Lumped-element Circuit Research Articles

Analysis and Applications of Magnetically Coupled Resonant Circuits

Magnetically coupled resonant circuits have been utilized in radio engineering for many years. Recently, these circuits have found new applications, particularly in supplying low- and medium-power devices through medium-range wireless power transmission technology based on magnetic resonance coupling. There is also a growing need to analyze magnetically coupled resonant circuits in the design of metamaterials, which exhibit specific electromagnetic properties within certain frequency bands. This paper provides a coherent and concise overview of the phenomena associated with magnetically coupled resonant circuits. The results encompass numerous established relations as well as new ones. They can be helpful in the design phase of magnetically coupled resonant circuits. The outcomes include equations for determining the coupling resonant frequencies and some parameters of resonance curves. These analytical results are accompanied by 3D and cross-sectional (contour) graphs for better visualization. Moreover, a lumped-element circuit model that includes magnetically coupled resonant circuits is proposed for the resonators used in metamaterials. Formulas for resonant frequencies are derived in the specific case of exciting such resonators. To validate the accuracy of the derived equations, the analytical results are compared with simulations from SPICE (IsSPICE4 ver. 8.1) and COMSOL 5.4 software, which are widely used tools for circuit analysis and electromagnetic simulations. The results of these comparative analyses indicate that the assumptions employed in the analytical solutions introduce only tiny errors.

Scanning microwave impedance microscopy and its applications: A review

Scanning microwave impedance microscopy (sMIM) has become a powerful tool for nanoscale characterization, utilizing microwave frequencies to probe the material properties of diverse systems with remarkable spatial resolution. This review offers an in-depth analysis of the foundational principles, technological advancements, and broad applications of sMIM. By harnessing near-field microwave interactions between a sharp metallic probe and the sample, sMIM enables simultaneous acquisition of both real (resistive) and imaginary (capacitive) components of the reflected signal, providing detailed insights into the local permittivity and conductivity of materials at the nanoscale. We address critical challenges, including impedance matching, probe–sample interactions, and the influence of environmental factors such as surface water layers and meniscus formation on resolution and contrast. Recent advancements in finite element modeling and the application of lumped-element circuit models have further enhanced the precision of signal interpretation, enabling more accurate analysis of complex systems. This review highlights sMIM’s wide-ranging applications, from material science and semiconductor diagnostics to biological systems, showcasing its ability to perform non-destructive, high-resolution imaging down to the single-digit nanometer scale. These capabilities position sMIM as an indispensable tool for advancing future innovations in nanotechnology and related fields.

Mathematical modeling development and synthesis of tapered transmission line resonators and filters

Abstract Tapered transmission line resonators can be used to achieve specific frequency responses and enhance the performance of microwave devices and impedance transformers. To develop a mathematical model (transfer function) of such a wideband resonator will facilitate the construction of an equivalent circuit and the synthesis of resonators of this type. This study discusses the system modeling of tapered transmission line (TTL) resonators using the singularity expansion method (SEM). The transfer function is analytically established for two types of wideband TTL resonators: exponential tapered transmission lines (ETTL) and linear tapered transmission lines (LTTL). The analytical transfer function is derived for the general tapered ratio (k/β). The physical poles of the structures are identified using the pole-energy matrix pencil (MP) approach. The transfer function expression is then utilized to develop an accurate equivalent lumped-element circuit for the TTL resonator. This study’s simplified approach for estimating the transfer function and associated poles and zeros from the S-parameters is the main contribution, whereas it is known that the transfer function becomes complicated for wideband frequency response. A direct synthesis approach is presented to develop two-stage and four-stage ultra-wideband (UWB) bandpass filters. The agreement between the frequency response data and the derived transfer function of the system model of the synthesized TTL filters demonstrates the reliability of the presented method. The proposed system modeling and synthesis methodology can be applied to more sophisticated filter TTL architectures.

