Copyright © 2009 Pearson Education, Inc. Admin: Assignment 9 is posted 2 more AC analysis problems RC circuits Due Monday (May 4 th ) There will be no new assignment next week (but labs and discussions as usual) Second mid-term on Wednesday The test will cover everything after Thevenin’s theorem Review Lecture Monday (May 4 th ). Any requests? Any students with accommodations can use the test center – fill out the DSS form. Extra Office hours: Monday 2pm – 4pm Tuesday 2pm – 4pm.

Copyright © 2009 Pearson Education, Inc. What’s the phasor angle of a complex number with no real part? e.g. 19j 0 + j19 tan -1 (19/0)= Plot the point on the complex plane (always a good idea anyway) Assignment 9 hint

Copyright © 2009 Pearson Education, Inc LC Oscillations with Resistance ( LRC Circuit) This figure shows the three cases of underdamping, overdamping, and critical damping. underdamped overdamped R 2 < 4L/C R 2 > 4L/C

Copyright © 2009 Pearson Education, Inc LC Oscillations with Resistance ( LRC Circuit) Example 30-8: Damped oscillations. At t = 0, a 40-mH inductor is placed in series with a resistance R = 3.0 Ω and a charged capacitor C = 4.8 μF. (a) Show that this circuit will oscillate. (b) Determine the frequency. (c) What is the time required for the charge amplitude to drop to half its starting value? (d) What value of R will make the circuit nonoscillating? Underdamped R 2 < 4L/C, overdamped for R 2 > 4L/C. Critical damping will occur when R 2 = 4L/C.

Filters: The Transfer Function 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. H v (jω) = Transfer function Since we are also interested in frequency response, use phasors.

Low pass filters What is V O at ω=0 and ω=∞ ? RC low-pass filter: preserves lower frequencies, attenuates frequencies above the cutoff frequency ω 0 =1/RC.

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

Build other filters by combining impedance response

Phase shifter applications Phase shifters are very useful for communications and radar applications (e.g. Electronically steerable microwave antenna arrays) PATRIOT= "Phased Array TRack to Intercept Of Target" ) Filters I understand… but what’s the point of phase shifting?

Which of the following is a low-pass filter? There will be a question like this on the test Answer: (c) What happens to the output voltage when ω→0 (DC condition)?

Which of the following are high-pass or low-pass filters? Answers: (b) and (c) are high- pass; (a) and (d) are low-pass There will be a question like this on the test