Showing papers on "RLC circuit published in 2016"

Wireless Power Transfer by Electric Field Resonance and Its Application in Dynamic Charging

Abstract: In this paper, the electric field resonance (EFR) method, similar to the four-coil configuration of the magnetic field resonance wireless power transfer, is proposed for the capacitive coupling power transfer. The characteristics of the proposed method are derived and analyzed. With the EFR method, not only unity power factor for the power source is achieved, but also high power factor and low reactive power for the capacitive coupling stage are achieved. Effective power transfer is realized by the EFR method. Based on the proposed method, a dynamic charging concept for railway vehicles is then proposed. A prototype powering system is designed and built to prove the validity of the proposed method. Analytical, simulation, and experimental results are given and compared. A 23-cm model vehicle is put on a 150-cm track. It is shown that about 700-W power is transferred through a 24-pF coupling capacitor. The proposed method reaches 91% dc–dc overall efficiency at switching frequency 2 MHz.

An Inductive and Capacitive Combined Wireless Power Transfer System With LC -Compensated Topology

Abstract: This paper proposes a combined inductive and capacitive wireless power transfer (WPT) system with LC -compensated topology for electric vehicle charging application. The circuit topology is a combination of the LCC -compensated inductive power transfer (IPT) system and the LCLC -compensated capacitive power transfer (CPT) system. The working principle of the combined circuit topology is analyzed in detail, providing the relationship between the circuit parameters and the system power. The design of the inductive and capacitive coupling is implemented by the finite-element analysis. The equivalent circuit model of the coupling plates is derived. A 3.0-kW WPT system is designed and implemented as an example of combined inductive and capacitive coupling. The inductive coupler size is 300 mm × 300 mm and the capacitive coupler is 610 mm × 610 mm. The air-gap distance is 150 mm for both couplers. The output power of the combined system is the sum of the IPT and CPT system. The prototype has achieved 2.84-kW output power with 94.5% efficiency at 1-MHz switching frequency, and performs better under misalignment than the IPT System. This demonstrates that the inductive–capacitive combined WPT system is a potential solution to the electric vehicle charging application.

Burst Mode Elimination in High-Power $LLC$ Resonant Battery Charger for Electric Vehicles

Abstract: In order to recover and fully charge batteries in electric vehicles, smart battery chargers should not only work under different loading conditions and output voltage regulations (close to zero to 1.5 times the nominal output voltage), but also provide a ripple-free charging current for battery packs and a noise-free environment for the battery management system (BMS). In this paper, an advanced $LLC$ design procedure is investigated to provide advantageous extreme regulation and eliminate detrimental burst mode operation. A modified, special $LLC$ tank driven by both variable frequency and phase shift proves to be a successful solution to achieve all the regulation requirements for battery charging (from recovery, bulk, equalization, to finish). The proposed solution can eliminate the negative impact of burst mode noises on the BMS, provide a ripple-free charging current for batteries in different states of charge, reduce the switching frequency variation, and facilitate the EMI filter and magnetic components designs procedure. In order to fully consider the characteristics of the full bridge $LLC$ resonant converter, especially the output voltage regulation range and soft transitions of the MOSFETs in the fixed frequency phase shift mode, a new set of analytical equations is obtained for the $LLC$ resonant converter with consideration of separated primary and secondary leakage inductances of the high frequency transformer. Based on the proposed strategy and analytical equations, multivariate statistical design methodology is employed to design and optimize a 120 VDC, 3-kW battery charger. The experimental results exhibit the excellent performance of the resulting converter, which has a peak efficiency of 96.5% with extreme regulation capability.

Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels

Abstract: In this work we obtain analytical solutions for the electrical RLC circuit model defined with Liouville–Caputo, Caputo–Fabrizio and the new fractional derivative based in the Mittag-Leffler function. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. Different source terms are considered in the fractional differential equations. The classical behaviors are recovered when the fractional order α is equal to 1.

