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Showing papers on "Equivalent circuit published in 2003"


Journal ArticleDOI
TL;DR: In this paper, the effect of surrounding an electrically small dipole antenna with a shell of double negative (DNG) material has been investigated both analytically and numerically, and it is shown that a properly designed dipole-DNG shell combination increases the real power radiated by more than an order of magnitude over the corresponding free space case.
Abstract: The effect of surrounding an electrically small dipole antenna with a shell of double negative (DNG) material (/spl epsiv//sub r/<0 and /spl mu//sub r/<0) has been investigated both analytically and numerically. The problem of an infinitesimal electric dipole embedded in a homogeneous DNG medium is treated; its analytical solution shows that this electrically small antenna acts inductively rather than capacitively as it would in free space. It is then shown that a properly designed dipole-DNG shell combination increases the real power radiated by more than an order of magnitude over the corresponding free space case. The reactance of the antenna is shown to have a corresponding decrease. Analysis of the reactive power within this dipole-DNG shell system indicates that the DNG shell acts as a natural matching network for the dipole. An equivalent circuit model is introduced that confirms this explanation. Several cases are presented to illustrate these results. The difficult problem of interpreting the energy stored in this dipole-DNG shell system when the DNG medium is frequency independent and, hence, of calculating the radiation Q is discussed from several points of view.

431 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed an RF circuit model for single walled carbon nanotubes for both dc and capacitively contacted geometries, by modeling the nanotube as a nanotransmission line with distributed kinetic and magnetic inductance and distributed quantum and electrostatic capacitance.
Abstract: We develop an RF circuit model for single walled carbon nanotubes for both dc and capacitively contacted geometries. By modeling the nanotube as a nanotransmission line with distributed kinetic and magnetic inductance as well as distributed quantum and electrostatic capacitance, we calculate the complex, frequency dependent impedance for a variety of measurement geometries. Exciting voltage waves on the nanotransmission line is equivalent to directly exciting the yet-to-be observed one dimensional plasmons, the low energy excitation of a Luttinger liquid.

425 citations


Journal ArticleDOI
TL;DR: In this article, a wideband physical and scalable 2-spl Pi/ equivalent circuit model for on-chip spiral inductors is developed based on physical derivation and circuit theory, closed-form formulas are generated to calculate the RLC circuit elements directly from the inductor layout.
Abstract: A wide-band physical and scalable 2-/spl Pi/ equivalent circuit model for on-chip spiral inductors is developed. Based on physical derivation and circuit theory, closed-form formulas are generated to calculate the RLC circuit elements directly from the inductor layout. The 2-/spl Pi/ model accurately captures R(f) and L(f) characteristics beyond the self-resonant frequency. Using frequency-independent RLC elements, this new model is fully compatible with both ac and transient analysis. Verification with measurement data from a SiGe process demonstrates accurate performance prediction and excellent scalability for a wide range of inductor configurations.

341 citations


Journal ArticleDOI
TL;DR: In this article, a systematic study of PVD ceramic (TiN and CrN) coated mild steel and AISI 316L stainless steel was carried out using the Electrochemical impedance spectroscopy (EIS) technique as the coated systems were immersed in 0.5 N NaCl solution.

340 citations


Journal ArticleDOI
TL;DR: A novel, long-type of magnetostrictive and piezoelectric laminate composite design in which the layers are, respectively, magnetized/poled along their length axes, and a theory for modeling its behavior is presented.
Abstract: This paper presents a novel, long-type of magnetostrictive and piezoelectric laminate composite design in which the layers are, respectively, magnetized/poled along their length axes, and a theory for modeling its behavior. Using piezoelectric and magnetostrictive constitutive equations, and an equation of motion, a magneto-elasto-electric bieffect equivalent circuit is developed. The circuit is used to predict the longitudinal and transverse magnetoelectric (ME) voltage coefficients of our Terfenol-D/Pb(Zr/sub 1-x/Ti/sub x/)O/sub 3/ laminate design. It is found that the longitudinal ME voltage coefficient is significantly higher (/spl sim/5x) than the transverse one, and that our new laminate design has significantly higher ME voltage coefficients under small applied direct current (DC) magnetic bias fields than designs reported previously by other groups. Experimental values were found to be coincidental with predicted ones.

