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15.1 SPICE AND PSPICE Spice (Simulation Program with Integrated Circuit Emphasis) is a computer program developed in the 1970s at the University of California at Berkeley for simulating electronic circuits. It is used as a tool for analysis, design, and testing of integrated circuits as well as a wide range of other electronic and electrical circuits. Spice is a public domain program. Commercial versions, such as PSpice by MicroSim Corporation, use the same algorithm and syntax as Spice but provide the technical support and addons that industrial customers need. This chapter introduces the basic elements of Spice/PSpice and their application to some simple circuits. Examples are run on the evaluation version of PSpice which is available free of charge.

TYPES OF FUNCTIONS It is worth realizing that there is a fundamental pool of functions at the foundation of calculus and advanced calculus These are called elementary functions Either they are generated from a real variable x by the fundamental operations of algebra, including powers and roots, or they have relatively simple geometric interpretations As the title elementary functions suggests, there is a more general category of functions (which, in fact, are dependent on the elementary ones) Some of these will be explored later in the book The elementary functions are described below 1 Polynomial functions have the form f x a0 xn a1 xn 1 an 1 x an 1 where a0 ; ; an are constants and n is a positive integer called the degree of the polynomial if a0 6 0.

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, sn 1} is a sorted sequence of n values of the same type as x) (Postcondition: either the index i is returned where si = x, or 1 is returned) 1 Let ss be a subsequence of the sequence s, initially set equal to s 2 If the subsequence ss is empty, return 1..

The circuit description is entered in the computer in the form of a series of statements in a text le prepared by any ASCII text editor and called the source le. It may also be entered graphically by constructing the circuit on the computer monitor with the Schematic Capture program from MicroSim. In this chapter, we use the source le with the generic name SOURCE.CIR. To solve the circuit, we run the circuit solver on the source le. The computer puts the solution in a le named SOURCE.OUT.

EXAMPLE 15.1 Use PSpice to nd the dc steady-state voltage across the 5-mF capacitor in Fig. 15-1(a).

Program to test the De Moivre s formula for Fibonacci numbers:

Fig. 15-1

The fundamental theorem of algebra states that in the eld of complex numbers every polynomial equation has at least one root As a consequence of this theorem, it can be proved that every nth degree polynomial has n roots in the complex eld When complex numbers are admitted, the polynomial theoretically may be expressed as the product of n linear factors; with our restriction to real numbers, it is possible that 2k of the roots may be complex In this case, the k factors generating them will be quadratic (The corresponding roots are in complex conjugate pairs) The polynomial x3 5x2 11x 15 x 3 x2 2x 5 illustrates this thought 2 Algebraic functions are functions y f x satisfying an equation of the form p0 x yn p1 x yn 1 pn 1 x y pn x 0 2 where p0 x ; .

public class Fibonacci { public static void main(String[] args) { final double SQRT5 = Math.sqrt(5.0); final double PHI = (1 + SQRT5)/2; final double PSI = (1 - SQRT5)/2; long f0, f1 = 0, f2 = 1; for (int n = 2; n < 32; n++) { f0 = f1; f1 = f2; f2 = f1 + f0; double fn = (Math.pow(PHI, n) - Math.pow(PSI, n))/SQRT5; System.out.print("%4d%12.2", f2, fn); } } }

CHAP. 15]

We rst label the nodes by the numbers 0, 1, 2 and the elements by the symbols R1, R2, C, and Vs [Fig. 15-1(b)]. We then create in ASCII the source le shown below and give it a name, for instance, EXMP1.CIR. DC analysis, Fig. Vs R1 R2 C .END 15-1 1 0 1 2 0 2 0 2 DC 3k 6k 5 uF 9V

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