Small-signal model for inhomogeneous helix traveling-wave tubes using transfer matrices

We introduce a practical method for modeling the small-signal behavior of frequency-dispersive and inhomogeneous helix-type traveling-wave tube (TWT) amplifiers based on a generalization of the one-dimensional (1D) Pierce model. Our model is applicable to both single-stage and multi-stage TWTs. Like the Pierce model, we assume that electrons flow linearly in one direction, parallel and in proximity to a slow-wave structure (SWS) that guides a single dominant electromagnetic mode. Realistic helix TWTs are modeled with position-dependent and frequency-dependent SWS characteristics, such as loss, phase velocity, plasma frequency reduction factor, interaction impedance, and the coupling factor that relates the SWS modal characteristic impedance to the interaction impedance. For the multi-stage helix TWTs, we provide a simple lumped element circuit model for combining the stages separated by a sever, or gap, which attenuates the guided circuit mode while allowing the space-charge wave on the beam to pass freely to the next stage. The dispersive SWS characteristics are accounted for using full-wave eigenmode simulations for a realistic helix SWS supported by dielectric rods in a metal barrel, all of which contribute to the distributed circuit loss. We compare our computed gain vs frequency, computed using transfer matrices, to results found through particle-in-cell simulations and the 1D TWT code LATTE to demonstrate the accuracy of our model. Furthermore, we demonstrate the ability of our model to reproduce gain ripple due to mismatches at the input and output ports of the TWT.

Modeling of Microstrip line Gap Discontinuity on Multilayer Substrate

In this paper, the modeling of microstrip line gap discontinuity on multilayer semiconductor substrate is presented. The reflection coefficient and transmission coefficient are computed from the equivalent lumped circuit model of microstrip line gap discontinuity. The lumped circuit elements- capacitance, inductance and resistance are calculated using closed-form expressions in term of the gap discontinuity, width of microstrip line and dielectric substrate thickness. Static Spectral Domain Analysis (SDA) method is used to compute characteristic impedance of microstrip line.

Mathematical Model of a Rectangular Double Negative Meta‐Structure for 5G Applications

AbstractThis article introduces the mathematical formulation of a proven rectangular double negative (DNZ) metamaterial (MTM) structure using a lumped element circuit model in terms of RLC components for millimeter‐wave (mmWave) 28 GHz applications. The structure is developed on a 0.254 mm‐thick substrate material: Rogers RT/duroid 5880 with an area of 8.7 mm2. The model accounts for different losses inherent in the system; a series resistance to take into account the losses in the conductor and a shunt resistance to describe the losses in the dielectric substrate, addressing the finite conductivity of conducting materials, the finite resistivity of the dielectric material, and the presence of a dielectric substrate with metallic rings on top. By incorporating these factors, it is possible to precisely predict the resonance frequency associated with this specific structure, however limits the formulation from being applied to other shapes. Numerical validation demonstrates a good agreement with analytical predictions, affirming the model's reliability. The study provides a robust analytical foundation and numerical validation for the double negative metamaterial unit cell, advancing the mmWave 5G wireless technology field.

Symmetric CRLH-TL filter based dual band microstrip antenna design approach

This paper presents a novel filter-based analysis for the conventional rectangular patch antenna (RPA) using the Composite Right/Left-Handed Transmission Line (CRLH-TL) theory. We introduce two circuit models for RPA, described by lumped components and transmission line (TL) elements. An RPA is considered a Symmetric CRLH-TL (SCRLH-TL). We validated the analysis by comparing the circuit model and full-wave analysis simulation results. The TL circuit model error in the full-wave analysis was less than 5%. A dual-band Zeroth-Order Resonant (ZOR) antenna is designed and manufactured based on the introduced Lumped element circuit model, which exhibits filtering characteristics in both bands. We obtain the antenna circuit model by incorporating the RPA lump circuit model with LC resonators. We implemented the antenna structure by combining the RPA and complementary split-ring resonators (CSRR) modeled by the LC resonators. We initialized the antenna center frequency bands for WiMAX 2.45 GHz and 3.60 GHz. The CSRRs control the configuration of the center frequencies. The simulation and measured results are in good agreement. The proposed antenna dimensions are 0.66×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document}0.66×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document}0.012 λg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _g$$\\end{document} at 2.45 GHz (43.22×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document}43.22×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document}0.81 mm3). The measured gains are 3.47 dB and 4.64 dB for 2.45 GHz and 3.60 GHz, respectively. Two radiation nulls were observed at 2.09 GHz and 2.98 GHz for the 2.45 GHz band and one radiation null at 3.45 GHz for the 3.60 GHz band. Also, the fractional bandwidth is 4.03% and 1.39%, respectively. The radiation pattern is nearly omnidirectional. The simulated efficiency is 90% for 2.45 GHz and 87% for 3.60 GHz frequency bands.