305 citations


Journal ArticleDOI
TL;DR: In this paper, the authors show that the maximum stable deflection is limited by 1) charge pull-in, in which the actuator snaps due to the presence of parasitic capacitance and 2) tip-in in which rotation mode becomes unstable.
Abstract: Controlling the charge, rather than the voltage, on a parallel-plate, electrostatic actuator theoretically permits stable operation for all deflections. Practically, we show that, using charge control, the maximum stable deflection is limited by 1) charge pull-in, in which the actuator snaps due to the presence of parasitic capacitance and 2) tip-in, in which the rotation mode becomes unstable. This work presents a circuit that controls the amount of charge on a parallel-plate, electrostatic actuator. This circuit reduces the sensitivity to parasitic capacitance, so that tip-in is the limiting instability. A small-signal model of the actuator is developed and used to determine the circuit bandwidth and gain requirements for stable deflections. Four different parallel-plate actuators have been designed and tested to verify the charge control technique as well as to verify charge pull-in, tip-in, and the bandwidth requirements. One design travels 83% of the gap before tip-in. Another design can only travel 20% of the gap before tip-in, regardless of whether voltage control or charge control is used.

276 citations


Journal ArticleDOI
TL;DR: In this article, an experimental study of the electrical and thermal behavior of supercapacitors for power electronics and transportation applications is presented, and simulation results are presented, analyzed and compared.

248 citations


Journal ArticleDOI
TL;DR: In this article, the authors propose transmission line models for studying and interpreting the electromagnetic propagation behavior of composite periodic media, and show that by periodically loading a network of transmission lines with series capacitors and shunt inductors, a negative refractive index medium can be synthesized without excess resonators, thus leading to wideband behavior.
Abstract: Recently, three-dimensional composite periodic media comprising split-ring resonators (SRR) and thin wires have been shown to exhibit a negative refractive index in the frequency range around the SRR resonance. In this letter, we propose transmission line models for studying and interpreting the electromagnetic propagation behavior of such materials. Based on these equivalent transmission line models, we show that by periodically loading a network of transmission lines with series capacitors and shunt inductors, a negative refractive index medium can be synthesized without excess resonators, thus leading to wideband behavior. These proposed media have tailorable properties over a broad frequency range. Moreover, they are completely planar, frequency scalable, more compact, and easier to implement for RF/microwave circuit applications than their SRR/wire counterparts.

245 citations


Journal ArticleDOI
01 Nov 2003
TL;DR: In this paper, a doubly periodic table of circuit elements is presented for modeling high-frequency nanodevices, which can be represented by a loop of four generic circuit elements wrapped around the surface of a torus.
Abstract: Not all molecular and nanodevices are useful from an information technology perspective. Such devices are said to be inept in a precise technical sense that can be easily tested from an explicit mathematical criteria to be presented in this two-part tutorial review. Often an inept device can be redesigned into a smart device capable of computing and artificial intelligence by massaging the device's parameters, such as doping, concentration, geometrical profile, chemical moiety, etc., in accordance with the principle of local activity to be articulated in Part II. In particular, designing a smart nanodevice amounts to fine tuning the device parameters into a much smaller niche within the device's locally active parameter region called the edge of chaos where complexity abounds. Molecular and nanodevices will remain novelty toys for nanodevice specialists unless they possess realistic nonlinear circuit models so that future nano circuit designers can simulate their exotic designs as easily and accurately as current CMOS circuit designers. A mathematically consistent theory for modeling nonlinear, high-frequency nanodevices, specially those which exploited exotic tunneling and entanglement quantum mechanical effects, such as Coulomb blockade, quasi-particle dynamics, Kondo resonance, Aharonov-Bohm nonlocal interactions, etc., will require the introduction of a complete family of fundamental circuit elements as model building blocks. They are presented via a doubly periodic table of circuit elements somewhat reminiscent of Mendeleev's periodic table of chemical elements. These fundamental circuit elements can be compactly represented by a loop of four generic species of circuit elements wrapped around the surface of a torus where any higher order element having an arbitrarily high order of frequency dependence can be generated from one of them, modulo the integer 4, ad infinitum. The significance of this four-element torus is that realistic circuit models of all current and future molecular and nanodevices must necessarily build upon an appropriate subset of nonlinear circuit elements begotten from this torus.