High-Efficiency LLC Resonant Converter With High Voltage Gain Using an Auxiliary LC Resonant Circuit

Abstract: To design an LLC resonant converter optimally in the wide input voltage range, the LLC resonant converter with high efficiency and high voltage gain using an auxiliary LC resonant circuit is proposed. In this paper, the auxiliary LC resonant circuit operates as a variable inductor according to the change of the switching frequency, and it is presented as an effective magnetizing inductance. In the nominal state, since the effective magnetizing inductance increases, the primary circulating current is decreased. Thus, the turn-off switching loss of the primary switches and the primary conduction loss are minimized. During the hold-up time, the effective magnetizing inductance decreases so that the proposed converter has a high voltage gain. As a result, an optimal design of the LLC resonant converter over the wide input voltage range is possible. The proposed converter is verified by experimental results with a 330–390 V input and 350 W(56 V/6.25 A) output prototype.

A Convoluted Structure for Miniaturized Frequency Selective Surface and Its Equivalent Circuit for Optimization Design

Abstract: A convoluted frequency selective surface (FSS) is proposed to provide the unit cell dimension as small as 4.84% of the free space wavelength at resonant frequency. The FSS exhibits high resonant stability for various polarizations and incident angles. Its simple geometry is beneficial for not only easy design but also realizing the single and dual bandpass performances. By introducing an inductance in series connected with the traditional LC parallel resonant circuit, an improved equivalent circuit is established, which can describe the FSS frequency responses more accurately. Furthermore, a set of closed forms related to circuit and dimension parameters are developed. It can serve as the substitute of the full-wave solver to enhance the FSS design efficiency significantly. Finally, a dual bandpass FSS operating at 2.5 and 4.95 GHz was fabricated and measured. The measurement results exhibit satisfactory consistency with the full-wave simulation results.

A ZVS Pulsewidth Modulation Full-Bridge Converter With a Low-RMS-Current Resonant Auxiliary Circuit

Abstract: This paper presents the description and analysis of a phase-shift-modulated full-bridge converter with a novel robust passive low-rms-current resonant auxiliary circuit for zero-voltage switching (ZVS) operation of both the leading and lagging switch legs. Detailed time-domain analysis describes the steady-state behavior of the auxiliary circuit in different operating conditions. An in-depth comparative study between a fully specified baseline converter and the equivalent converter using the proposed resonant auxiliary circuit is presented. For a similar peak auxiliary current to ensure ZVS operation, a minimum of 20% reduction in rms current is obtained, which decreases the conduction losses. Key characteristics and design considerations are also fully discussed. Experimental results from a 750-W prototype confirm the predicted enhancements using the proposed resonant auxiliary circuit.

Soft-switching solid state transformer (S4T)

Abstract: This paper presents a new topology for a fully bidirectional soft-switching solid state transformer (S4T). The minimal topology, featuring 12 main devices and a high-frequency transformer, does not use an intermediate DC voltage link, and provides sinusoidal input and output voltages. The S4T can be configured to interface with two-or multi-terminal DC, single-or multi-phase AC systems. An auxiliary resonant circuit creates zero-voltage-switching (ZVS) conditions for main devices from no-load to full-load, and helps manage interactions with circuit parasitic elements. The modularized structure allows series and/or parallel stacking of converter cells for high-voltage and high-power applications.

Chaos control and sensitivity analysis of a double pendulum arm excited by an RLC circuit based nonlinear shaker

Abstract: In this paper the dynamical interactions of a double pendulum arm and an electromechanical shaker is investigated. The double pendulum is a three degree of freedom system coupled to an RLC circuit based nonlinear shaker through a magnetic field, and the capacitor voltage is a nonlinear function of the instantaneous electric charge. Numerical simulations show the existence of chaotic behavior for some regions in the parameter space and this behaviour is characterized by power spectral density and Lyapunov exponents. The bifurcation diagram is constructed to explore the qualitative behaviour of the system. This kind of electromechanical system is frequently found in robotic systems, and in order to suppress the chaotic motion, the State-Dependent Riccati Equation (SDRE) control and the Nonlinear Saturation control (NSC) techniques are analyzed. The robustness of these two controllers is tested by a sensitivity analysis to parametric uncertainties.

