1. Announcements Assignment 0 solutions posted Assignment 1 due on Thursday DC circuit Lab reports due to Sajan today and tomorrow This week’s lab – AC circuits

2. Lecture 6 Overview AC Circuit Analysis Filters

3. The Story so far… Voltage and current not in phase: Current leads voltage by 90 degrees Impedance of Capacitor decreases with increasing frequency Voltage and current not in phase: Current lags voltage by 90 degrees Impedance of Inductor increases with increasing frequency Voltage and current in phase no frequency dependece Generalized Ohm's Law: V S (jω)=ZI S (jω)

4. Inductors in AC circuits Voltage and current not in phase: Current lags voltage by 90 degrees Impedance of Inductor increases with increasing frequency Inductive Load http://arapaho.nsuok.edu/%7Ebradfiel/p1215/fendt/phe/accircuit.htm (back emf ) from KVL

6. AC circuit analysis Effective impedance: example Procedure to solve a problem –Identify the sinusoid and note the excitation frequency –Convert the source(s) to complex/phasor form –Represent each circuit element by it's AC impedance –Solve the resulting phasor circuit using standard circuit solving tools (KVL,KCL,Mesh etc.) –Convert the complex/phasor form answer to its time domain equivalent

7. Example

9. Top: Bottom:

10. Transfer Function H v (jω) = Transfer function Since we are interested in frequency response, use phasors. V L (jω) is a phase-shifted and amplitude -scaled version of V S (jω) H v (jω) describes what the phase shift and amplitude scaling are.

11. Low pass filters RC low-pass filter: preserves lower frequencies, attenuates frequencies above the cutoff frequency ω 0 =1/RC.

12. Low pass filters Break frequency ω=ω 0 =1/RC, H V =1/√2 N.B. decibels: For voltage For power

13. Build other filters by combining impedance response

14. Which of the following is a low-pass filter? Answer: (c) What happens to the output voltage when ω→0 (DC condition)?

15. Which of the following are high-pass or low-pass filters? Answers: (b) and (c) are high- pass; (a) and (d) are low-pass

16. RLC Band-pass filters C L Measuring voltage output signal over R, V r Low frequencies, C open, L shorted, V r minimum High frequency, C shorted, L open, V r minimum so, at high and low frequencies, see an open circuit - V r minimum

17. Band-stop (Notch) filters Measuring voltage output signal over L and C Low frequencies, C open, L shorted, V lc maximum High frequency, C shorted, L open, V lc maximum so, at high and low frequencies, see an open circuit - V lc maximum

18. Another Example: Measuring voltage output signal over L and C, but this time in parallel (i.e. at high and low frequencies, see a short - V 0 =0)