![]() The equivalent voltage source is equal to the open-circuit voltage V ^ o c, while the source impedance is equal to the input impedance Z in. Thevenin's theorem states that any active network can be replaced at a given pair of nodes by a nonideal voltage source. Nonideal voltage and current sources can be converted equivalently into one another via the formulas: Z s = 1 / Y s and V ^ s = I ^ s Z s. Ī nonideal current source is modeled by an ideal independent current source in parallel with a (normally small) admittance.Ī nonideal voltage source is modeled by an ideal independent voltage source in series with a (normally small) impedance.The main concepts and definitions are summarized below. Along with these concepts came some definitions which we will continue to use throughout the text. In this chapter we introduced a number of important concepts and rules that can be used to simplify the analysis of electric circuits. ![]() Estimating the number of dc operating points or even their upper bounds for an arbitrary nonlinear circuit is still an open problem ( Lagarias and Trajković, 1999). For example, a circuit containing two bipolar transistors possesses at most three isolated dc operating points ( Lee and Willson, 1983). These circuits may possess multiple operating points with an appropriate choice of circuit parameters and biasing of transistors ( Trajković and Willson, 1992). Other circuits, such as flip-flops and memory cells, possess feedback structures ( Nielsen and Willson, 1980). Many transistor circuits possess the same property based on their topology alone. Many resistive circuits consisting of independent voltage sources and voltage-controlled resistors, whose v–i relation characteristics are continuous strictly monotone-increasing functions, have at most one solution ( Duffin, 1947 Minty, 1960 Willson, 1975). ![]() In contrast, circuits consisting of positive linear resistors possess either one dc operating point or, in special cases, a continuous family of dc operating points. Ljiljana Trajković, in The Electrical Engineering Handbook, 2005 Existence and Uniqueness of SolutionsĬircuits with nonlinear elements may have multiple discrete dc operating points (equilibriums).
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