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In the chapter we shall introduce the study of circuits characterized by a single energy-storage element--a capacitor or a inductor. It will be shown that the equations describing such a circuit may be put in a form involving an unknown variable and its first derivative. Such an equation is referred to as a first-order differential equation, thus we shall refer to circuits which contain only a single energy-storage element as first-order circuits
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In the chapter we shall study the properties of second-order circuits, i.e., circuits containing two energy-storage elements. Such circuits will, in general, be characterized by second-order differential equations
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In the chapter we shall introduce some two-terminal element which have properties, which are quite different than those of the resistor. These elements are the inductor and capacitor. The inductor and capacitor are passive elements, which are capable of storing and delivering finite amounts of energy
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In the chapter we present resistive circuit analysis methods. The first is based on KCL and determines all the node-to-datum voltages in a given circuit and is known as node analysis. The second method, based on KVL, determines all loop current and is known as loop analysis. After discussing superposition, we will introduce Thevenin's and Norton's theorems
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18-7 General nonlinear resistor circuit
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18-5 Combination of i-v characteristics 1. Series combination
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n--a large constant voltage source (t)-- small time-varying- voltage source(small signal) >>(3) bsin +i=(),+ (o)=: JOX tniog gin9go int---(1)←0=()2utJ
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1. Nonlinear resistor A nonlinear resistor is an element whose voltage and current are related by a nonlinear equation
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The set of variables is a hybrid set that may include both currents and voltages. They are the inductor currents and the capacitor voltages. Each of these quantities may be used directly to express the energy stored in the inductor or capacitor at any instant of time. They collectively describe the energy state of the system. They are called the state variables
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The node-to-datum voltage vector:
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