DC Solutions Research Articles

A SPICE-Oriented Nonexistence Test for DC Solutions of Nonlinear Circuits

As a powerful computational test for nonexistence of a DC solution of a nonlinear circuit, the LP test is well-known. This test is useful for finding all solutions of nonlinear circuits; it is also useful for verifying the nonexistence of a DC operating point in a given region where operating points should not exist. However, the LP test has not been widely used in practical circuit simulation because the programming is not easy for non-experts or beginners. In this paper, we propose a new LP test that can be easily implemented on SPICE without programming. The proposed test is useful because we can easily check the nonexistence of a solution using SPICE only.

Solving Low-Frequency EM-CKT Problems Using the PEEC Method

The partial element equivalent circuit (PEEC) formulation is an integral equation based approach for the solution of combined electromagnetic and circuit (EM-CKT) problems. In this paper, the low-frequency behavior of the PEEC matrix is investigated. Traditional EM solution methods, like the method of moments, suffer from singularity of the system matrix due to the decoupling of the charge and currents at low frequencies. Remedial techniques for this problem, like loop-star decomposition, require detection of loops and therefore present a complicated problem with nonlinear time scaling for practical geometries with holes and handles. Furthermore, for an adaptive mesh of an electrically large structure, the low-frequency problem may still occur at certain finely meshed regions. A widespread application of loop-star basis functions for the entire mesh is counterproductive to the matrix conditioning. Therefore, it is necessary to preidentify regions of low-frequency ill conditioning, which in itself represents a complex problem. In contrast, the charge and current basis functions are separated in the PEEC formulation and the system matrix is formulated accordingly. The incorporation of the resistive loss (R) for conductors and dielectric loss (G) for the surrounding medium leads to better system matrix conditioning throughout the entire frequency spectrum, and it also leads to a clean dc solution. We demonstrate that the system matrix is well behaved from a full-wave solution at high frequencies to a pure resistive circuit solution at dc, thereby enabling dc-to-daylight simulations. Finally, these techniques are applied to remedy the low-frequency conditioning of the electric field integral equation matrix

1D and 2D Cole‐Cole‐inversion of time‐domain induced‐polarization data

ABSTRACTA new method for the 2D inversion of induced polarization (IP) data in the time domain has been developed. The entire IP transients were observed and inverted into 2D Cole‐Cole earth models, including resistivity, chargeability, relaxation time and the frequency constant. Firstly, a modified 1D time‐domain electromagnetic algorithm was used to calculate the response of a layered polarizable ground. The transient signals were then inverted using the Marquardt method to derive the Cole‐Cole parameters of each layer. However, model calculations showed that the EM effects could be neglected for the time range (>1 ms) and for the transmitter–receiver distances (<50 m) used in this study. Therefore, the induction effects were not considered for the solution of the 2D inverse problem and a DC solution was applied. An approximative forward algorithm was introduced in order to calculate the IP transients directly in the time domain and in order to speed up the inverse procedure. The approximation is highly accurate, and this is demonstrated by comparing the approximations with their exact solutions up to 3D.The inverse algorithm presented consists of two steps. The transient voltages of an array data set were inverted separately into a two‐dimensional resistivity model for each time channel. The time‐dependent resistivity of each cell was then interpreted as the response of a homogeneous half‐space. In the 2D inversion algorithm, a 3D DC algorithm was used as a forward operator. The method only requires a standard 2D DC inversion and a homogenous half‐space Cole‐Cole inversion.The developed algorithm has been successfully applied to synthetic data sets and to a field data set obtained from a waste site situated close to Düren in Germany.

