C H A P T E R 4 AC Network Analysis

Figure 4.1 Structure of parallel-plate capacitor + _ Circuit symbol C = A d F permittivity of air Parallel-plate capacitor with air gap (air is the dielectric) 10 12 m 8.854 x

Figure 4.2 Combining capacitors in a circuit 1 2 3 Capacitances in parallel add EQ = C + C Capacitances in series combine like resistors in parallel = +

Figure 4.8 Iron-core inductor Magnetic flux lines Iron core inductor i ( t ) L Circuit symbol di dt v ) = _ +

Figure 4.9 Combining inductors in a circuit L EQ = 1 + 2 3 Inductances in series add Inductances in parallel combine like resistors in parallel

Figure 4.13 Analogy between electrical and fluid resistance v 1 2 i q f p R

Figure 4.14 Analogy between fluid capacitance and electrical capacitance q f P 1 p gas 2 + _ C i v

Figure 4.15 Analogy between fluid inertance and electrical inertance v 1 p 2 I f q L + –

Figure 4.18 Time-dependent signal sources + _ v ( t ) i ), Generalized time-dependent sources Sinusoidal source

Figure 4.19 Periodic signal waveforms T 2 3 4 Time Sawtooth wave Square wave Triangle wave Pulse train Sine wave _

Figure 4.20 Sinusoidal waveforms t A T _ Reference cosine Arbitrary sinusoid

Figure 4.27 Euler’s identity Im j _ 1 Re sin cos e = cos +

Figure 4.33 The impedance element + ~ – v S ( t ) j i R L C AC circuits AC circuits in phasor/impedance form Z is the impedance of each circuit element

Figure 4.34 Impedances of R, L and C in the complex plane Z R = R L = j C = 1 j Im Re – 2 -90

Figure 4.42 An AC circuit v ( t ) i R L C j Z A sample circuit 1 2 R L x C j Z A sample circuit for AC analysis The same circuit in phasor form + ~ –

Figure 4.45 AC equivalent circuits Source Z L (b) Equivalent source S ( j ) Load (a) Equivalent load + ~ –

Figure 4.46 Rules for impedance and admittance reduction Z 1 2 Impedances in parallel behave like resistors in parallel: + Y Admittances in parallel add: Admittances in series behave like conductances in series: Impedances in series add:

Figure 4.47 Reduction of AC circuit to equivalent form S Z 2 A phasor circuit with load L 3 1 4 ab a b Circuit for the computation of the equivalent impedance, T OC = SC N Circuit for the computation of the Th é venin equivalent voltage Circuit for the computation of the Norton equivalent current + ( || ) + O C + ~ –