Circuit-theoretic phenomenological model of an electrostatic gate-controlled bi-SQUID

Abstract A numerical model based on a lumped circuit element approximation for a bi-superconducting quantum interference device (bi-SQUID) operating in the presence of an external magnetic field is presented in this paper. Included in the model is the novel ability to capture the resultant behaviour of the device when a strong electric field is applied to its Josephson junctions by utilising gate electrodes. The model is used to simulate an all-metallic SNS (Al-Cu-Al) bi-SQUID, where good agreement is observed between the simulated results and the experimental data. The results discussed in this work suggest that the primary consequences of the superconducting field effect induced by the gating of the Josephson junctions are accounted for in our minimal model; namely, the suppression of the junctions super-current. Although based on a simplified semi-empirical model, our results may guide the search for a microscopic origin of this effect by providing a means to model the voltage response of gated SQUIDs. Also, the possible applications of this effect regarding the operation of SQUIDs as ultra-high precision sensors, where the performance of such devices can be improved via careful tuning of the applied gate voltages, are discussed at the end of the paper.

Plasmonic devices - equivalent circuit representations.

An equivalent circuit model for plasmonic slot waveguide-based devices is presented. Taking advantage of the high mode confinement provided by this waveguide geometry, we express plasmonic waveguide geometries using transmission line parameters and express T-junctions using lumped equivalent circuit elements. By combining these fundamental building blocks, we subsequently introduce equivalent circuit models for stub filters and branch-line couplers. We show that plasmonic circuits, if designed with sharp discontinuities, feature low losses that are comparable to losses from RF circuits and even the corresponding photonic circuits. The framework presented here gives insight into the design of novel microwave-inspired plasmonic devices and circuits and significantly speeds up the design time, as a large part of the geometry optimization can be performed in the equivalent circuit domain. For instance, we use this framework in a follow-up paper to design ultra-compact plasmonic hybrids, such as those needed for coherent detection.

Geometrical description and Faddeev-Jackiw quantization of electrical networks

In lumped-element electrical circuit theory, the problem of solving Maxwell's equations in the presence of media is reduced to two sets of equations, the constitutive equations encapsulating local geometry and dynamics of a confined energy density, and the Kirchhoff equations enforcing conservation of charge and energy in a larger, topological, scale. We develop a new geometric and systematic description of the dynamics of general lumped-element electrical circuits as first order differential equations, derivable from a Lagrangian and a Rayleigh dissipation function. Through the Faddeev-Jackiw method we identify and classify the singularities that arise in the search for Hamiltonian descriptions of general networks. The core of our solution relies on the correct identification of the reduced manifold in which the circuit state is expressible, e.g., a mix of flux and charge degrees of freedom, including the presence of compact ones. We apply our fully programmable method to obtain (canonically quantizable) Hamiltonian descriptions of nonlinear and nonreciprocal circuits which would be cumbersome/singular if pure node-flux or loop-charge variables were used as a starting configuration space. We also propose a specific assignment of topology for the branch variables of energetic elements, that when used as input to the procedure gives results consistent with classical descriptions as well as with spectra of more involved quantum circuits. This work unifies diverse existent geometrical pictures of electrical network theory, and will prove useful, for instance, to automatize the computation of exact Hamiltonian descriptions of superconducting quantum chips.

