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 Circuits
editGeneral solution steps for RL and LC circuits with a voltage source (with out voltage source Vc=0):
- Use KVL and KCL, get 1st order differential equation
- Find particular solution (Forcing Function) (Table is at bottom of page)
- The complete solution is the particular + the complementary.
- Substitute solution into differential equation to find and s. (Or find by solving in steady state.)
- Use the given initial conditions to find
- 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
editValue | Approximation |
---|---|
Cons. | A |
sin(t)/cos(t) | |