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This announcement provides an overview of AC circuit analysis with a focus on filters and frequency response. Topics include low-pass, high-pass, band-pass, and band-stop filters. Additional information on impedance and voltage and current phase relationships is also covered.

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Announcements

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  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… Generalized Ohm's Law: VS(jω)=ZIS(jω) • 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

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

  5. 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

  6. Example

  7. Top: Bottom:

  8. Transfer Function Hv(jω)= Transfer function Since we are interested in frequency response, use phasors. VL(jω) is a phase-shifted and amplitude -scaled version of VS(jω) Hv(jω)describes what the phase shift and amplitude scaling are.

  9. Low pass filters • RC low-pass filter: preserves lower frequencies, attenuates frequencies above the cutoff frequency ω0=1/RC.

  10. For voltage For power Low pass filters Break frequency ω=ω0=1/RC, HV=1/√2 N.B. decibels:

  11. Build other filters by combining impedance response

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

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

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

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

  16. 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 - V0=0)

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