Design of a microstrip Wilkinson power divider using a low pass filter with the particle swarm optimization algorithm

In this paper, a microstrip Wilkinson power divider (MWPD) based on particle swarm optimization (PSO) algorithm is designed, simulated, and fabricated using novel resonators. In addition, attenuators and open-ended stubs are incorporated to generate a broad cut-off band and reduce unwanted harmonics. The proposed power divider has a central frequency of 1 GHz. The performance of each used resonator is analyzed based on lumped-element circuit models.The L and C parameters of the equivalent circuit of the used resonators are predicted and optimized with the assistance of the PSO method. The subsequent phase was the fabrication of the proposed MWPD, after which its performance was evaluated in the light of the results obtained from the simulation. It was discovered that there was a high degree of concordance between the two. On the other hand, the fabricated circuit has several benefits, including a suitable S12 of − 3.15 dB, a high return loss of less than − 24 dB at the operating frequency, a compact size of 0.058 λg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\lambda}}_{{\\varvec{g}}}$$\\end{document} × 0.064 λg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\lambda}}_{{\\varvec{g}}}$$\\end{document}, and the ability to remove undesired harmonics. The results show a high level of suppression of the unwanted harmonics (up to the 16th harmonic) and a great responsiveness in the passband, while having very low ripple. As a result, the proposed circuit may be used in a wide variety of electronic devices, such as radar transmitter and receiver circuits, and many other high-frequency systems.

High power, broadband, coaxial to microstrip bi‐directional coupler in the VHF/UHF band

AbstractBroadband couplers consist usually of multiple coupled lines that are each a quarter wave‐length long. Herein, in contrast to conventional methods, a short length of a microstrip line is coupled to a coaxial line. The length of the coupled microstrip line is small compared to the wavelength at the lowest operating frequency. The coupling is weak and the microstrip line is λ/8 at the highest operating frequency. The proposed structure resembles a pair of coupled lines with a linear coupling response. The coupling exhibits a slope of 6 dB/octave over multi‐octave bandwidth. The microstrip line is connected to a lumped element compensating network at the coupled port. The compensating network is a low‐pass circuit with a slope of −6 dB/octave. The power handling of the coupler is high due to the coaxial line and the weakly coupled microstrip line. Electromagnetic simulations and analytical formulations are presented. The broadband coupler handles nearly 1 kW of input power. Due to the weak coupling of the microstrip‐coaxial coupler, the lumped element circuit needs to handle <1.5 W. A high‐power coupler has been fabricated for the frequency range of 30 to 500 MHz. It exhibits a coupling response of 56 ± 0.4 dB.

Dynamics of Leaky Integrate‐and‐Fire Neurons Based on Oxyvanite Memristors for Spiking Neural Networks

Neuromorphic computing implemented with spiking neural networks (SNNs) based on volatile threshold switching is an energy‐efficient computing paradigm that may overcome future limitations of the von Neumann architecture. Herein, threshold switching in oxyvanite (V3O5) memristors and their application as a leaky integrate‐and‐fire (LIF) neuron are explored. The spiking response of individual neurons is examined as a function of circuit parameters, input pulse train, and temperature and reveals a pulse height‐dependent spike rate in which devices exhibit excitatory spiking behavior under low input voltages and protective inhibition spiking under high voltages. Resistively coupled LIF neurons are shown to exhibit additional neural functionalities (i.e., phasic, regular and adaptation, etc.) depending on the input voltage and circuit parameters. The behavior of both individual and coupled neurons is shown to be described by a physics‐based lumped element circuit model, which therefore provides a solid foundation for exploring more complex systems. Finally, the performance of a perceptron SNN employing these LIF neurons is assessed by simulating the classification of image recognition algorithm. These results advance the development of robust solid‐state neurons with low power consumption for neuromorphic computing.