Modeling of Quantization Effects in Digitally Controlled DC–DC Converters

In digitally controlled dc-dc converters with a single voltage feedback loop, the two quantizers, namely the analog-to-digital (A/D) converter and the digital pulse-width modulator (DPWM), can cause undesirable limit-cycle oscillations. In this paper, static and dynamic models that include the quantization effects are derived and used to explain the origins of limit-cycle oscillations. In the static model, existence of dc solution, which is a necessary no-limit-cycle condition, is examined using a graphical method. Based on the generalized describing function method, the amplitude and offset-dependent gain model of a quantizer is applied to derive the dynamic system model. From the static and dynamic models, no-limit-cycle conditions associated with A/D, DPWM and compensator design criteria are derived. The conclusions are illustrated by simulation and experimental examples

Efficient DC fault simulation of nonlinear analog circuits: one-step relaxation and adaptive simulation continuation

Efficient dc fault simulation of nonlinear analog circuits is addressed in this paper. Two techniques, one-step relaxation and adaptive simulation continuation, are proposed. By one-step relaxation, only one Newton-Raphson iteration is performed for each faulty circuit with the dc solution of the good circuit as the initial point, and the approximate solution is used for detecting the fault. The paper shows experimentally and justifies theoretically that approximate dc fault simulation by one-step relaxation can accomplish almost the same fault coverage as exact dc fault simulation. Exact dc fault simulation by adaptive simulation continuation is first to order faulty circuits based on the results of one-step relaxation, and then to use the solution of the previous faulty circuit as the initial point for the Newton-Raphson iteration of the next faulty circuit. Experiments on a set of 29 MCNC Circuit Simulation and Modeling Workshop benchmark circuits show that exact dc fault simulation by adaptive simulation continuation can achieve an average speedup of 4.4 and as high as 15 over traditional stand-alone fault simulation

A method for the analysis of transistor circuits having multiple DC solutions

The paper deals with circuits containing bipolar and MOS transistors. Both BJTs and MOSFETs are characterized by the Ebers–Moll-type models composed of two diodes and two current-controlled current sources. The basic and still open question of finding multiple DC solutions is discussed. To find all the DC solutions, the diodes are considered as piecewise-linear and represented by the series connection of an ideal diode, a voltage source and a linear resistor. Thus, the ideal diodes are the only nonlinear elements of the circuits. To find all the DC solutions, a method having combinatorial nature is applied. The main achievements of the paper are new algorithms enabling us to discard a huge number of combinations of the ideal diodes states immediately, without any solving of equations, or by performing a considerably reduced amount of computation. The method guarantees finding all the DC solutions of the piecewise-linear circuits. Next, each of the obtained solutions is corrected in succession by means of a controlled SPICE simulation. Four numerical examples of circuits containing bipolar and MOS transistors are presented, showing the efficiency of the proposed approach.

A study of pulsed plasma oxidation effects on the corrosion resistance of brass

The plasma oxidation process and the corrosion resistance mechanism of oxidized (α+β) brass (65Cu35Zn) in pulsed dc oxygen plasma and Mattson's solution are reported. The brass was exposed to pulsed DC oxygen plasma with various pulse frequencies. When the brass was exposed to the oxygen plasma, ZnO was identified dominantly in the passive layer and α-brass sublayer was formed because Zn in the (α+β) brass diffused to the surface. These multi-passive layers contribute to the corrosion resistance behavior of (α+β) brass with 92.5% corrosion protection efficiency for the untreated sample. But as input pulse frequency decreases, it becomes more effective in corrosion resistance and has relation with surface behavior in corrosion processing.

A study of plasma oxidation effects on the passive layer synthesis for the corrosion resistance of (α+β) brass

The plasma oxidation process and the corrosion resistance mechanism of oxidized (α+β) brass (63.5Cu36.5Zn) in pulsed dc oxygen plasma and Mattson's solution are reported. The brass was exposed to pulsed dc oxygen plasma with various working pressures. As increasing oxygen pressure, the ZnO layer was formed on the surface dominantly and α-brass sublayer was formed under the ZnO since Zn in the (α+β) brass diffuse to surface. These multipassive layers contribute the corrosion resistance behavior of (α+β) brass with 92.5% corrosion protection efficiency to untreated sample.

DC Solutions of Postbuckling Problems

In this paper we present an approach to determine the local minima of a specific class of minimization problems. Attention is focused on the inextensibility condition of flexible rods expressed as a non convex constraint. Two algorithms are derived from a special splitting of the Lagrangian into the difference of two convex functions (DC). They are compared to the classical augmented Lagrangian method used in this context. These DC formulations are easily extended to contact problems and applied to the determination of confined postbuckling shapes and to microbuckling in a cellular structure.

