Download Full PowerPoint

MIDTERM EXAM 1
Not graded on curve – students are not in competition
Graded based on what I feel is average (B-, 71.5%)
and minimally acceptable (C-, 55%)
Mean: 79
Median: 77
Low: 38
High: 100 (6 students)
A’s
B’s
C’s
F’s
87
79
51
9
38% of class
35% of class
22% of class
4% of class
60
50
40
30
20
10
0
F
C-
C
C+
B-
B
B+
A-
A
A+
Dependent Voltage and Current Sources
A linear dependent source is a voltage or current source that
depends linearly on some other circuit current or voltage.
Example: you watch a certain voltmeter V1 and manually adjust a
voltage source Vs to be 2 times this value. This constitutes a
voltage-dependent voltage source.
Circuit A
+
V1
-
Vs=2V1
+
-
Circuit B
This is just a (silly) manual example, but we can
create such dependent sources electronically. We
will create a new symbol for dependent sources.
Dependent Voltage and Current Sources
• A linear dependent source is a voltage or current source that
depends linearly on some other circuit current or voltage.
• We can have voltage or current sources depending on voltages
or currents elsewhere in the circuit.
Here the voltage V is proportional to the voltage across the element c-d .
c
+
Vcd
+
-
V = A v x Vcd
-
d
A diamond-shaped symbol is used for dependent sources, just
as a reminder that it’s a dependent source.
Circuit analysis is performed just as with independent sources.
EXAMPLE OF THE USE OF DEPENDENT SOURCE
IN THE MODEL FOR AN AMPLIFIER
AMPLIFIER SYMBOL
Differential Amplifier
V+
V
+
A

V0  A(V  V )
AMPLIFIER MODEL
Circuit Model in linear region
V0
Ri
+

V1
+

AV1
V0 depends only on input (V+  V-)
See the utility of this: this Model when used
correctly mimics the behavior of an amplifier but
omits the complication of the many many
transistors and other components.
+

V0
The 4 Basic Linear Dependent Sources
Constant of proportionality
Parameter being sensed
Output
Voltage-controlled voltage source … V = Av Vcd
Current-controlled voltage source … V = Rm Ic
Current-controlled current source … I = Ai Ic
Voltage-controlled current source … I = Gm Vcd
+
Av Vcd
-
+
- Rm Ic
Ai Ic
Gm Vcd
NODAL ANALYSIS WITH DEPENDENT SOURCES
Example circuit: Voltage controlled voltage source in a branch
R5
R1
R3
Va
Vb
Vc
R2
+

VAA
+

AvVc
R4
R6
ISS
Write down node equations for nodes a, b, and c.
(Note that the voltage at the bottom of R2 is “known” so current
flowing down from node a is (Va  AvVc)/R2.)
Va  VAA Va  A v Vc Va  Vb


0
R1
R2
R3
Vc  Vb Vc
Vb  Va Vb Vb  Vc

 ISS


0
R5
R6
R3
R4
R5
CONCLUSION:
Standard nodal
analysis works
ANOTHER EXAMPLE OF NODAL ANALYSIS WITH
DEPENDENT SOURCES
R1
I
Va
I2
R3
R2
R4
+
-
Rm I2
I2
Standard technique, except an additional equation is needed if the
dependent variable is an unknown current as here.
Dependent voltage
sources also have
I = Va / R2 + (Va - Rm I2)/ R3 and I2 = Va / R2
unknown current—so
no KCL at attached
nodes. Supernode
I = Va (1/R2 + 1/R3 - Rm /R2 R3 )
Solving:
around floating
dependent voltage
So Va = I R2 R3 /(R2 + R3 - Rm )
sources!
Thevenin Equivalent Revisited
1 Calculate VOC. VT = VOC
2a) If have only resistors and independent voltage/current
sources, turn off independent voltage/current sources and
simplify remaining resistors
2b) If only dependent sources and resistors present, you will
need to apply test voltage, calculate i and use RT  v TEST
i
2c) If both independent and dependent sources (with
resistors) present, you may find ISC and let RT=VOC/ISC, or turn
v TEST
off independent sources and use
RT 
i
THEVENIN EQUIVALENT: DEPENDENT SOURCES
Apply VTEST, measure unassociated current I
RT = VTEST / I = 20 W
Rework using “trick”:
Assign a value to any one voltage or current—why not Ix?
MORE THEVENIN TRICKS:
SOURCE TRANSFORMATIONS
R
V
A
+
_
A
=
B
I = V/R
R
B
EXAMPLE: SOURCE TRANFORMATIONS
Use source transformation when only
independent sources and resistors present
Find VT = 69 V, RT = 7.3 W