beyond 15% using material systems such as scandium-doped aluminum nitride (ScAlN) or LNOI/LTOI, this typically comes at the cost of reduced quality factor. In contrast, bridge-T (BT) topologies decouple the relationship between the $k_{t}^{2}$ and the FBW through the introduction of balanced parallel-connected branches, enabling solutions that require significantly lower $k_{t}^{2}$ . This work presents the complete design methodology for four BT topologies that demonstrate excellent performance in broadband applications, including a lowpass filter (LPF), a highpass filter (HPF), an LPF–HPF cascade, and two bandpass filters (BPFs). Since wideband filters cannot be synthesized using narrowband techniques, a direct bandpass (DB) approach based on the coupling matrix (CM) is employed to achieve full control over the entire design procedure. For validation purposes, the four BAW-assisted filters are fabricated using Sc-doped AlN solidly mounted BAW resonators, achieving extremely wideband responses with FBWs of 33% and insertion loss below 1.5 dB across the entire passband. The total device area, including the die mounted on the laminate, is $3\times 2$ mm2.
We report the design, simulation, fabrication, and measurement of optically excited vanadium dioxide (VO2) switches operating from DC to 330 GHz, which is the widest demonstrated bandwidth among phase-change material (PCM) devices. PCM switches typically rely on integrated microheaters to excite the phase transition, which contribute parasitic capacitance that degrades performance at millimeter wave (mmWave) bands. We propose optical excitation as an alternative to microheaters, fully decoupling the PCM control from the RF signal and significantly enhancing the achievable bandwidth. In this work, a VO2-based single-pole, single-throw switch on sapphire is excited via topside optical injection using a 785-nm laser. The switches exhibit a competitive $R_{\mathrm {ON}}C_{\mathrm {OFF}}$ figure-of-merit of 10.9 fs, with wider demonstrated bandwidth, lower insertion loss (IL), and faster transition times compared to microheater-based PCM switches. The switch was measured across four bands spanning DC–330 GHz, with an average IL of 0.8 dB, >13.7 dB isolation (IX), and >15 dB return loss (RL) at room temperature. Furthermore, we demonstrate a turn-on time of 248 ns (10%–90%) and turn-off time of 283 ns (90%–10%). The maximum power handling at 2 GHz is 30 dBm in the on state and 39 dBm in the off state. The on state input third-order intercept point (iIP3) is 37 dBm at 2 GHz, and off state reflected iIP3 is >68 dBm up to $50~^{\circ }$ C. The minimum optical power to excite the phase transition is 37 mW, corresponding to a power density of 7.9 kW/cm2 at the center of the beam.
To address the high-frequency integration requirements of a millimeter-wave low-noise amplifier (LNA), through 3-D electromagnetic simulation optimization, equivalent circuit modeling, noise cascading, and microwave link budget analysis, the Ka-band LNA flip-chip integration based on a rectangular microcoaxial transmission line (R $\mu $ CL) vertical transition structure is implemented for the first time using flip-chip technology. Testing results of the R $\mu $ CL exhibit an insertion loss (IL) better than −1.12 dB and a return loss (RL) superior to −13.84 dB across the 40-GHz band. The integrated module exhibits a noise figure (NF) of 3.47–4.31 dB; the gain reaches 17–21 dB in the main band of 32–36 GHz and rolls off to 12.77–15.70 dB at 37–38 GHz, with an RL better than −10-dB over most of the band. No significant performance degradation is observed after three reflow cycle tests. Owing to inherent passive losses and high-frequency parasitics, there is a slight noise degradation, but this low-cost flip-chip scheme satisfies practical millimeter-wave engineering requirements with outstanding thermal cycling reliability. It provides new approaches and technical support for the high-frequency integration of millimeter-wave LNA chips and 3-D heterogeneous integration of multi-MMIC systems at elevated frequencies.
RF transversal signal-interference filters with co-designed in-band amplitude-equalization capabilities for both lowpass and bandpass applications are presented for the first time. These dual-function RF equalizer $\boldsymbol {/}$ filtering components are based on transversal filtering sections (TFSs) composed of two in-parallel stepped-impedance transmission-line paths. By exploiting an in-band frequency-selective RF-power-reflection mechanism inherent to this TFS topology, power transmission responses with adjustable amplitude slopes can be synthesized while preserving the sharp-rejection characteristics of conventional RF transversal signal-interference filters. The lowpass case is first addressed, demonstrating multitransmission-zero (TZ) extended-stopband lowpass filters (LPFs) with frequency-dependent in-band shaping, including controllable linear slopes in dB in one-level and multilevel amplitude-equalization profiles. Subsequently, equalizer bandpass filters (BPFs) based on the proposed TFS are introduced, featuring in-band amplitude responses with monotonic linear increase or decrease in dB versus frequency, together with multiple out-of-band TZs. Furthermore, the potential of these RF equalizer $\boldsymbol {/}$ BPF structures to implement advanced RF-analog-signal-processing functionalities is explored, such as causal finite-bandwidth approximations of integer-order and fractional-order temporal differentiators—i.e., time-delayed quasi-derivatives. For experimental-validation purposes, four microstrip prototypes are designed, fabricated, and characterized. These proof-of-concept circuits include DC-to-1-GHz RF LPFs with one-level and three-level negative-slope equalization, as well as two 2.5-GHz RF BPFs with positive in-band slopes, realized using one-stage reflective and two-stage in-band-matched $\boldsymbol {/}$ absorptive schemes, respectively.
