Transient analysis of circuits

Transient analysis of circuits

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There are three basic elements in an electric circuit, the resistor R, capacitor C, and inductor L. The circuits in this chapter will combine the resistor(s) R with an energy storage element capacitor C or an inductor L to form an RL (resistor-inductor) or RC (resistor-capacitor) circuit. These circuits exhibit the important behaviors that are fundamental to much of analogue electronics, and they are used very often in electric and electronic circuits. Analysis RL or RC circuits still use KCL and KVL. The main difference between RL or RC circuits and pure resistor circuits is that the pure resistor circuits can be analyzed by algebraic methods. The relationship of voltages and currents in the capacitor and inductor circuits is expressed by the derivative and differential equations (the equations with the derivative). RL or RC circuits that are described by the first-order differential equations, or the circuits that include resistor(s), and only one single energy storage element (inductor or capacitor), are called the first-order circuits.

Chapter Contents:

  • 7.1 The first-order circuit and its transient response
  • 7.1.1 First-order circuit
  • 7.1.2 Transient and steady state
  • 7.1.3 Step response
  • 7.1.4 Source-free and unit-step response
  • 7.1.5 The initial condition of the dynamic circuit
  • 7.2 The step response of an RC circuit
  • 7.2.1 The charging process of an RC circuit
  • 7.2.2 Quantity analysis of the RC charging process
  • 7.2.3 Charging equations for an RC circuit
  • 7.2.4 Example with RC circuit
  • 7.3 The source-free response of the RC circuit
  • 7.3.1 The discharging process of the RC circuit
  • 7.3.2 Quantity analysis of the RC discharging process
  • 7.3.3 RC time constant
  • 7.3.4 The RC time constant and charging/discharging
  • 7.3.5 Different time constants for charging/discharging
  • 7.3.6 Discharging process examples
  • 7.4 The step response of an RL circuit
  • 7.4.1 RL circuit
  • 7.4.2 Energy-storing process of the RL circuit
  • 7.4.3 Quantity analysis of the RL energy-storing process
  • 7.5 Source-free response of an RL circuit
  • 7.5.1 Energy-releasing process of an RL circuit
  • 7.5.2 Quantity analysis of the RL energy-releasing process
  • 7.5.3 RL time constant
  • 7.5.4 RL time constant and energy storing/releasing
  • Summary
  • Practice problems

Inspec keywords: resistors; RLC circuits; RC circuits; capacitors; transient analysis; differential equations; algebra; inductors; network analysis

Other keywords: resistor-capacitor circuit; inductor; algebraic methods; derivative equations; RC circuits; first-order differential equations; electric circuit; first-order circuits; resistor-inductor circuit; energy storage element; RL circuits; resistor; circuit transient analysis; capacitor; analogue electronics

Subjects: Capacitors; Algebra; General circuit analysis and synthesis methods; Inductors and transformers; Mathematical analysis; Resistors

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