© The McGraw-Hill Companies, Inc McGraw-Hill 1 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I 5 Transient Analysis C H A P T E R

© The McGraw-Hill Companies, Inc McGraw-Hill 2 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.1 Examples of transient response

© The McGraw-Hill Companies, Inc McGraw-Hill 3 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.2 Circuit with switched DC excitation

© The McGraw-Hill Companies, Inc McGraw-Hill 4 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.3 A general model of the transient analysis problem R S V s Circuit containing RL/RC combinations Switch t = 0

© The McGraw-Hill Companies, Inc McGraw-Hill 5 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.5 Circuit containing energy-storage element + _ v R i R i C v C (t) C _ + v S (t) R + _ di C dt + 1 RC i C = dv S dt A circuit containing energy-storage elements is described by a differential equation. The differential equation describing the series RC circuit shown is

© The McGraw-Hill Companies, Inc McGraw-Hill 6 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.9 Differential equations of first-order circuits

© The McGraw-Hill Companies, Inc McGraw-Hill 7 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.10 Decay through a resistor of energy stored in a capacitor t = 0

© The McGraw-Hill Companies, Inc McGraw-Hill 8 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.15 t = 0 i L L I S R

© The McGraw-Hill Companies, Inc McGraw-Hill 9 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure mA i L (t) 0 t i L ( t ) Lv R (t) i L (0 + ) + –

© The McGraw-Hill Companies, Inc McGraw-Hill 10 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.22 A more involved RC circuit R 1 t= 0 V 1 v C + _ C R 2 R 3 V 2

© The McGraw-Hill Companies, Inc McGraw-Hill 11 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.23 The circuit of Figure 6.45 for t > 0 R 1 v C C + _ R 2 R 3 V 1 V 2

© The McGraw-Hill Companies, Inc McGraw-Hill 12 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.24 Reduction of the circuit of Figure 5.23 to Thevenin equivalent form

© The McGraw-Hill Companies, Inc McGraw-Hill 13 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.25 The circuit of Figure 5.22 in equivalent form for t > 0 + _ R T CV C + _ V T

© The McGraw-Hill Companies, Inc McGraw-Hill 14 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.39 Second-order circuits

© The McGraw-Hill Companies, Inc McGraw-Hill 15 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.43 Response of overdamped second-order circuit

© The McGraw-Hill Companies, Inc McGraw-Hill 16 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.44 Response of critically damped second-order circuit

© The McGraw-Hill Companies, Inc McGraw-Hill 17 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.45 Response of underdamped second-order circuit

© The McGraw-Hill Companies, Inc McGraw-Hill 18 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.46

© The McGraw-Hill Companies, Inc McGraw-Hill 19 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.48

© The McGraw-Hill Companies, Inc McGraw-Hill 20 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 5.52