Index

A L Admittance matrix, 139, 141, 143, 144 Laplace domain, 29–31, 35, 38, 39, 45–49, 52, 53, 55–57, 59, 60, 62, Angular frequency, 74 64–70, 72, 74, 75, 77, 79, 81, 123, 124, 139 Laplace transform and network function, 29–32, 34, 35, 37, 40, 47, 51, 62 C Linear time-invariant (LTI), 85, 88, 89, 116–118, 123 Capacitor, 39–43, 70 resistors, 115, 121 system, 32, 36 Loop, 79 D DC voltage source, 39, 69 Dependent source, 59 M Dependent voltage source, 59, 71 Mesh, 49, 59, 63, 79 Differential equation, 30, 34

N E Natural frequencies Electrical circuits, solutions of problems capacitor/inductor, 86, 95 capacitor, current-voltage relation, 10, 11, 13 characteristic equation, 101, 103 capacitor, voltage-current relation, 24 damped status, 87, 101 inductor, current-voltage relation, 10, 13, 15, 18 damping status, 98, 99, 102 input vector, 22 energy-saving components, 93 KCL, 10, 17 impedances, 96, 97 KVL, 9, 10, 13, 24, 26 infinite frequency, 105, 107 matrices, 15, 22 input admittance, 88, 105, 109 network, 20 input impedance, 89 source transformation theorem, 25 Laplace domain, 96–99, 102 state vector, 11, 14, 15, 17, 22 LC circuit, 104 Equivalent impedance, 55, 56, 59, 78 loops, 95 LTI network, stability, 108 mesh impedance matrix, 99, 101, 102 H nodal admittance matrix, 98 Hybrid matrix, 141 nonzero, 83, 91, 93, 111 nonzero primary voltage and current, 86 one-port network, 104 I parallel RLC circuit, 111 Impedance in Laplace domain, 35 resonance frequency, 105 Impedances, 45–47 RLC circuit, 112 Impulse function, 32, 36, 65 series LC circuit, 105 Impulse response, 33, 37 state variables, 84, 94 Independent current source, 62 supermesh, 109 Independent sources, 59 time domain, 108 Independent voltage source, 59, 62, 64, 68–70, 72, 75, 79, 81 transfer function, 84, 86, 96, 97, 109 Inductor, 39–42, 62, 70, 72 undamped status, 87, 100 Input admittance, 30 voltage and current sources, 111 Input impedance, 29, 31, 38, 46, 48 zero and pole, 97 Input signal, 32, 36 zero frequency, 107 Inverse Laplace transform, 55, 74 zero/poles, 84, 90, 104

# The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 151 M. Rahmani-Andebili, Advanced Electrical Circuit Analysis, https://doi.org/10.1007/978-3-030-78540-6 152 Index

Network function, 29–32, 34, 35, 37, 40, 51, 62 system matrix, 6 Node, 52, 57, 65–67, 71, 73, 77, 81 variables, 1 Nonzero primary current, 62 vector, 2, 5 Nonzero primary voltage, 62, 72, 79, 81 Steady-state output, 41 Steady-state response, 74 Supernode, 71, 77 O Switching operation, 43 Ohm’s law, 55, 56, 69, 74, 127 Symmetric circuit, 75 Open circuit, 46 Output response of system, 32, 36 Output voltage, 46 T Tellegen’s theorem, 122–125, 127 Thevenin equivalent circuit, 70, 126 P Thevenin impedance, 49, 59 Phasor domain, 125, 127 Three-port network, 115, 117 Primary circuit, 70 Transfer function, 29–32, 34, 35, 37, 40, 51, 62, 96 Primary current of inductor, 39, 41 Two-port network, 116–118, 133 Primary energy, 40 admittance matrix, 131–134, 139, 143, 144 Primary voltage, 39, 40, 70 hybrid matrix, 132, 135, 138, 142, 146 hybrid parameter, 130, 138 impedance matrix, 129, 131, 132, 137, 141, 143, 146 R parallel, 145 Resistive load, 118 phasor domain, 140 Resistor, 42 series connection, 148 Response of circuit, 32, 33 transmission matrix, 130, 136, 138, 147, 148

S V Source transformation theorem, 25, 59, 62, 75 Voltage division formula, 57 State equations Voltage division rule, 45, 46, 61, 64–67, 69, 75 capacitor/inductor, 3 Voltage source, 48, 65 circuit, 8 input vector, 7 matrix, 4 Z resistors, 6 Zero state, 38 state vector, 1