239 citations


Journal ArticleDOI
TL;DR: The PEEC formulation is systematically extended to nonorthogonal geometries since many practical EM problems require a more general formulation and is consistent with the classical PEEC model for rectangular geometry.
Abstract: Electromagnetic solvers based on the partial element equivalent circuit (PEEC) approach have proven to be well suited for the solution of combined circuit and EM problems. The inclusion of all types of Spice circuit elements is possible. Due to this, the approach has been used in many different tools. Most of these solvers have been based on a rectangular or Manhattan representation of the geometries. In this paper, we systematically extend the PEEC formulation to nonorthogonal geometries since many practical EM problems require a more general formulation. Importantly, the model given in this paper is consistent with the classical PEEC model for rectangular geometries. Some examples illustrating the application of the approach are given for both the time and frequency domain.

228 citations


Journal ArticleDOI
TL;DR: In this paper, a method for the synthesis of SPICE-compatible broadband electrical models of frequency-domain responses approximated by rational functions is proposed, which is suitable for providing equivalent circuits of interconnects, power/ground plane structures and PCB discontinuities.
Abstract: The paper proposes a method for the synthesis of SPICE-compatible broad-band electrical models of frequency-domain responses approximated by rational functions. First- and second-order equivalent circuits with controlled sources are used as building blocks to generate equivalent circuit representations-totally compatible with commercial circuit solvers - of the frequency-dependent responses. Fundamental properties of the method are discussed and details of its implementation are described. The proposed approach has demonstrated to be suitable for providing equivalent circuits of interconnects, power/ground plane structures and PCB discontinuities.

Journal ArticleDOI
TL;DR: In this article, a linear electromechanical model is developed for ionic polymer materials, which is based on an equivalent circuit representation that is related to the mechanical, electrical, and electromagnetic properties of the material.
Abstract: A linear electromechanical model is developed for ionic polymer materials. The model is based on an equivalent circuit representation that is related to the mechanical, electrical, and electromechanical properties of the material. Expressions for the quasi-static and dynamic mechanical impedance are derived from beam theory. The Golla-Hughes-McTavish model of viscoelasticity is incorporated into the model to include effects due to a rate dependent modulus. Similar to previous research, the electrical impedance is modeled as a series combination of resistive and capacitive elements. The major contribution of this work is the derivation of an electromechanical coupling term that is related to an effective bending strain coefficient. This parameter is also frequency dependent to model the low-frequency relaxation that has been measured in certain ionic polymer materials. The resulting linear electromechanical model is based on the measurement of the effective permittivity, elastic modulus, and effective stra...


Journal ArticleDOI
TL;DR: In this article, the authors used impedance spectroscopy (IS) data from oxide-ion conducting La 0.80Sr0.20Ga0.83Mg0.17O2.82 ceramics over the range 182 to 280°C.
Abstract: Modelling of impedance spectroscopy (IS) data of electroceramics depends critically on the correct choice of equivalent electrical circuit so that the extracted parameters have physical significance. The strategy proposed to choose the correct circuit involves analysis of IS data in several of the four complex formalisms: impedance, electric modulus, admittance and permittivity together with consideration of the frequency and temperature dependence of data and the magnitude and temperature dependence of extracted resistance and capacitance values. This is demonstrated using IS data from oxide-ion conducting La0.80Sr0.20Ga0.83Mg0.17O2.82 ceramics over the range 182 to 280°C. Low temperature data are fitted first, to allow a full characterisation of the bulk response; some of the bulk parameters may then be fixed to enable fitting of the higher temperature data which increasingly feature lower frequency phenomena such as grain boundary impedances. The most appropriate circuit in this case is found to consist of a parallel combination of a resistor, capacitor and constant phase element (CPE) for the bulk response in series with a resistor and capacitor in parallel for a constriction resistance. The origin of the constriction resistance may be associated with the presence of plate-like LaSrGaO4 secondary phase within the grains and/or with the presence of pores at the grain boundaries. The importance of choosing (a) the correct equivalent circuit and (b) approximately correct input values for the various circuit parameters to be fitted and refined are demonstrated.

Journal ArticleDOI
TL;DR: In this paper, the authors present a systematic approach to employ electrochemical impedance spectroscopy for determining model structure and parameters of a simulation model for a VRLA battery, focusing on the interpretation of the impedance data in terms of equivalent circuit models.

