Finding DC operating points of nonlinear circuits is an important and difficult task in circuit simulation. The program for simulating the circuit is called the circuit simulator.

From the mid-1960s, the computers are widly used in circuit design or verification.

The circuit simulators developed At this time of year are called the first-generation simulators. Since then, it has developed into the second-generation simulators, and the third-generation simulators.

Although the circuit simulators exists many variations, SPICE(Simulation Program with Integrated Circuit Emphasis) is the high-quality circuit simulator. Hence, SPICE is widly used in the LSI design spot in the world now.

SPICE is circuit simulator developed in University of California at Berkeley in 1972. The prototype of SPICE is CANCER(Computer Analysis of Nonlinear Circuits Excluding Radiation) presented in 1971.

CANCER is the simulator for simulating the small or middle scale circuits. The number of provides circuit elements, nodes and nonlinear elements (transistors and diodes) that are avairable to simulate are limitted 400, 100, and 100, respectively. CANCER is used nodal analysis to fomulate the circuit equation, which makes a big difference between CANCER and SPICE. CANCER provides for the analysis of circuits in the following four modes of operation: nonlinear DC, transient, small-signal AC, and noise.

The most major method for DC analysis is the Newton Raphson (NR) method. However, the NR method or its variants often fails to converge to a solution unless the initial point is sufficiently close to the solution. Therefore, this problem is major fault in circuits simulation.

Since transient analysis is excuted by solbing the differential equations, CANCER is implmented the numerical integration method. At this time of year, as the numerical integration method, the trapezoidal method and the backward Euler’s method are well known. CANCER is provided the trapezoidal method because it is the high stability method. Furthermore, CANCER is introduced the sparse matrix techniques for simulating the circuit efficiently. SPICE is also introduced this method for circuit simulation. In CANCER, the transistors in the cicuits are modelling using the Ebers-Moll model. Hence, the simple transistor model is implemeted.

CANCER was added some further improvement, and was presented by the name of SPICE1 in 1972. The main difference between CANCE and SPICE1 is to add the Gummel-Poon model as the transisotr model. This model can express more accuracy the transistors in circuits than the Ebers-Moll model. Moreover, SPICE1 is added JFET and MOSFET that are the new circuit elements, and Modelling it is proveided Shichman-Hodges model. Furthermore, as the new method to shorten simularion time, macromodelling is introduced. Today, the idea of macromodelling is the major method to express the complicated circuits with the equivalent circuits.

SPICE1 was developed into SPICE2, and presented in 1975. The main difference between CANCE (or SPICE1) and SPICE2 is to change the formulation of circuit equations from nodal analysis to modified nodal analysis. Furthermore, to advance analysis accuracy and make analysis time faster, SPICE1 is introduced the time-step controll algorithm and the Gear method.

Then, SPICE2 was developed into SPICE3. This is the thing which designed SPICE2 again to be based on a CAD study program of UCB, and basic performances such as computing speed or convergence characteristics are not advanced in comparison with SPICE2. The main difference between SPICE2 and SPICE3 is the description language. Although SPICE2 is described FORTRAN, SPICE3 is described C language. In addition, the input and output interfaces were changed of from the batch type to the interactive type, and the function for indicating graphics was added. Therefore, the circuit simulators using in the circuit design are SPICE based on SPICE2 or SPICE3 now.

In SPICE, various efficient techniques such as sparse matrix techniques, LU decomposition (for solving linear equations), modified Newton method (for solving nonlinear equations), and stiffly stable numerical integration methods with efficient time-step control algorithms (for solving ordinary differential equations) are implemented. Moreover, there are many variations of SPICE, and most of them include various know-hows accumulated over many years. Hence, SPICE is an excellent software.