Gyrator-Based Analysis of Resonant Circuits in Inductive Power Transfer Systems

Abstract: In this paper, first, it is found that not only the magnetically coupled inductors but also all inductive power transfer systems (IPTSs) inherently have the nature of a gyrator. Widely known characteristics of IPTSs such as impedance inversion and source-type conversion are proved to be the nature of the gyrator. A graphical approach that utilizes the gyrator is proposed for the modeling of IPTSs in general. The proposed graphical technique enables manipulations on the circuit diagram instead of on the circuit equations, which are difficult to handle when the system order is higher than 4. Hence, the equivalent model can be obtained almost by inspection conveniently, giving fruitful physical insights that are limitedly achieved with the equation manipulations. Steady-state analyses at any frequency are possible, and equivalent series resistances can also be included in the proposed model. Five selected electrical characteristics, i.e., source-to-load gain, load-independent output voltage/current characteristics, power factor at the source, sign of the source phase angle, and allowances of open/short loads are evaluated for three widely used IPTS topologies. Also, this technique is extended to the mistuned case for verifying the general use of the approach. An experimental prototype of the voltage-source-type inductor–capacitor–inductor secondary-parallel (V-LCL-P) topology was built to demonstrate the proposed approach for both perfectly tuned and mistuned situations at 85 W and 100 kHz.

A Single-Stage Single-Switch LED Driver Based on Class-E Converter

Abstract: This paper proposes a single-stage single-switch light-emitting diode (LED) driver that integrates a buck–boost circuit with a Class-E resonant converter by sharing single-switch device. The buck–boost circuit, working as a power-factor correction (PFC) stage, operates in the discontinuous conduction mode (DCM) to shape the input current. The Class-E converter steps down the voltage to drive the LED. For specific component parameters, the Class-E converter can achieve soft-switching on the power switch and two rectifier diodes, and reduce switch losses at high frequencies. Electrolytic capacitors are used in the proposed converter to achieve a lower cost, but the system reliability decreases. To overcome this disadvantage, film capacitors can be used, but the current ripple increases. Neglecting the cost, multilayered film capacitors are the best option, if higher reliability and lower current ripple are required. The proposed driver features high efficiency (90.8%), and a high power factor (PF) (0.995). In this paper, analytical results and design considerations at 100 kHz are presented, and a 100-W prototype with 110 $\text{V}_{\text{AC}}$ input was built to validate the theoretical analysis.

A Single-Stage Single-Switch LED Driver Based on the Integrated SEPIC Circuit and Class-E Converter

Abstract: A novel high-power-factor single-stage single-switch light-emitting diodes (LEDs) driver for street lighting system is proposed in this paper. By integrating the single-ended primary-inductor converter (SEPIC) power factor correction circuit and Class-E resonant dc/dc converter, the proposed converter exhibits extreme simplicity and high reliability, as there is only one active power switch. The LED driver could achieve nearly a unit power factor by operating the SEPIC circuit at discontinuous conduction mode. With careful parameters design of a single Class-E resonant converter, the proposed converter can achieve soft-switching characteristics, which could significantly reduce the switching losses and greatly improve the system efficiency. Operational principle, analytical results, and design considerations at 100 kHz are presented, and a 100-W laboratory prototype is proposed to verify the theoretical analysis, whose efficiency is as high as 91.2% in full-load state under 110 VAC input.

Modified Z-Source DC Circuit Breaker Topologies

Abstract: The Z-source dc circuit breaker has been introduced as a new circuit for quickly and automatically switching off in response to faults. A modified Z-source breaker design is introduced for the operation at medium-voltage dc with future applications in naval ship power systems. Compared to existing designs, the respective design will allow for greater control of step changes in load. This new design also limits capacitor current in the circuit and can be easily modified for fault detection. Analysis of the breaker operation is presented during both the fault and step changes in load. Low-voltage laboratory validation of the breaker was carried out on two different versions of the proposed circuit.

A loosely coupled capacitive power transfer system with LC compensation circuit topology

Abstract: This paper proposes a double-sided LC compensated capacitive power transfer (CPT) system, which is the dual of the conventional series-series (SS) compensated inductive power transfer (IPT) system. Four metal plates are arranged as the capacitive coupler, and there are coupling capacitances between each pair of plates. At each side, a compensation capacitor is connected in parallel with the plates, and its value is usually much larger than the coupling capacitance between the plates, which results in a loosely coupled CPT system. In this paper, the fundamental harmonics approximation (FHA) method is used to analyze the circuit working principle. It shows that the system can work at constant current mode. An expression for the system output power is expressed, which is similar to that of the SS compensated IPT system. A 150W input power CPT system is therefore designed as an example to validate the compensation topology. The experimental results show that the dc to dc efficiency of the system is 66.67% when the air-gap distance is 180 mm and the switching frequency is 1.5 MHz.

