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ELECTRIC CIRCUITS
ECSE-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/ECSE2010/index.html
TA’S
• Section 1:
• Tong Zhang ([email protected])
• Section 2:
• Amit Kekare ([email protected])
• Rahul Kalaskar ([email protected])
•
Section 3:
• Sunil Rao ([email protected])
• Shahab Uddin ([email protected])
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/down
loads/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
(1  a)R p
Rp
aR p
0  a 1
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
i
2
10 V


Current Controlled Voltage Source (CCVS)
6i Volts
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
 v1 
2
10 V


Voltage Controlled Voltage Source (VCVS)
3v1 Volts
CONTROLLED SOURCES
 v1 
2
10 V
Voltage Controlled Current Source (VCCS)
4v1 Amps
CONTROLLED SOURCES
i1
2
10 V
4
Current Controlled Current Source (CCCS)
5i1 Amps
CONTROLLED SOURCES
i
2
10 V


Current Controlled Voltage Source (CCVS)
6i Volts
CONTROLLED SOURCES
USING SCHEMATICS
ACTIVITY 4-1
i
R
v


vC  6i Volts
Find expressions for i and vc 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
R()
10
8
6
vc (V)
30
60
  60
i (A)
5
10
  10
R eq ()
4
2
0
4
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
(1  a)R p
Rp
aR p
0  a 1
VOLTAGE AMPLIFIER
Ro
io


Ri

vi

bvi

If io  0; vo  b vi
vo

ACTIVITY 4-2
aR p
R1
(1  a)R p
vi
100 
R2
2 M
15 V
15 V

bvi
vi




Select R1 , R 2 , R p , b to get
~ .1Volt/degree of rotation of Pot Shaft at output
vo

ACTIVITY 4-2
KCL at Node vi :
vi
vi  15
vi  (15)


0
2M R1  aR p R 2  (1  a)R p
1
1
1
15
15
vi (


)

2M R1  aR p R 2  (1  a)R p
R1  aR p R 2  (1  a)R p
Can Solve for v1  Messy Equation
ACTIVITY 4-2
Choose R1  R 2  R
Choose R and R p  2 M
1
1
1
1
vi (

)  15(

)
R  aR p R  (1  a)R p
R  aR p R  (1  a)R p
 vi 
R p (1  2a)15
2R  R p
ACTIVITY 4-2
a is a linear function of  ; 0  a  1
  angle of potentiometer shaft

1
0
0
a

for

180



180
0
360
2
 R p   15 V 
 vi   

 2R  R   1800 
p 

ACTIVITY 4-2
Let R  5 k, R p  10 k (  2M)
 7.5 V 
 vi   
 ; v 0  b vi
0 
 180 
To get 0.1 V/degree at output:  b  2.4
 vo  

100
EQUIVALENT RESISTANCE
i
i


v
v


R eq
v

i
R eq
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
R eq  3 
2
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
it
[with Controlled
Source(s)]
Connect vt ; define i t
Use KCL, KVL to
express v t in terms of i t
vt
vt
R eq 
it
Req with Controlled Sources
1
 vx 

R eq  ?
2vx

Req with Controlled Sources
it
1
 vx 

vt
2vx

v t  v x  2v x  0  v t  3v x
vx vt
it 

1
3
vt
 R eq   3 
it
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
 vin
iin


ia
v in
60 
ic
4
vb


30 
ib
vx 
 vx


v out



ACTIVITY 4-3
• Part a): KVL
•
vin   vin  v x   v x  0
(1   ) v x  (1   ) vin  v x  vin
• Part b): “Supernode” around
•
iin  i a  i b  i c
i a  vin /60
v b  vin   vin , i b  v b /30
i c  v x /4   vin /4
 vin :
ACTIVITY 4-3
iin  ia  i b  ic
iin  i a  i b  i c
vin vin   vin (  vin )



60
30
4
(9   )

vin
30
vin
30
 R in 


iin
(9   )
ACTIVITY 4-3
• Part c):
 0
 3 Resistors in Parallel
1
1
1 1




R in 60 30 4
30
 R in 

9
Checks with Equation
ACTIVITY 4-3
• Part d):
• .2 A source in parallel with 10 ohms
• Model Amplifier with Rin

0.2 A
10 
v in

iin
R in
ACTIVITY 4-3
10
2
iin 
x .2 
10  R in
10  R in
2R in
vin  R in iin 
10  R in
v out   v x    vin
ACTIVITY 4-3

R in ()
iin (A)
6
10
0.1
1
6
9
10

 30
0
 0.1
2
3
 18
 30
12
15
 10
5

0.4

2

 30
vin (V) v out (V)