1. Frequency Responses Up to now, we have learnt –ac circuit analysis with periodic sources (fixed frequency, if multiple frequencies, use superposition principle) –Transient analysis Now, frequency responses: filters and resonant circuits.

2. Transfer Function Since we are interested in frequency responses, we use phasors (frequency domain). V L (j  ) is a phase-shifted and amplitude- scaled version of V S (j  ) CD PlayerAmplifierSpeaker (Source) (Circuit) (Load) VSVS ZSZS Z1Z1 Z2Z2 ZLZL

3. Filters Low-pass filters (LP)

4. Low-Pass Filters Break frequency  o =1/RC, H V =1/  2 working example quick determination of filter type

5. Build other filters by combing impedance

6. Concept Check: filter Which of the following circuits is a low-pass filter? (a)(b)(c) Answer: (c)

7. High-pass Filters (HP) 1/  2

8. Concept Check: filters Which are the following circuits high-pass or low-pass filters? Answers: High-Pass Filters: (b) and (c) low-pass filters: (a) and (d)