1. Second Order Circuits ES-3 Download: http://www.ece.tufts.edu/~hopwood/downloads/es3/SecondOrderCircuits.ppt

2. Second Order Circuits Contain two independent reactive components This results in a second order differential equation containing d 2 i/dt 2 or d 2 v/dt 2

3. Example: Series RLC circuit + - V S (t) L C R i(t) KVL: V L + V R + V C = V s

6. Three Cases Case 1 - Overdamped:    large R:

7. Three Cases Case 2 - Underdamped:    small R:

8. Three Cases Case 3 – Critically damped:  

9. Examples + - V S (t) L C R i(t) L = 10uH C = 10nF  o = 3.16x10 6 rad/sec (504 kHz) R = 10, 63.2, and 1000 ohms  = 5x10 5, 3.16x10 6, and 5x10 7 s -1 Underdamped Critically Damped Overdamped t vsvs

10. Overdamped: R=1000 

11. Underdamped: R=10 

12. Critically Damped: R=63.2 

13. Mechanical Analogy Automobile: Mass  inductor Suspension: Spring  capacitor Shock Absorber: Damper  resistor Force  voltage Velocity  current Wikipedia.com