An efficient algorithm for finding multiple DC solutions based on the SPICE-oriented Newton homotopy method

It is a very important, but difficult, task to calculate the multiple dc solutions in circuit simulations. In this paper, we show a very simple SFICE-oriented Newton homotopy method which can efficiently find out the multiple de solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. Thus, our simulator can be efficiently applied to calculate the multiple dc solutions and perhaps all the solutions.

Fluorescence intensity and lifetime measurement of free and particle-bound fluorophore in a sample stream by phase-sensitive flow cytometry

We report a novel method to quantify fluorescence intensity and lifetime of free (solution) and particle-bound fluorophore in a flow stream. The technique combines flow cytometry and frequency-domain lifetime spectroscopy principles to make unique fluorescence measurements on free fluorophore and fluorophore-labeled particles. Fluorophore-labeled microspheres suspended in a fluorophore solution are analyzed as they flow through a chamber and pass across an intensity-modulated laser beam consisting of a continuous-wave (cw) direct-current (dc) and high-frequency (sine wave) excitation component. Fluorescence emission signals consisting of a dc-offset steady-state sinusoidal signal (fluorophore solution) and a sinusoidally modulated Gaussian-shaped signal pulse (fluorophore-labeled particles) are processed electronically to quantify intensities and lifetimes. The cw-excited, particle-associated fluorophore (pulse) and steady-state (dc) solution fluorescence intensity signals are measured using low-pass filtering to remove the high-frequency signal components and an ac-coupled and a gated dc amplifier to process the respective particle-bound and free fluorophore signals. The high-frequency excited, particle-bound fluorophore and free fluorophore lifetimes are individually measured using two pairs of phase-sensitive detectors to provide signals proportional to the sine and cosine of the respective phase shifts, which are ratioed to determine the respective lifetimes. The fluorescence signal intensity and lifetime detection channel outputs are displayed as frequency distribution histograms using a computer-based data acquisition system.

Finding all the DC solutions of a certain class of piecewise-linear circuits

The problem of finding all the DC solutions of a certain class of piecewise-linear electronic circuits containing locally passive and locally active one-ports is considered in this paper. An effective method enabling us to locate the solutions is developed. The method constitutes the crucial point of an algorithm based on the idea of successive contraction, division, and elimination that is capable of determining all the solutions. Several numerical examples are given, and some comparison analyses are performed confirming the usefulness of the proposed approach.

A note on the semiconductor laser equivalent circuit

The small-signal rate equations for a semiconductor laser can be represented as a network of electrical components, as shown by Tucker and Kaminow [R. S. Tucker and I. P. Kaminow, J. Lightwave Technol. LT-2, 385 (1984)] for the case of finite gain compression ε>0. However, a calculation of small-signal response curves δS/δI vs I derived from this equivalent circuit exhibit a linear decrease (“droop”) above threshold that is inconsistent with the dc solutions of the original rate equations. This problem flags a subtle flaw in the formulation of the circuit model. We observe, moreover, that the expression for the resonance damping parameter used throughout the laser literature follows exactly from this same RLC circuit model. The derivation of the circuit model from the rate equations is revisited. Consistency between the dc and ac solutions is achieved when the differential of the net gain δ{G/(1+εS)} is appropriately represented as a shunt element with zero admittance. The corrected circuit model resolves the “droop” problem in the small-signal δS/δI vs I relation. As expected, the new circuit model leads to a modified expression for the damping parameter.

Improvement of the sign test for finding all the DC solutions of piecewise-linear circuits

Improvement of the sign test for finding all the DC solutions of piecewise-linear circuits

Stability of characteristic curves of nonlinear resistive circuits

In this paper, we discuss the stability of the characteristic curves for nonlinear resistive circuits including parasitic elements. Although the dc solution is determined by analyzing the nonlinear resistive circuit, its equilibrium point will be stable or unstable because every resistive element has a small parasitic component in practice. We consider here two parasitic elements: a capacitor between every resistor node and ground and an inductor in series with each resistor. Of course, the stability can be decided by solving the variational equation at each equilibrium point obtained by the dc analysis; however, this is very time consuming. We show here that the stability is mainly changed at the boundary of the presence of negative differential resistance (NDR) and the bifurcation points, such as turning and pitchfork points on the dc characteristic curves. The instability regions of the solution curve are easily found by both the locations of bifurcation points and NDR regions of the nonlinear resistors.

