ELECTRIC CIRCUITSECSE-2010

Spring 2003 Class 4

ASSIGNMENTS DUE

• Today (Tuesday/Wednesday):• HW #1 Due• Activities 4-1, 4-2, 4-3 (In Class)• 4-2 in NOT in your Supplement

• Thursday:• Activities 5-1, 5-2, 5-3 (In Class)

• Next Monday:• HW #2 Due• Experiment #1 Report Due• Activities 6-1, 6-2, 6-3, 6-4 (In Class)

WEBSITE

• Main Website: http://www.ecse.rpi.edu• Academics• Course Homepages• Spring 2003 – ECSE 2010

• Backup Site :

http://128.113.60.136/ECSE-2010/index.html

TA’S

• Section 1:• Tong Zhang (zhant@rpi.edu)

• Section 2:• Amit Kekare (kekara@rpi.edu)• Rahul Kalaskar (kalasr@rpi.edu)

• Section 3:• Sunil Rao (raos@rpi.edu)• Shahab Uddin (uddins@rpi.edu)

GRADING ASSIGNMENTS

• Activities:• Amit Kekare – Sections 1&3• Rahul Kalaskar – Section 2

• Experiments:• Sunil Rao

• Homework:• Shahab Uddin

• Computer Projects:• Tong Zhang

REVIEW

• PSpice:• Download a copy and start practicing• http://www.cadencepcb.com/products/

downloads/PSpicestudent/default.asp• Practice with Activities, Homework, etc.• Get comfortable with “rules” for Circuit

Files and Learn to use Schematics• We will slowly build our list of commands

MORE CIRCUIT ELEMENTS

• Potentiomenter:• Variable Resistor with 3 terminals• Resistance varies as shaft is turned• Will Use Digital Pots in our Experiments

• Controlled or Dependent Sources:• Source whose Voltage or Current Output Depends

on a Voltage or Current Somewhere Else in the Circuit

POTENTIOMETER

pR

paR

0 a 1

p(1 a)R

CONTROLLED SOURCES• 2 Types of Sources for Circuit Models:

• Independent Voltage and Current Sources• Usually Model with Ideal Sources

• Controlled Voltage and Current Sources• Also called Dependent Sources

• Controlled/Dependent Source:• Voltage or current source whose value depends

on the v or i at some other point in the circuit• Cannot buy a controlled source!• Used to model the behavior of electronic devices

• Controlled Sources Make Ckt Analysis Much, Much Harder!

CONTROLLED SOURCES

• Controlled Source cannot be the only source of Energy in a complete circuit• Need an Independent Source to create the

controlling current or voltage

• All circuit models for Transistors and other Electronic Devices involve Controlled Sources• Whole field of analog electronics is based on

controlled sources

CONTROLLED SOURCES

10 V

2

i

6i Volts

Current Controlled Voltage Source (CCVS)

CONTROLLED SOURCES

• See Example:• Special Symbol for Controlled Sources• Diamond

• 4 Types of Controlled Sources• Voltage Controlled Voltage Source (VCVS)• Voltage Controlled Current Source (VCCS)• Current Controlled Voltage Source (CCVS)• Current Controlled Current Source (CCCS)

• See Examples:

CONTROLLED SOURCES

10 V

2

1 v

13v Volts

Voltage Controlled Voltage Source (VCVS)

CONTROLLED SOURCES

10 V

2

1 v

14v Amps

Voltage Controlled Current Source (VCCS)

CONTROLLED SOURCES

Current Controlled Current Source (CCCS)

10 V

2

4

1i

15i Amps

CONTROLLED SOURCES

10 V

2

i

6i Volts

Current Controlled Voltage Source (CCVS)

CONTROLLED SOURCES USING SCHEMATICS

ACTIVITY 4-1

v

R

i

Cv 6i Volts

cFind expressions for i and v in terms of R

ACTIVITY 4-1• KVL:

• v - i R + 6 i = 0 => v = i (R - 6)

• i = v / (R - 6)• Note: Singularity at R = 6!; Current “blows up”• Interesting things can happen with controlled

sources

• vc = 6 i = 6 v / (R - 6) • Controlled source tries to put out infinite voltage

when R ~ 6 ohms• What really happens is that circuit model fails

ACTIVITY 4-1

• Equivalent Resistance “Seen” by Source:• Req = v / i

• Req => 0 as R => 6 ohms

• Controlled sources allow much more interesting things to happen, but make circuit analysis much harder

