ne solution of which accurately describes the motion of the physical systems. There is, of course, no exception to this in the field of electrical engineering. A physical electrical system such as an amplifier circuit for example first represented by a circuit drawn on paper. The circuit is composed of resistors, capacitors, inductors, and voltage and/or current sources, and each of these circuit elements is given a symbol together with a mathe matical expression (i. e, the voltage-current or simply v-i relation) relating its terminal voltage and current at every instant of time. Once the network and the v-i relation for each element is specified, Kirchhoff's voltage and current laws can be applied, possibly together with the physical principles to be introduced in Chapter 3.1 to establish the mathematical model in the form of differential equations In Section I, focus is on analysis only (leaving coverage of synthesis and design to Section Ill, Electronics") Specifically, the passive circuit elements--resistors, capacitors, inductors, transformers, and fuses-as well a voltage and current sources(active elements)are discussed. This is followed by a brief discussion on the elements of linear circuit analysis. Next, some popularly used passive filters and nonlinear circuits are introduced. Then, Laplace transform, state variables, z-transform, and T and T configurations are covered. Finally, transfer functions, frequency response, and stability analysis are discussed Nomenclature Symbol Quantity Symbol Quantity Unit area rad/s magnetic flux density Tesla P power factor induced voltage large dielectric constant F/m ripple factor R resistance R(T temperature coefficient ]2/C of resistance resistivity current Jacobian t Boltzmann constant 1. 38x 10-23 J/K 0 degree dielectric coefficient K coupling coefficient V voltage inductance energy eigenvalue X reactance mutual inductance Y admittance filter order Here, of course, active elements such as transistors are represented by their equivalent circuits as combinations of resistors and dependent soure c2000 by CRC Press LLC© 2000 by CRC Press LLC the solution of which accurately describes the motion of the physical systems. There is, of course, no exception to this in the field of electrical engineering. A physical electrical system such as an amplifier circuit, for example, is first represented by a circuit drawn on paper. The circuit is composed of resistors, capacitors, inductors, and voltage and/or current sources,1 and each of these circuit elements is given a symbol together with a mathe￾matical expression (i.e., the voltage-current or simply v-i relation) relating its terminal voltage and current at every instant of time. Once the network and the v-i relation for each element is specified, Kirchhoff’s voltage and current laws can be applied, possibly together with the physical principles to be introduced in Chapter 3.1, to establish the mathematical model in the form of differential equations. In Section I, focus is on analysis only (leaving coverage of synthesis and design to Section III, “Electronics”). Specifically, the passive circuit elements—resistors, capacitors, inductors, transformers, and fuses—as well as voltage and current sources (active elements) are discussed. This is followed by a brief discussion on the elements of linear circuit analysis. Next, some popularly used passive filters and nonlinear circuits are introduced. Then, Laplace transform, state variables, z-transform, and T and p configurations are covered. Finally, transfer functions, frequency response, and stability analysis are discussed. Nomenclature 1 Here, of course, active elements such as transistors are represented by their equivalent circuits as combinations of resistors and dependent sources. Symbol Quantity Unit A area m2 B magnetic flux density Tesla C capacitance F e induced voltage V e dielectric constant F/m e ripple factor f frequency Hz F force Newton f magnetic flux weber I current A J Jacobian k Boltzmann constant 1.38 ¥ 10–23 J/K k dielectric coefficient K coupling coefficient L inductance H l eigenvalue M mutual inductance H n turns ratio n filter order Symbol Quantity Unit w angular frequency rad/s P power W PF power factor q charge C Q selectivity R resistance W R(T) temperature coefficient W/°C of resistance r resistivity Wm s Laplace operator t damping factor q phase angle degree v velocity m/s V voltage V W energy J X reactance W Y admittance S Z impedance W