Electric field directed nucleic acid hybridization on microchips.

Selection and adjustment of proper physical parameters enables rapid DNA transport, site selective concentration, and accelerated hybridization reactions to be carried out on active microelectronic arrays. These physical parameters include DC current, voltage, solution conductivity and buffer species. Generally, at any given current and voltage level, the transport or mobility of DNA is inversely proportional to electrolyte or buffer conductivity. However, only a subset of buffer species produce both rapid transport, site specific concentration and accelerated hybridization. These buffers include zwitterionic and low conductivity species such as: d- and l-histidine; 1- and 3-methylhistidines; carnosine; imidazole; pyridine; and collidine. In contrast, buffers such as glycine, beta-alanine and gamma-amino-butyric acid (GABA) produce rapid transport and site selective concentration but do not facilitate hybridization. Our results suggest that the ability of these buffers (histidine, etc.) to facilitate hybridization appears linked to their ability to provide electric field concentration of DNA; to buffer acidic conditions present at the anode; and in this process acquire a net positive charge which then shields or diminishes repulsion between the DNA strands, thus promoting hybridization.

Rate-equation-based laser models with a single solution regime

Even with the use of variable transformations, quantum-well (QW)-laser models based on the standard rate equations and a linear gain-saturation term can possess multiple dc solution regimes for nonnegative values of injection current. In this paper, we demonstrate analytically that rate-equation-based models that employ more realistic gain-saturation terms can be transformed so that they do indeed possess a unique solution regime. We also present circuit-level implementations of these models suitable for use in SPICE.

DC analysis of circuits with idealized diodes considering reverse bias breakdown phenomenon

The resistive circuits containing idealized diodes are considered in this paper. The diodes are represented by three-segment characteristics enabling us to take into account the effect of reverse bias breakdown phenomenon. A parametric representation is developed leading to a well-defined description of the circuits. It is shown that this equation always has at least one solution and a region containing all the solutions can be easily determined. The necessary and sufficient conditions for uniqueness of the solution are also developed. The problem of finding a unique or multiple dc solutions of the circuits is considered in detail. It is shown that the Newton-Raphson algorithm can be used, in a very effective way, to determine a unique solution. The structure of the Jacobian matrix makes it possible to considerably improve the process of solving linear simultaneous equations at each iteration. Exploiting some properties of the parametric equation an algorithm is developed enabling us to determine all the dc solutions of this class of circuits. Moreover, some suggestions are given concerning computation of circuits including more realistic models of diodes and transistors. Several numerical examples are presented conforming usefulness of the proposed approach.

Finding all DC solutions of nonlinear resistive circuits by exploring both polyhedral and rectangular circuits

A new fast method for finding all the DC solutions of piecewise-linear (PWL) resistive circuits is presented. The structure of the algorithm is based on the exploration of a binary tree: each node represents a specific PWLsub circuit, derived from the original PWL circuit by truncating the original PWL characteristics. The terminal nodes of the tree represent the linear circuits related to single linear regions. The natural exponential growth of the tree is controlled by two different criteria. They are based on the investigation of the convex solution domains of the so-called polyhedral circuits or, alternatively, of the so-called rectangular circuits. The first criterion is more efficient but more CPU-time consuming than the second one. An appropriate combination of both allows the realisation of an overall algorithm faster than those based on a unique criterion.

Non-Incremental Loss Allocation in Multiple Interarea Power Transfers

The allocation of losses caused by interarea power transfers is studied in a general framework where no overall system optimization is assumed for each additional transfer. This study points out the influence on loss allocation of the order in which transfers were decided. If this order is known, an exact allocation can be found, with a “sequential” method. Otherwise an “aggregate” method can provide an average solution. 12 methods are defined and tested numerically, out of which 2 are advisable for sequential solutions and 2 for aggregate solutions. In both cases, one AC solution and one DC approximate solution are satisfactory. The AC solutions are accurate, the DC solutions are faster and introduce a maximum error of 6%. The proposed techniques are general and can be applied to power transfers inside an area.