## References

- W.J. McCalla and W.G. Howard Jr, “BIAS-3—A program for the nonlinear DC analysis of bipolar transistor circuits,” IEEE J. Solid-State Circuits, vol.SC-6, no.1, pp.14–19, Feb. 1971.
- F.H. Branin, G.R. Hogsett, B.L Lunde, and L.E. Kugel, “ECAP-II—A new electronic circuit analysis program,” IEEE J. Solid-State Circuits, vol.SC-6, no.4, pp.146–166, Aug. 1971.
- L.W. Nagel and R.A. Rohrer, “Computer analysis of nonlinear circuits excluding radiation (CANCER),” IEEE J. Solid-State Circuits, vol.SC-6, no.4, pp.166–182, Aug. 1971.
- L.W. Nagel and D.O. Pederson, “SPICE—Simulation program with integrated circuit emphasis,” Univ. California, Berkeley, CA, April 1973.
- W.T. Weeks, A.J. Jimenez, G.W. Mahoney, D. Mehta, H. Qassemzadeh, and T.R. Scott, “Algorithms for ASTAP—A network analysis program,” IEEE Trans. Circuit Theory, vol.CT-20, no.6, pp.628–634, Nov. 1973.
- L.W. Nagel, “SPICE2: A computer program to simulate semiconductor circuits,” Univ. California, Berkeley, CA, May 1975.
- B.R. Chawla, H.K. Gummel, and P. Kozak, “MOTIS—An MOS timing simulator,” IEEE Trans. Circuits Syst., vol.CAS-22, no12. pp.901–909, Dec. 1975.
- A.R. Newton, “Techniques of the simulation of large-scale integrated circuits,” IEEE Trans. Circuits Syst., vol.CAS-26, no.9, pp.741–749, Sept. 1979.
- E. Lelarasmee, A.E. Ruehli, and A.L. Sangiovanni-Vincentelli, “The waveform relaxation method for time-domain analysis of large scale integrated circuits,” IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., vol.CAD-1, no.3, pp.131–145, July 1982.
- A. Vladimirescu, The SPICE Book, John Wiley \& Sons, New York, 1994.
- 浅井秀樹, 渡辺貴之, 電子回路シミュレーション技法, 科学技術出版, 東京, 2003.
- 三浦道子, 名野隆夫, 回路シミュレ－ション技術とＭＯＳＦＥＴモデリング, サイペック, 東京, 2003.
- J.J. Ebers and J.L. Moll, “Large-signal behavior of junction transistors,” Proc. IRE, vol.42, pp.1761–1772, Dec. 1954.
- H. Shichman, “Integration system of a nonlinear network-analysis program,” IEEE Trans. Circuit Theory, vol.CT-17, no.3, pp.378–386, Aug. 1970.
- E.C. Ogbuobiri, W.F. Tinney, and J.W. Walker, “Sparsely-directed decomposition for gaussian elimination on matrices,” Proc. Power Appl. Conf., pp.215–225, May 1969.
- W.F. Tinney and J.W. Walker, “Direct solutions of sparse network equations by optimally ordered triangular factorization,” Proc. IEEE, vol.55, pp.1801–1809, Nov. 1967.
- F. Gustavson, W. Liniger, and R. Willoughby, “Symbolic generation of an optimal Crout algorithm for sparse systems of linear equations,” J. Assoc. Comput. Mach., vol.17, no.1, pp.87–109, Jan. 1970.
- H.K. Gummel and H.C. Poon, “An integral charge-control model of bipolar transistors,” Bell Syst. Tech. J., vol.49, no.4, pp.827–854, May 1970.
- 新原 盛太郎, SPICEとデバイス・モデル—IC設計者に必須のバイポーラ・トランジスタの基礎知識, CQ出版社, 東京, 2005.
- H, Shichman and D.A. Hodges, “Modeling and simulation of insulated-gate field-effect transistor switching circuits,” IEEE J. Solid-State Circuits, vol.SC-3, no.3, pp.285–289, Sept. 1968.
- C.W. Ho, A.E. Ruehli, and P.A. Brennan, “The modified nodal approach to network analysis,” IEEE Trans. Circuits Syst., vol.CAS-22, no.6, pp.504–509, June 1975.
- H. Shichman, “Integration system of a nonlinear network-analysis program,” IEEE Trans. Circuit Theory, vol.CT-17, no.3, pp.378–386, Aug. 1970.
- C.W. Gear, “Numerical integration of stiff ordinary differential equations,” Report 221, Dept. of Computer Science, Univ. of Illinois, Urbana, 1967. Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.
- L.O. Chua and P.M. Lin, Computer-Aided Analysis of Electronic Circuits : Algorithms and Computational Techniques, Prentice-Hall, Englewood Cliffs, New Jersey, 1975.
- J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, New York, 1980.
- 山本哲朗, 数値解析入門, サイエンス社, 東京, 1976.
- 伊理正夫, 数値計算, 朝倉書店, 東京, 1981.