1. lecture 211 Impedance and Admittance (7.5) Prof. Phillips April 18, 2003

2. lecture 212 Impedance AC steady-state analysis using phasors allows us to express the relationship between current and voltage using a formula that looks likes Ohm’s law: V = I Z Z is called impedance (units of ohms,  )

3. lecture 213 Impedance Resistor:V = I R –The impedance is Z R = R Inductor:V = I j  L –The impedance is Z L = j  L

4. lecture 214 Impedance Capacitor: –The impedance is Z C = 1/j  C

5. lecture 215 Some Thoughts on Impedance Impedance depends on the frequency,  f Impedance is (often) a complex number. Impedance is not a phasor (why?). Impedance allows us to use the same solution techniques for AC steady state as we use for DC steady state.

6. lecture 216 Impedance Example: Single Loop Circuit 20k  +–+– 1F1F10V  0  VCVC + –  = 377 Find V C

7. lecture 217 Impedance Example How do we find V C ? First compute impedances for resistor and capacitor: Z R = 20k  = 20k  0  Z C = 1/j (377·1  F) = 2.65k  -90 

8. lecture 218 Impedance Example 20k  0  +–+– 2.65k  -90  10V  0  VCVC + –

9. lecture 219 Impedance Example Now use the voltage divider to find V C :

10. lecture 2110 What happens when  changes? 20k  1F1F10V  0  VCVC + –  = 10 Find V C +–+–

11. lecture 2111 Low Pass Filter: A Single Node-pair Circuit Find v(t) for  =2  3000 1k  0.1  F 5mA  0  + – V

12. lecture 2112 Find Impedances 1k  -j530  5mA  0  + – V

13. lecture 2113 Find the Equivalent Impedance 5mA  0  + – VZ eq

14. lecture 2114 Parallel Impedances

15. lecture 2115 Computing V

16. lecture 2116 Change the Frequency Find v(t) for  =2  455000 1k  0.1  F 5mA  0  + – V

17. lecture 2117 Find Impedances 1k  -j3.5  5mA  0  + – V

18. lecture 2118 Find an Equivalent Impedance 5mA  0  + – VZ eq

19. lecture 2119 Parallel Impedances

20. lecture 2120 Computing V

21. lecture 2121 Impedance Summary

22. lecture 2122 Class Examples