Transformer Windings’ $RLC$ Parameters Calculation and Lightning Impulse Voltage Distribution Simulation

Abstract: This paper presents a numerical method for calculating the resistance, inductance, and capacitance matrices of transformer windings. Importance of their precise calculation is shown in the simulation of voltage distribution over the windings for a lightning-impulse test. The results obtained in frequency domain analysis are in good agreement with the measurement data. All the parameters are calculated using the self-developed solvers, the theory and the novelty of which are described in this paper. The presented approach allows fast and accurate high-frequency modeling of transformer windings.

A Virtual RLC Damper to Stabilize DC/DC Converters Having an LC Input Filter while Improving the Filter Performance

Abstract: The $LC$ filter at the input of a dc/dc converter may cause instability when the converter is controlled as a constant power load (CPL) and one of the effective solutions is to reduce the output impedance of the $LC$ input filter with different stabilization dampers. In this letter, the impact of these dampers on the $LC$ filter is analyzed with two-port network analysis and it is found that the existing dampers all degrade the performance of the original $LC$ input filter to some extent. In order to overcome this drawback, an $RLC$ damper is proposed to stabilize the whole system while improving the performance of the $LC$ input filter. In addition, this $RLC$ damper is also designed to achieve high robustness against the parameter variations of the $LC$ input filter. Furthermore, in order to avoid the power loss when implementing the damper physically, a control strategy for the CPL is proposed to implement the $RLC$ damper as a virtual $RLC$ ( $VRLC$ ) damper. The actual effectiveness of the $VRLC$ damper and its impact on the CPL are fully evaluated via two-port network analysis as well. Finally, experimental results from a 100-W 48–24-V buck converter with an $LC$ input filter are presented to demonstrate the proposed $VRLC$ damper.

Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network

Abstract: A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform (RT) method, a problem that has never been resolved before, for the Green's function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h 1 = 1 − cos i − sin i cot n i . This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.

A Management Circuit with Upconversion Oscillation Technology for Electric-Field Energy Harvesting

Abstract: Traditional LC resonance circuit can continuously and efficiently accumulate energy from the harvester at optimal impedance matching. Due to electric-field frequency (50 Hz, in China) and small equivalent capacitance (tens or hundreds of picofarads) of electric-field capacitive harvester, it is difficult to manufacture a huge transformer with a large inductance (>10 000 H) to optimally match the capacitive harvester. An upconversion oscillation circuit with a smaller size transformer around high-voltage power line is proposed to achieve efficient electric-field energy harvesting in this paper. The power-frequency output signal is transformed into higher frequency oscillation signal in the upconversion circuit consisting of the switch and the transformer. In this case, optimal impedance matching with the smaller size transformer is realized. Therefore, weak energy from harvester is fast accumulated into the storage capacitor by using the upconversion oscillation circuit. For a 10-kV power line, the upconversion maximum charging power reaches 663 μW in experiment. Due to optimal impedance matching in the upconversion oscillation circuit, the maximum harvesting efficiency is increased from 3% to 90.5%, compared with the traditional harvesting method. While the voltage across the storing capacitor is 3.26 V, the instantaneous discharge circuit can drive a wireless sensor node with an output power of 110 mW.

Highly Efficient Asymmetrical PWM Full-Bridge Converter for Renewable Energy Sources

Abstract: This paper presents a highly efficient asymmetrical pulse-width modulated (APWM) full-bridge converter for renewable energy sources. The proposed converter adopts full-bridge topology and asymmetric control scheme to achieve the zero-voltage switching (ZVS) turn-on of the power switches of the primary side and to reduce the circulating current loss. Moreover, the resonant circuit composed of the leakage inductance of the transformer and the blocking capacitor provides the zero-current switching (ZCS) turn-off for the output diode without the help of any auxiliary circuits. Thus, the reverse recovery problem of the output diode is eliminated. In addition, voltage stresses of the power switches are clamped to the input voltage. Due to these characteristics, the proposed converter has the structure to minimize power losses. It is especially beneficial to the renewable energy conversion systems. To confirm the theoretical analysis and validity of the proposed converter, a 400 W prototype is implemented with the input voltage range from 40 to 80 V.

