Yoshihiro Yamagami

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.

Frequency response of nonlinear networks using curve tracing algorithm

For designing of nonlinear circuits, it is very important to know the frequency response characteristics and the intermodulation. In this paper, we propose an efficient method for calculating the characteristic curves of nonlinear circuits, which is based on the harmonic balance method and a curve tracing algorithm for solving the determining equation. Firstly, applying the harmonic balance method to each element in the circuit, we obtain the determining equation which is realized by two coupled resistive circuits corresponding to the sine and cosine components. Then, the frequency response characteristic curve is calculated by solving the circuit with a STC (solution curve tracing circuit) of Spice.

An efficient algorithm for finding multiple DC solutions based on Spice oriented Newton homotopy method

For circuit designing, it is very important to calculate the DC operating points. It is known that if the circuit contains positive feedback loops such as flip-flop and negative resistance circuits, it may have many DC solutions. It is very difficult to find all of the solutions for these circuits. In this paper, we show a very simple Spice oriented Newton homotopy method which can efficiently find out the multiple DC solutions, and perhaps all of the solutions.

Analysis of communication circuits based on multidimensional Fourier transformation

There are many communication circuits driven by multitone signals such as modulators and mixers, and so on. In this case, if frequency components of the modulators are largely different, the brute force numerical integration will take an enormous computation time to get the steady-state responses, because the step size must be chosen depending on the highest frequency input. The same situation happens to mixer circuits which generate very low frequency output. In this paper, an efficient algorithm is shown to solve the communication circuits driven by multitone signals which is based on the frequency-domain relaxation method and the multi-dimensional Fourier transformation. Attenuation of the transient phenomena mainly depends on the reactive elements such as capacitors and inductors, so that we partition the circuit into two groups of the nonlinear resistive subnetworks and the reactive elements using the substitution sources. The steady-state response can he calculated in such a manner that the responses at each partitioning point have the same waveform. We have developed a simple simulator carrying out our algorithm that only uses the transient, dc-analysis and ac-analysis of SPICE. It can be easily applied to relatively large scale integrated circuits, efficiently, We found from many simulation results that the convergence ratio at the iteration of our relaxation method is sufficiently large, and can be applied to wide class of the communication circuits.

A reduction technique of large-scale RCG interconnects in the complex frequency domain

High-speed digital LSI chips usually consist of many sub-circuits coupled with multi-conductor interconnects embedded in the substrate. They sometimes cause serious problems of the fault switching operations due to the time-delays, crosstalks, reflections, etc. In order to solve these problems, it is very important to develop a user-friendly simulator for the analysis of LSIs coupled with interconnects. In this paper, we consider a large-scale gate-array circuit coupled with multi-conductor RCG interconnects. At first, we propose a new method for calculating the dominant poles of the impedance matrix, which give the large effects to the transient response. The corresponding residues are estimated by the least squares method. Using these poles and residues, the input–output relation of each interconnect can be described by the partial fractions. After then, the interconnect is replaced by the equivalent circuit realizing the partial fractions. In this way, we can easily develop a user-friendly simulator familiar with SPICE. We found from many examples that the good results can be obtained using only few dominant poles around the origin. Furthermore, the reduction ratio of our method is very large especially for large scale interconnects. Copyright

Envelope analysis of nonlinear electronic circuits based on harmonic balance method

We propose here a Spice-oriented envelope analysis based on the HB (harmonic balance) method, where Fourier coefficients are assumed to be slowly varying. The Fourier expansions of nonlinear devices are executed by MATLAB in the symbolic forms. In this time, the nonlinearities need to be approximated by the polynomial functions. The determining equation of the HB method is formulated as Sine–Cosine circuit in the form of schematic diagram using ABMs (analog behavior models) of Spice. Each sub-circuit corresponding to the higher harmonic component is almost the same circuit topology as the original one and has dynamic elements such as capacitors and inductors. The Sine–Cosine circuit can be solved by the transient analysis of Spice. Thus, our method is rather a symbolic approach in the meaning that the HB determining equation is given by the schematic diagram of Spice. Our method can be easily applied to the analysis of middle order of nonlinear communication circuits such as mixers and amplitude modulators and to the analysis of interesting phenomena in the nonlinear oscillations. After many simulation experiments, the results show that our envelope analysis is about 50 times faster than the direct transient analysis. Copyright

Spice-Oriented Frequency-Domain Analysis of Nonlinear Electronic Circuits

Distortion analysis of nonlinear circuits is very important for designing analog integrated circuits and communication systems. In this letter, we propose an efficient frequency-domain approach for calculating frequency response curves, which is based on HB (harmonic balance) method combining with ABMs (Analog Behavior Models) of Spice. Firstly, nonlinear devices such as bipolar transistors and MOSFETs are transformed into the HB device modules executing the Fourier transformations. Using these modules, the determining equation of the HB method is formed by the equivalent sine-cosine circuit in the schematic form or net-list. It consists of the coupled resistive circuits, so that it can be efficiently solved by the DC analysis of Spice. In our algorithm, we need not to derive any troublesome circuit equations, and any kinds of the transformations.

Asymptotic analysis of nonlinear electronic circuits

It is very important to analyze mixers and modulators for designing communication circuits. They are driven by multiple frequencies, one of which is usually very high carrier frequency compared to the other. To know the transient behaviors, we need to calculate many carrier waveforms, so that the transient analysis is very time-consuming. Hence, we propose an efficient envelope analysis for calculating the asymptotic behaviors of the amplitudes, which is based on the harmonic balance (HB) method with the slowly varying coefficients. In order to develop the Spice-oriented simulators, the Fourier expansions of nonlinear devices such as bipolar transistors are executed with MATLAB, and the Fourier modules should be stored in our computer library. Thus, we can easily formulate the determining equations of HB method called sine-cosine circuit. We found from many examples that the envelope method is several ten times faster than the transient analysis.

Distortion analysis of nonlinear networks based on SPICE-oriented harmonic balance method

Distortion analysis in the frequency domain is very important for designing analog integrated circuits. We propose here a new method based on the SPICE-oriented harmonic balance method, where the Fourier transformations to the bipolar transistors and/or MOSFETs are carried out using a new Fourier transfer circuit model. The circuit is composed of the analog behavior models (ABM) of SPICE, which can be applied to any kind of nonlinear circuit elements described by exponential and/or piecewise linear functions. Furthermore, the determining equation of our harmonic balance method is schematically described by coupled resistive DC, Cosine and Sine circuits, so that we can easily obtain the frequency response curves with the DC analysis of SPICE. Thus, our approach is quite user-friendly, because we need not derive the circuit equation and the determining equations in our harmonic balance method.

A reduction technique of large scale RCG interconnects in complex frequency domain

High frequency digital LSIs usually consist of many subcircuits coupled with multi-conductor interconnects embedded in the substrate. They sometimes cause serious problems in fault switching operations due to time-delays, crosstalk, reflections and so on. In order to solve these problems, it is very important to develop a user-friendly simulator for the analysis of LSIs coupled with interconnects. In our reduction algorithm, we first calculate the dominant poles which make a large contribution to the transient response, and the corresponding residues are estimated by the least squares method. Thus, the interconnect is replaced by an equivalent circuit realizing the partial fractions.