Journal ArticleDOI
TL;DR: An improved version of the SC-CMFB circuit is analyzed, which has very low errors due to charge injection and leakage currents and settles much faster than the traditional SC- CMFB circuit.
Abstract: A detailed analysis of the dc behavior of switched-capacitor common-mode feedback circuit (SC-CMFB) is presented. A mathematical model, useful for analysis, is developed and the expressions for the output common-mode (CM) voltage, with and without considering the charge injection of switches and leakage currents, are derived. Further, the expression for dc CM settling time, is presented. The effect of parasitic capacitances, dc CM gain, charge injection error, and leakage currents, on the steady-state value of the dc CM voltage is analyzed and design guidelines to minimize these errors are presented. Finally, an improved version of the SC-CMFB circuit is analyzed. This circuit has very low errors due to charge injection and leakage currents and settles much faster than the traditional SC-CMFB circuit.

Journal ArticleDOI
TL;DR: In this paper, two simple and very useful techniques for the efficiency optimization of the indirect vector-controlled induction motor drives are presented for the synchronously rotating reference frame the flux-producing current is controlled until the power at the DC link is minimum.
Abstract: This paper presents two simple and very useful techniques for the efficiency optimization of the indirect vector-controlled induction motor drives. In the synchronously rotating reference frame the flux-producing current is controlled until the power at the DC link is minimum. Of the two techniques, the first method controls the flux-producing current in a regular and smooth manner. The second technique combines loss model and search approaches in a unique way to propose a hybrid method, where the first estimate is from the loss model approach and the subsequent adjustment of the flux is through the search technique. Both the algorithms are simple, easily realizable, and offer fast convergence. Also, smooth control of the flux offers excellent dynamic performance. A comparative assessment shows that the hybrid method is the best, even if an approximate equivalent circuit for the induction motor is used for the analysis and optimization of the losses. The close agreement between the simulation and the experimental results confirms the validity and usefulness of the proposed techniques.

Patent
18 Feb 2003
TL;DR: In this paper, a method for determining a voltage based or current based state of charge (SOC) and state of health (SOH) of a battery system is provided.
Abstract: A method for determining a voltage based or current based state of charge (SOC) and state of health (SOH) of a battery system is provided. The method includes: providing a model of the battery system including an equivalent circuit having both low frequency and high frequency elements; establishing a plurality of functional relationships comprising relationship of the equivalent circuit with SOC; reducing at least part of the plurality of functional relationships into a set of time segmented recursive functional relationships, wherein a state at a first time t can be modeled by a functional presentation of a state at a second time t−Δt that occurred before the first time t; and computing a set of data points based upon the set of time segmented recursive functional relationships using a matrix for operation in matrix algebra.

Journal ArticleDOI
TL;DR: This paper proposes a balanced switching converter circuit, which is an effective way to reduce the common-mode conducted noise, and a boost converter version of thebalanced switching converter is presented.
Abstract: Because conventional switching converters have usually used unbalanced circuit topologies, parasitic capacitance between the drain/collector of an active switch and the frame ground through its heat sink may generate the common-mode conducted noise. This paper proposes a balanced switching converter circuit, which is an effective way to reduce the common-mode conducted noise. As an example, a boost converter version of the balanced switching converter is presented, and the mechanism of the common-mode noise reduction is explained using an equivalent circuit. This good feature is confirmed by experimental results. The concept of the balanced switching converter is applied to some other types of switching converters.

Journal ArticleDOI
12 Oct 2003
TL;DR: In this article, a simple nonlinear magnetic analysis for a surface-mounted permanent-magnet synchronous motor is presented as an assistant design tool of finite-element analysis (FEA).
Abstract: This paper presents a simple nonlinear magnetic analysis for a surface-mounted permanent-magnet synchronous motor as an assistant design tool of finite-element analysis (FEA). The equivalent magnetic circuit of the motor used in the proposed analysis is composed of the saturable permeance tips in the stator teeth for considering the local magnetic saturation. As a result, the proposed analysis is capable of calculating the flux distribution and the torque characteristics in the presence of magnetic saturation. The effectiveness of the proposed analysis is verified by comparing with three-dimensional (3-D) FEA in terms of the analytical accuracy. The computation time is greatly reduced as short as 1.5 s while the 3-D FEA requires as much as 32 min for the same evaluation.

