Copyright © 2009 Pearson Education, Inc.

Admin:• Assignment 9 is posted

• 2 more AC analysis problems• RC circuits• Due Monday (May 4th)• 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 4th). 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.

30-6 LC Oscillations with Resistance (LRC Circuit)

This figure shows the three cases of underdamping, overdamping, and critical damping.

underdamped

overdamped

R2 < 4L/C

R2 > 4L/C

Copyright © 2009 Pearson Education, Inc.

30-6 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 R2 < 4L/C,

overdamped for R2 > 4L/C.

Critical damping will occur when R2 = 4L/C.

Filters: The Transfer Function

)(V

)(V)(H

S

LV

j

jj

)(I

)(I)(H

S

LI

j

jj

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

Low pass filters

• What is VO at ω=0 and ω=∞ ?

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

RC

10

Low pass filters

01

2

/tan

)(1

1

o

i

iVo

VRC

VHV

Break frequency ω=ω0=1/RC,

|HV|=1/√2

N.B. decibels:

db32

1log20

log10

log20

10

010

010

X

XX

X

XX

dB

dB

For voltage

For power

Build other filters by combining impedance response

http://www.animations.physics.unsw.edu.au/jw/RCfilters.html

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