ELECTRIC CIRCUITSECSE-2010Spring 2003

Class 38

ASSIGNMENTS DUE

• Today (Tuesday/Wednesday):• Will do Computer Project #5 in Class (CP-5)• Activities 38-1, 38-2 (In Class)

• Thursday:• Experiment #9 Report Due• Activities 39-1, 39-2 (In Class)

• Next Monday:• Homework #14 Due• Experiment #10 Report Due• Computer Project #5 Report Due• Activity 40-1, Experiment 11 (In Class)

FINAL EXAM

• Wednesday, May 7

• 8 - 11 am

• Sage 3303 for All Sections

• 2-8 1/2 x 11 inch Crib Sheets

• Laplace Tables Will Be Included with the Final Exam

• Students with Conflict should Notify Prof. Jennings (jenniw@rpi.edu)

REVIEW

V I

REVIEW

0 0

0 0

series parallel

eq 0

Series Resonance: Parallel Resonance:

X 0 at B 0 at

1 1

LC LC

1 L CQ Q R

R C L

Z ( ) MINIM

eq 0UM Z ( ) MAXIMUM

NOTES ON RESONANCE

• In “real” circuits, often do not have a “pure” Series or pure Parallel situation:• Inductors always have Rw

• Elements may not all be in series or parallel• Will still have Resonance, but at a slightly

different Resonant Frequency• May have Multiple Resonances in same Circuit• Define Resonance as when X (series-like circuit)

or B (parallel-like circuit) => 0 • Let’s do a problem => Activity 38-1

ACTIVITY 38-1

v

L 20

100 CCv

L v R v

Find Z( ) R jX 0Find when X 0

ACTIVITY 38-1a

V

j L 20

100 j

C

CV

L V R V

1 100 ( )

j C100 j C

1

100j C

4

4 2 2

100 j10 C

1 10 C

ACTIVITY 38-1a

V

j L 20

100 j

C

CV

L V R V

4

4 2 2

100 j10 CZ j L 20

1 10 C

4

4 2 2 4 2 2

100 10 C 20 j L

1 10 C 1 10 C

R( ) jX( )

ACTIVITY 38-1a

V

j L 20

100 j

C

CV

L V R V

4

4 2 2 4 2 2

100 10 C Z 20 j L

1 10 C 1 10 C

40

0 0 4 2 20

10 CX( ) 0 L

1 10 C

20 4 2

1 1

LC 10 C

ACTIVITY 38-1a

V

j L 20

100 j

C

CV

L V R V

20 4 2

1 1

LC 10 C

114,142 radians/sec

LC

0 10,000 radians/sec

ACTIVITY 38-1b

V

0j (5mH) 20

100 0

j

(1 F)

CV

L V R V

0 4 2 20

100Z( ) 20 70

1 10 C

0V 70/0 Volts

0I V/Z 1/0 Amps

I

0 10,000 radians/sec

ACTIVITY 38-1b

V

0j (5mH) 20

100 0

j

(1 F)

CV

L V R V

0V 70/0 Volts

I

0 10,000 radians/sec

0L 0V j (.005)I 50/90 Volts

0RV 20I 20/0 Volts

L R CV V V V 0I 1/0 Amps

ACTIVITY 38-1b

V70

50LV

01 0Z ( ) 50 j50 50 2/ 45

RV20

50 2

045

CV

50

R L CV V V V

L CV V

ACTIVITY 38-1c

V

0j (5mH) 20

100 0

j

(1 F)

CV

L V R V

I

20 4 2

1 1

LC 10 C 2

0 0 does not exist if 0

4 2

1 1 L 10,000

LC 10 C C

AC PSPICE

• Now want to simulate AC Circuits using PSpice:• AC Sources• C’s and L’s

• Usually want to look at behavior as a function of Frequency:• AC Sweep (Schematics)• .ac Statement (Circuit file)

AC PSPICE-CIRCUIT FILE

• AC Voltage Source:V 1 0 AC 10

• AC Current Source:I 0 1 AC 3

• Do Not have to designate frequency when specifying source:• Do later with .ac statement

AC PSPICE-SCHEMATICS• AC Voltage Source:• Use VAC • Doubleclick on VAC• Designate Amplitude and Phase

• AC Current Source with Schematics:• Use IAC; Designate same as VAC

• Do Not have to designate frequency when specifying source:• Do later with AC Sweep in Analysis

AC PSPICE

• Capacitors/Inductors:C 1 0 2u

L 1 0 .1m• Start “name” with C or L• Connected between nodes 1 and 0 (+, -)• C = 2 uF; L = .1mH• Do Not need Initial Conditions for AC

Steady State• Use IC’s when doing Transient Analysis• Doubleclick C and L in Schematics to set

Values and IC’s

AC PSPICE• .ac Statement:

.ac lin 400 10 16k• Perform AC Sweep (Sweep AC

frequencies)• Perform a linear sweep (will do decade

sweeps later)• Divide frequency range into 400 points• starting frequency = 10 Hz (note: f)• ending frequency = 16 kHZ

AC PSPICE

• In Schematics:• Doubleclick Set Up Analysis• Choose AC Sweep and Doubleclick• Choose Type of Sweep• Choose Start and End Frequencies• Choose Number of Points• Remember PSpice uses Frequencies in Hz

ACTIVITY 38-2

i100 2 F

0.2 mHWRv

W 0 parallelIf R 0; f 8 kHz and Q 10 9

WLet R 10 ; 2

ACTIVITY 38-2• Similar to Activity 38-1:

• Not a “Pure” Parallel Resonant Circuit• Inductor has Winding Resistance• Want to see how this affects Resonance

• Let Rw = 10-9 ~ 0, 2 ohms

• When Rw = 0, fo ~ 8 kHz, Qparallel ~ 10

• See what happens when Rw = 2 ohms

• Let’s Practice using Schematics

ACTIVITY 38-2

ACTIVITY 38-2• Need to Set X Axis to Linear:

• Probe automatically uses a Log scale• Go to Plot, X Axis Settings, Linear

• To Look at Amplitude/Magnitude:• Plot Vm(1)@1 or Im(C)@1• Amplitude/Magnitude of the Voltage at Node 1

for Case 1 (Rw = 10-9 ohms)

• To Look at Angle/Phase:• Plot Vp(1)@2 or Ip(C)@1• Angle/Phase of the Voltage at Node 1 for Case

2 (Rw = 2 ohms)

ACTIVITY 38-2• With RW = 10-9 Ohms:

• f0=7.985 kHz

• iC,max = 10 Amps

• Qparallel = 10

• With RW = 2 Ohms:• f0 = 8.225 kHZ

• iC,max = 3.47 Amps

• Qparallel = 3.47

• Change f0 a little

• Reduce Qparallel a lot:

COMPUTER PROJECT 5

inv

100 5

15

12 mH

6 mH

40 nF

ini

1i 2i

COMPUTER PROJECT 5

• Circuit is both “Series-like” and “Parallel-like”:• Will have both Series and Parallel

Resonances• Resonances occur at different frequencies• Identify by Minimum or Maximum of /Z/• /Z/ is a Minimum at Series Resonance• /Z/ is a Maximum at Parallel Resonance

COMPUTER PROJECT 5

• PSpice wants frequencies in Hertz:• Project asks to sweep • Must convert = 2 f• Plot as function of = f * 6.28• Use Linear X Axis

• Note: Zin = Vin / Iin

• Vin = Volts

• => Yin = Iin /1 Siemons

o/0 1

COMPUTER PROJECT 5

Using Schematics