Journal ArticleDOI
TL;DR: In this article, a method to estimate characteristics of interior permanent magnet motors considering effects of iron loss is introduced, where the equivalent circuit parameters including the iron loss resistance are calculated as functions of d-q axis currents by the finite-element method with the consideration of movement of the rotor.
Abstract: A method to estimate characteristics of interior permanent magnet motors considering effects of iron loss is introduced. The equivalent circuit parameters including the iron loss resistance are calculated as functions of d-q axis currents by the finite-element method with the consideration of movement of the rotor. The characteristics of the motor are calculated from the equivalent circuit. By using this procedure, we can calculate the torque and the efficiency of the motor considering the harmonic iron losses of both the stator and rotor at any operating conditions instantaneously after parameter calculation. The results of the calculated characteristics are compared with the experimental results to examine the validity.

Journal ArticleDOI
P. Gunupudi1, Roni Khazaka, Michel Nakhla, Tom J. Smy, D. Celo 
TL;DR: An algorithm is proposed to form passive parametrized macromodels of large linear networks that match the characteristics of the original network in time, as well as other design parameters of the circuit.
Abstract: There is a significant need for efficient and accurate macromodels of components during the design of microwave circuits. Increased integration levels in microwave devices and higher signal speeds have produced the need to include effects previously neglected during circuit simulations. Accurate prediction of these effects involve solution of large systems of equations, the direct simulation of which is prohibitively CPU expensive. In this paper, an algorithm is proposed to form passive parametrized macromodels of large linear networks that match the characteristics of the original network in time, as well as other design parameters of the circuit. A novel feature of the algorithm is the ability to incorporate a set of design parameters within the reduced model. The size of the reduced models obtained using the proposed algorithm were less than 5% when compared to the original circuit. A speedup of an order of magnitude was observed for typical high-speed transmission-line networks. The algorithm is general and can be applied to other disciplines such as thermal analysis.

Journal ArticleDOI
TL;DR: In this paper, the electrical properties of polycrystalline Bi6Fe2Ti3O18 were investigated by impedance spectroscopy in the temperature range 30-550°C.
Abstract: The electrical properties of polycrystalline Bi6Fe2Ti3O18 are investigated by impedance spectroscopy in the temperature range 30–550°C. The imaginary part of impedance as a function of frequency shows Debye like relaxation. Impedance data are presented in the Nyquist plot which is used to identify an equivalent circuit and the fundamental circuit parameters are determined at different temperatures. The grain and grain-boundary contributions are estimated. The results of bulk a.c. conductivity as a function of temperature and frequency are presented. The activation energies for the a.c. conductivity are calculated. The polaron hopping frequencies are estimated from the a.c. conductivity data.

Journal ArticleDOI
TL;DR: In this paper, a series of experiments are performed to assess the validity of an equivalent circuit model of ionic polymer transducers, where the fundamental parameters of the model are the dielectric permittivity of the material, the viscoelastic modulus, and the effective strain coefficient of the transducers.
Abstract: A series of experiments are performed to assess the validity of an equivalent circuit model of ionic polymer transducers. The fundamental parameters of the model are the dielectric permittivity of the material, the viscoelastic modulus, and the effective strain coefficient of the transducer. The results demonstrate the validity of a simplifying assumption regarding the reflected impedance of the polymer. This allows us to use a simpler set of expressions to predict the time and frequency response of the polymer. The expressions for sensing and actuation are verified in a series of step response and frequency response tests of cantilevered transducers. The curvefit algorithm used for parameter identification works well but there is always a tradeoff in accuracy between the time domain and frequency domain measurements. This could imply the existence of an input-level dependence on the parameters. In spite of this level dependence, the linear model is able to predict the response of an input-output pair tha...

Journal ArticleDOI
TL;DR: In this paper, the double-layer capacitor (DLC) is represented by a distributed parameter system and a ladder circuit is used to model the DC bias and manufacturing parameters for different ladder circuits.
Abstract: The double-layer capacitor (DLC) is a very complex device that is best represented by a distributed parameter system. Many different lumped-parameter equivalent circuits have been proposed for the DLC. An examination into utilizing a ladder circuit to model a DLC is presented. Parameters for different ladder circuits are determined from AC impedance data. Variations in circuit parameters with DC bias and manufacturing have been investigated. The performance of the ladder circuit has been evaluated in slow discharge and pulse load applications.