A UHF RFID Tag With Improved Performance on Liquid Bottles

Abstract: The effect of liquid on the performance of a UHF RFID tag is investigated in this letter. It is found that the presence of the liquid increases the loss resistance in the equivalent circuit of the antenna. This leads to impedance mismatching with a narrower bandwidth and degraded return loss. The proposed solution for compensating this effect is to add a resonant $RLC$ circuit with smaller resistance in parallel to the antenna body. This resistance corrects the increased loss resistance when the resonant frequency of the added part is close to the working frequency of the tag. The simulation and measurement results confirm an improvement in impedance matching that leads to the increase of the reading range.

Divide-by-2 LC injection-locked frequency divider with wide locking range at low and high injection powers

Abstract: A wide locking range nMOS divide-by-2 RLC injection-locked frequency divider ILFD was designed and implemented in the TSMC 0.18-µm BiCMOS process. The ILFD is based on a cross-coupled oscillator with one direct injection MOSFET and a RLC resonator. The RLC resonator is used to extend the locking range so that dual-band locking ranges can be merged in one locking range at both low and high injection powers. At the drain-source bias of 0.9V for switching transistors, and at the incident power of 0dBm the locking range of the divide-by-2 ILFD is 7.24GHz, from the incident frequency 2.65 to 9.89GHz, the locking range percentage is 115.47%. The power consumption of ILFD core is 8.685mW. The die area is 0.726×0.930mm2. Copyright © 2016 John Wiley & Sons, Ltd.

Multielement Resonant Converters With a Notch Filter on Secondary Side

Abstract: This letter proposes novel multielement resonant converters, which are improved topologies of the conventional LLC resonant converter, for voltage step-up applications. A notch filter is introduced into the secondary side of the LLC resonant converter. The voltage gain of the proposed resonant converters can be as low as zero with limited switching frequency range. Therefore, the start-up and short output circuit protection issues of the conventional LLC resonant converter can be solved with the proposed solutions. Furthermore, the circulating energy of the resonant tank can be reduced as well. In comparison with the multielement resonant converters with a notch filter on primary side, the proposed converter can help to reduce the conduction losses associated with the notch filter and provide higher voltage gain at the resonant frequency. The topologies and characteristics of the proposed resonant converters are analyzed. Experimental results are given to verify the effectiveness and the advantages of the proposed solutions.

A Comparative Study of Output Metrics for an MEMS Resonant Sensor Consisting of Three Weakly Coupled Resonators

Abstract: This paper systematically investigates the characteristics of different output metrics for a weakly coupled three degree-of-freedom microelectromechanical systems resonant sensor. The key figures-of-merit examined are sensitivity and linear range. The four main output metrics investigated are mode frequency shift, amplitude difference, amplitude ratio, and eigenstate shift. It is shown from theoretical considerations, equivalent RLC circuit model simulations and electrical measurements, that there is a strong tradeoff between sensitivity and linear range. For instance, the amplitude difference has the best sensitivity but the worst linear range, whereas frequency shift has the widest linear range but the lowest sensitivity. We also show that using the vibrational amplitude ratio as an output metric provides the best balance between sensitivity and linear range. [2016-0077]

Systems and methods for providing vector control of a grid connected converter with a resonant circuit grid filter

Abstract: An example system for controlling a grid-connected energy source using a neural network is described herein. The example system can include a grid-connected converter (“GCC”) operably coupled between an electrical grid and an energy source, a n-order grid filter (e.g., where n is an integer greater than or equal to 2) operably coupled between the electrical grid and the GCC, and a nested-loop controller. The nested-loop controller can have inner and outer control loops and can be operably coupled to the GCC. A d-axis loop can control real power, and a q-axis loop can control reactive power. Additionally, the inner control loop can include a neural network that is configured to optimize dq-control voltages for controlling the GCC. The neural network can account for circuit dynamics of the n-order grid filter while optimizing the dq-control voltages.