Entangling Interactions Between Artificial Atoms Mediated by a Multimode Left-Handed Superconducting Ring Resonator

Superconducting metamaterial transmission lines implemented with lumped circuit elements can exhibit left-handed dispersion, where the group and phase velocity have opposite sign, in a frequency range relevant for superconducting artificial atoms. Forming such a metamaterial transmission line into a ring and coupling it to qubits at different points around the ring results in a multimode bus resonator with a compact footprint. Using flux-tunable qubits, we characterize and theoretically model the variation in the coupling strength between the two qubits and each of the ring-resonator modes. Although the qubits have negligible direct coupling between them, their interactions with the multimode ring resonator result in both a transverse exchange coupling and a higher-order ZZ interaction between the qubits. As we vary the detuning between the qubits and their frequency relative to the ring-resonator modes, we observe significant variations in both of these interqubit interactions, including zero crossings and changes of sign. The ability to modulate interaction terms such as the ZZ scale between zero and large values for small changes in qubit frequency provides a promising pathway for implementing entangling gates in a system capable of hosting many qubits. Published by the American Physical Society 2024

Collective neural network behavior in a dynamically driven disordered system of superconducting loops

Collective properties of complex systems composed of many interacting components such as neurons in our brain can be modeled by artificial networks based on disordered systems. We show that a disordered neural network of superconducting loops with Josephson junctions can exhibit computational properties like categorization and associative memory in the time evolution of its state in response to information from external excitations. Superconducting loops can trap multiples of fluxons in many discrete memory configurations defined by the local free energy minima in the configuration space of all possible states. A memory state can be updated by exciting the Josephson junctions to fire or allow the movement of fluxons through the network as the current through them surpasses their critical current thresholds. Simulations performed with a lumped element circuit model of a 4-loop network show that information written through excitations is translated into stable states of trapped flux and their time evolution. Experimental implementation on a high-Tc superconductor YBCO-based 4-loop network shows dynamically stable flux flow in each pathway characterized by the correlations between junction firing statistics. Neural network behavior is observed as energy barriers separating state categories in simulations in response to multiple excitations, and experimentally as junction responses characterizing different flux flow patterns in the network. The state categories that produce these patterns have different temporal stabilities relative to each other and the excitations. This provides strong evidence for time-dependent (short-to-long-term) memories, that are dependent on the geometrical and junction parameters of the loops, as described with a network model.

Numerical impedance matching via extremum seeking control of single-frequency capacitively coupled plasmas

Abstract Impedance matching is a critical component of semiconductor plasma processing for minimizing the reflected power and maximizing the plasma absorption power. In this work, a more realistic plasma model is proposed that couples lumped element circuit, transmission line, and particle-in-cell (PIC) models, along with a modified gradient descent algorithm (GD), to study the impact of presets on the automatic matching process. The effectiveness of the proposed conceptual method is validated by using a single-frequency capacitively coupled plasma as an example. The optimization process with the electrode voltage and the reflection coefficient as the objective function and the optimized state, including plasma parameters, circuit waveforms, and voltage and current on transmission lines, is provided. These results show that the presets, such as initial conditions and objective functions, are closely related to the automatic matching process, resulting in different convergence speeds and optimization results, proving the existence of saddle points in the matching network parameter space. These findings provide valuable information for future experimental and numerical studies in this field.

New Complementary Resonator for Permittivity- and Thickness-Based Dielectric Characterization.

The design of high-performance complementary meta-resonators for microwave sensors featuring high sensitivity and consistent evaluation of dielectric materials is challenging. This paper presents the design and implementation of a novel complementary resonator with high sensitivity for dielectric substrate characterization based on permittivity and thickness. A complementary crossed arrow resonator (CCAR) is proposed and integrated with a fifty-ohm microstrip transmission line. The CCAR's distinct geometry, which consists of crossed arrow-shaped components, allows for the implementation of a resonator with exceptional sensitivity to changes in permittivity and thickness of the material under test (MUT). The CCAR's geometrical parameters are optimized to resonate at 15 GHz. The CCAR sensor's working principle is explained using a lumped-element equivalent circuit. The optimized CCAR sensor is fabricated using an LPKF protolaser on a 0.762-mm thick dielectric substrate AD250C. The MUTs with dielectric permittivity ranging from 2.5 to 10.2 and thickness ranging from 0.5 mm to 1.9 mm are used to investigate the properties and calibrate the proposed CCAR sensor. A two-dimensional calibration surface is developed using an inverse regression modelling approach to ensure precise and reliable measurements. The proposed CCAR sensor is distinguished by its high sensitivity of 5.74%, low fabrication cost, and enhanced performance compared to state-of-the-art designs, making it a versatile instrument for dielectric characterization.

