Circuit Theory/Transients Summary and Study guide

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


RC or LC CircuitsEdit

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 CircuitsEdit

  • 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 functionsEdit

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