ACTIVITY 4-1

• v = 20 Volts

c

eq

R( ) 10 8 6 4

v (V) 30 60 60

i (A) 5 10 10

R ( ) 4 2 0 2

APPLICATION OF CONTROLLED SOURCES

• Controlled Sources are used to Model the Behavior of Electronic Devices• Single devices such as Transistors• Complete circuits such as Amplifiers

• A good Example is given in Section 4.1 of your Text – Design Challenge• Uses a Potentiometer and an Amplifier• Models Audio Control on Stereo• Let’s take a quick look at this – Activity 4-2

POTENTIOMETER

pR

paR

0 a 1

p(1 a)R

VOLTAGE AMPLIFIER

iR

oR

iv

ibv ov

oi

o o iIf i 0; v b v

ACTIVITY 4-2

15 V 15 V

1R 2R

paRp(1 a)R

2 M

100

ibviv

ov

1 2 pSelect R , R , R , b to get

~ .1Volt/degree of rotation of Pot Shaft at output

iv

ACTIVITY 4-2

i

i i i

1 p 2 p

KCL at Node v :

v v 15 v ( 15)0

2M R aR R (1 a)R

1Can Solve for v Messy Equation

i1 p 2 p 1 p 2 p

1 1 1 15 15v ( )

2M R aR R (1 a)R R aR R (1 a)R

ACTIVITY 4-2

1 2

p

Choose R R R

Choose R and R 2 M

ip p p p

1 1 1 1v ( ) 15( )

R aR R (1 a)R R aR R (1 a)R

pi

p

R (1 2a)15v

2R R

ACTIVITY 4-2

0 00

pi 0

p

a is a linear function of ; 0 a 1

angle of potentiometer shaft

1a for 180 180

360 2

R 15 Vv

2R R 180

ACTIVITY 4-2

p

i 0 i0

o 0

Let R 5 k , R 10 k ( 2M )

7.5 Vv ; v b v

180

To get 0.1 V/degree at output: b 2.4

v10

EQUIVALENT RESISTANCE

v

eqR

i

v

i

eq

vR

i

EQUIVALENT RESISTANCE

• LOAD Network:• Any Circuit with R’s and Controlled Sources• No Independent Sources

• See Example:• Define v, i using Passive Convention

• Req = v / i • Can Replace Any Load Network with its Req

• Powerful Ckt Analysis Technique• See Example

EQUIVALENT RESISTANCE

1

2 eqR 3

Req With Controlled Sources

• “Connect” Test Voltage, vt:• Independent Source (Active Element)

• Define it using Active Convention

• Use Ckt Analysis to find it in terms of vt:• Linear equation relating it to vt

• 1 Equation; 2 Unknowns

• Req = vt / it:• See Example

Req with Controlled Sources

tv

ti

teq

t

vR

i

[with Controlled

Source(s)]

t t

Use KCL, KVL to

express v in terms of it tConnect v ; define i

Req with Controlled Sources

1

x v

x2veqR ?

Req with Controlled Sources

1

x v

x2vtv

ti

t x x t xv v 2v 0 v 3v

txt

vvi

1 3

teq

t

vR 3

i

ACTIVITY 4-3

• Electronic devices allow for “amplification” of a current or voltage:• Make it bigger or smaller• Will examine in more detail soon• Model electronic devices with controlled sources

• Models will use controlled sources with “Variable Gain”:• Variable depends on characteristics of the

particular electronic device being used• Usually want to solve general circuit - then put in

characteristics of particular device - from spec’s

ACTIVITY 4-3

inv

ini in v

60 30

4

x v

x v

outv

ai bi

ci

bv

ACTIVITY 4-3• Part a): KVL

•

• Part b): “Supernode” around

•

in in x x

x in x in

v v v v 0

(1 ) v (1 ) v v v

: vin

in a b c

a in

b in in b b

c x in

i i i i

i v /60

v v v , i v /30

i v /4 v /4

ACTIVITY 4-3

in a b ci i i i

in a b c

in in in in

in

inin

in

i i i i

v v v ( v )

60 30 4(9 )

v30

v 30 R

i (9 )

ACTIVITY 4-3

• Part c):

in

in

0

3 Resistors in Parallel

1 1 1 1

R 60 30 4

30 R Checks with Equation

9

ACTIVITY 4-3• Part d):• .2 A source in parallel with 10 ohms

• Model Amplifier with Rin

0.2 A10

inR

ini

inv

ACTIVITY 4-3

inin in

inin in in

in

out x in

10 2i x .2

10 R 10 R

2Rv R i

10 R

v v v

ACTIVITY 4-3

in in in out R ( ) i (A) v (V) v (V)

6 10 0.1 1 6

9 0 2 18

10 30 0.1 3 30

12 10

15 5 0.4 2 30