Proceedings ArticleDOI
08 Jun 2003
TL;DR: In this article, a micromechanical 131 MHz bulk acoustic mode (BAW) silicon resonator is demonstrated, which can be characterized as a 2D plate expansion that preserves the original square shape.
Abstract: A micromechanical 131 MHz bulk acoustic mode (BAW) silicon resonator is demonstrated The vibration mode can be characterized as a 2-D plate expansion that preserves the original square shape The prototype resonator is fabricated of single-crystal silicon by reactive ion etching a silicon-on-insulator (SOI) wafer The measured high quality factor (Q=130000) and current output (i/sub MAX/ /spl ap/ 160 /spl mu/A) make the resonator suitable for reference oscillator applications An electrical equivalent circuit based on physical device parameters is derived and experimentally verified

Journal ArticleDOI
TL;DR: In this paper, a small-signal circuit model for pulsewidth-modulated DC-DC converters operated in discontinuous conduction mode is presented, which is composed of controlled current sources, an independent voltage source and resistances.
Abstract: A small-signal circuit model for pulsewidth-modulated DC-DC converters operated in discontinuous conduction mode is presented. The model is composed of controlled current sources, an independent voltage source and resistances. The principle of energy conservation approach is used to take into account parasitic resistances of the transistor and diode and the diode threshold voltage. The proposed model is suitable for small-signal, frequency-domain representation of the converters. This model is used to derive the expressions for a boost converter control-to-output transfer function, input-to-output voltage transfer function, input impedance and the output impedance. Bode plots are also given for these transfer functions. The predicted and experimental results were in excellent agreement.

Journal ArticleDOI
TL;DR: The methodology developed to account for polarization effects exhibits a significant improvement over the conventional approaches and points up a deficiency in often-used equivalent circuit models.

Journal ArticleDOI
TL;DR: In this article, a derivation of the Thevenin and Norton equivalent circuits from the basic principles of uniqueness and superposition applied to electromagnetic fields is presented, which can be used to find a reradiated electromagnetic field that is a part of the total field scattered by a receiving antenna.
Abstract: The investigation carried out in this paper was stimulated by a recent paper published by Love (2002), in which the appropriateness of the use of the Thevenin and Norton equivalent circuits for a receiving antenna was questioned. A review of the available literature led to the conclusion that the limitations inherent in the Thevenin and Norton equivalent circuits had not been adequately examined, and this led to the investigation that is reported on in this paper. The Thevenin and Norton equivalent circuits are useful in the reduction of the equivalent circuit for a transmitting-receiving antenna system to simpler networks that facilitate the evaluation of the received power. One finds in the literature that the calculated power dissipation within these equivalent circuits is often equated to the reradiated and scattered power from the receiving antenna. Such calculations are not correct, because power dissipation in the network from which the Thevenin and Norton equivalent circuits were obtained cannot be made using the Thevenin and Norton equivalent circuits. However, as we will show, the Thevenin and Norton equivalent circuits can be used to find a reradiated electromagnetic field that is a part of the total field scattered by a receiving antenna. As part of the derivation of this new result, we develop a derivation of the Thevenin and Norton equivalent circuits from the basic principles of uniqueness and superposition applied to electromagnetic fields.

Journal ArticleDOI
TL;DR: In this article, a new four-port scattering parameter (S-parameter) and broad-band noise deembedding methodology is presented, which considers distributed on-wafer parasitics in the millimeter-wave band (f>30GHz).
Abstract: A new four-port scattering parameter (S-parameter) and broad-band noise deembedding methodology is presented. This deembedding technique considers distributed on-wafer parasitics in the millimeter-wave band (f>30GHz). The procedure is based on simple analytical calculations and requires no equivalent circuit modeling or electromagnetic simulations. Detailed four-port system analysis and deembedding expressions are derived. Comparisons between this new method and the industry-standard "open-short" method were made using measured and simulated data on state-of-the-art SiGe HBTs with a maximum cutoff frequency of approximately 180 GHz. The comparison demonstrates that better accuracy is achieved using this new four-port method. Based on a combination of measurements and HP-ADS simulations, we also show that this new technique can be used to accurately extract the S-parameters and broad-band noise characteristics to frequencies above 100 GHz.