Circuit Theory/Transients Summary and Study guide

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This cover the basics of transients, the analysis of circuit response that goes away after a long time.


RC or LC Circuits[edit]

General solution steps for RL and LC circuits with a voltage source (with out voltage source Vc=0):

  1. Use KVL and KCL, get 1st order differential equation
  2. Find particular solution (Forcing Function) (Table is at bottom of page)
  3. The complete solution is the particular + the complementary.

  1. Substitute solution into differential equation to find and s. (Or find by solving in steady state.)
  2. Use the given initial conditions to find
  3. Write final solution

RLC Circuits[edit]

  • DC circuits -> constant forcing functions
  • AC circuits -> sinusoidal forcing functions
  • Particular solution for VDc =>L-> SC, C-> OC
Concept Formula notes
Damping Coefficiant (series LC)
Damping Coefficiant (parallel LC)
Undamped resonant frequency
General Form
Characteristic equation
Roots Characteristic eqn
Damping ratio
Overdamped roots real and distinct

Critically damped roots real and equal

Natural Frequency
Underdamped roots complex

Table of Forcing functions[edit]

Value Approximation
Cons. A
sin(t)/cos(t)