Superfluid transport dynamics in a capacitive atomtronic circuit

Abstract: We simulate transport in an atomtronic circuit of a Bose-Einstein condensate that flows from a source region into a drain through a gate channel. The time-dependent Gross-Pitaevskii equation (GPE) solution matches the data of a recent experiment. The atomtronic circuit is found to be similar to a variable-resistance RLC circuit, which is critically damped at early times and shows $\mathit{LC}$ oscillations later. The GPE also predicts atom loss from the drain. Studies of the dependence of condensate transport upon gate parameters suggest the utility of the GPE for investigation of atomtronic circuits.

Analytical Solutions to H2 and H∞ Optimizations of Resonant Shunted Electromagnetic Tuned Mass Damper and Vibration Energy Harvester

Abstract: When optimized, tuned mass dampers (TMDs) can effectively mitigate the vibration of the primary structure, because additional resonance and damping are introduced by the auxiliary mass-spring-damper system. Similar effect can be realized without auxiliary mass when an electromagnetic transducer shunt with the R-L-C resonant circuit is placed between the primary structure and the base. This paper is to analytically optimize the parameters of the R-L-C circuits for vibration mitigation. Both H2 and H∞ optimization criteria are investigated, which are to minimize the root-mean-square (RMS) vibration under random excitation and the peak magnitude in the frequency domain, respectively. The concise closed-form solutions of the optimal parameters are then summarized together with the ones obtained the using fixed-point method, for practical implementation convenience. The H2 and H∞ optimizations of energy harvesting are also discussed in this paper. Furthermore, we also investigate the sensitivity of system performances to the tuning parameter changes of the electromagnetic shunt circuit.

Soft switched single stage wireless power transfer

Abstract: A control scheme and architecture for a wireless electrical energy transmission circuit employs two solid-state switches and a zero voltage switching (ZVS) topology to power an antenna network. The switches drive the antenna network at its resonant frequency and simultaneously energize a separate resonant circuit that has a resonant frequency lower than the antenna circuit. The resonant circuit creates out of phase voltage and current waveforms that enable the switches to operate with (ZVS).

Novel SPICE model for common mode choke including complex permeability

Abstract: A highly accurate filter simulation requires a high precision SPICE model for the common mode choke. Conventional SPICE models for chokes consist of parallel RLC circuits and show a substantial difference between the measured and simulated impedance characteristics due to the lack of frequency-dependent complex permeability considerations. Here, we propose a novel SPICE model for a common mode choke that includes the frequency-dependent complex permeability. This model uses a transfer function in the s-domain to describe frequency-dependent elements. Moreover, two model parameter estimation methods are proposed; a measurement based method and a datasheet based method. High accuracy is achieved with the measurement based model by extracting the model parameter using the measured impedance characteristics of the actual coil. In the datasheet based method, the model parameter is estimated from the datasheet and the shape of the coil without the actual coil. Finally, we show that not only the impedance characteristics of a choke can be expressed, but also the insertion loss of a T-type filter can be predicted much more accurately than presently possible using a conventional model. This SPICE model is the first to express the frequency-dependent inductance and resistance of the choke with high accuracy; therefore, it is expected to be useful for filter design.

Direct Mesh-Based Model Order Reduction of PEEC Model for Quasi-Static Circuit Problems

Abstract: In this paper, a new concept of matrix-inversion-less derived physically expressive circuit method of model order reduction for large-scale high-speed/microwave circuit problems is proposed. It is the first model that is derived based on the mesh information of partial element equivalent circuit modeling. This new proposed method absorbs insignificant nodes and parallel branches while retaining the physical meaning of all the inductive and capacitive elements. This method does not involve any matrix inversions or decompositions and its computational overhead is dominated by outer products that can be simply accelerated by the massive GPU acceleration technique. The resultant order-reduced circuit is very useful for not only speeding up the analysis of a large-scale high-speed/microwave circuit but also interpreting the physical insight of the circuit layout from the circuit domain point of view. Three numerical examples are given, demonstrating the versatility, scalability, accuracy, and simplicity of the method.