Compact Quasi-Elliptic-Type Inline Waveguide Bandpass Filters With Nonlinear Frequency-Variant Couplings

This work presents the design techniques to synthesize a class of compact inline quasi-elliptic-type waveguide cavity bandpass filters based on novel nonlinear frequency-variant couplings (NFVCs). These highly dispersive frequency-variant couplings (FVCs) are realized by means of a pair of partial-height posts that are placed at the junctions between every two cavity resonators. Each NFVC produces a transmission pole in between a pair of independently adjustable transmission zeros (TZs). Although the pole is added to the overall filtering function to augment its order, the TZs can be placed at each side of the filter passband to attain sharp rejection capability and increase the stopband attenuation levels. To synthesize these filters, two coupling-routing-diagram (CRD) approaches for the NFVC are presented that either consider: 1) an arbitrary FVC (AFVC) or 2) two resonating nodes interacting with a zero-susceptance nonresonating node through constant inverters. An equivalent lumped-element circuit model associated with both CRD approaches is provided. It is demonstrated that both CRD models can be exploited for the theoretical synthesis of this type of filter, whereas the equivalent lumped-element circuit model can provide a deeper insight into the systematic dimensioning of the posts. For experimental validation purposes, three design examples are synthesized, and 10-GHz proof-of-concept filter prototypes of two of them are EM-simulated, fabricated, and characterized. The measured results agree well with the simulations and the design theory, thus verifying the concept of inline waveguide cavity filters with TZs using NFVCs.

Compact dual-band balanced bandpass filter using CRLH resonator with intrinsic common-mode suppression and multiple transmission zeros

In this paper, a newly composite right-/left-handed (CRLH) resonator is presented and applied to constitute a compact dual-band balanced bandpass filter (BPF). The proposed CRLH resonator contains two spiral coupled line segments. By imposing the differential-mode (DM) and common-mode (CM) excitation, the DM and CM equivalent circuits of the presented resonator and their lumped-element circuit models are built for investigating the resonant property. The CRLH resonator has two DM resonances and are adopted to design two DM passbands. Also, the CM resonances are all far away from DM resonances, achieved intrinsic desirable CM rejection within DM frequency range without any auxiliary elements. Attributing to the mixed electric and magnetic coupling between two coupled resonators and the introduced source-loaded coupling, multiple transmission zeros are obtained and therefore enhance the selectivity and attenuation in stopband. Finally, a well-designed dual-band balanced BPF is fabricated. Verification of the presented structure and design method’s validity is evidenced by the measured results, which are in agreement with the simulations.

GHz operation of a quantum point contact using stub-impedance matching circuit

Quantum point contacts (QPC) are the building blocks of quantum dot qubits and semiconducting quantum electrical metrology circuits. QPCs also make highly sensitive electrical amplifiers with the potential to operate in the quantum-limited regime. Though the inherent operational bandwidth of QPCs can eclipse the THz regime, the impedance mismatch with the external circuitry limits the operational frequency to a few kHz. Lumped-element impedance-matching circuits are successful only up to a few hundreds of MHz in frequency. QPCs are characterised by a complex impedance consisting of quantized resistance, capacitance, and inductance elements. Characterising the complex admittance at higher frequencies and understanding the coupling of QPC to other circuit elements and electromagnetic environments will provide valuable insight into its sensing and backaction properties. In this work, we couple a QPC galvanically to a superconducting stub tuner impedance matching circuit realised in a coplanar waveguide architecture to enhance the operation frequency into the GHz regime and investigate the electrical amplification and complex admittance characteristics. The device, operating at ∼ 1.96GHz, exhibits a conductance sensitivity of 2.92×10−5(e2/h)/Hz with a bandwidth of 13MHz. Besides, the RF reflected power unambiguously reveals the complex admittance characteristics of the QPC, shining more light on the behaviour of quantum tunnel junctions at higher operational frequencies.