Transcript 8. Source transformation & Resistor combinations

Lecture 7. Realistic Sources &
Source Transformation
• Ideal sources vs. realistic sources
• Open circuit voltage, Voc
• Short circuit current, Isc
• I - V relationship
• Source transformation
1
Equivalent Sources
• An ideal current source has the voltage necessary to provide its
rated current.
• An ideal voltage source supplies the current necessary to provide its
rated voltage.
• A real voltage source cannot supply arbitrarily large amounts of
current.
• A real current source cannot have an arbitrarily large terminal
voltage.
2
A More Realistic Source Model
i(t)
+
vs(t)
Rs
+
v(t)
-
The
Circuit
A Realistic Source:
Modeled by an ideal source
in series with a resistor
3
I-V Relationship
The I-V relationship for this source model is
v(t) = vs(t) - Rs i(t)
v(t)
i(t)
4
Open Circuit Voltage
• If the current flowing from a source is zero, then it is connected to an
open circuit.
• The voltage at the source terminals with i(t) equal to zero is called
the open circuit voltage:
voc(t)
5
Short Circuit Current
• If the voltage across the source terminals is zero, then the source is
connected to a short circuit.
• The current that flows when v(t) is zero is called the short circuit
current:
isc(t)
6
voc(t) and isc(t)
v(t)
voc(t)
isc(t)
i(t)
7
voc(t) and isc(t)
• Since the open circuit voltage and the short circuit current
determine where the I-V line crosses both axes, they completely
define the line.
• Any circuit that has the same I-V characteristics is an equivalent
circuit.
8
Equivalent Current Source
i(t)
+
is(t)
Rs
v(t)
The
Circuit
-
vs (t )
i s (t ) 
Rs
9
Voltage and Current Sources
Rs
Vs
+
Is
-
V s  Rs I s
Rs
Vs
Is 
Rs
10
Source Transformation
• Equivalent sources can be used to simplify the analysis of some
circuits.
• A voltage source in series with a resistor is transformed into a
current source in parallel with a resistor.
• A current source in parallel with a resistor is transformed into a
voltage source in series with a resistor.
11
Example: Averaging Circuit
1kW
V1
+
-
1kW
+
Vout
+
1kW
-
V2
How can source transformation make analysis of this circuit easier?
12
Source Transformations
1kW
V1
+
-
1kW
+
Vout
+
1kW
-
V2
-
13
Source Transformations
1kW
V1 /1kW
+ 1kW
1kW
V2 /1kW
Vout
-
14
A Single Node-Pair Circuit!
1
1
Req 
 kW
1
1
1
3


1kW 1kW 1kW
I eq
V1
V2


1kW 1kW
V0  Req I eq
1
 V1  V2 
3
15
Class Examples
• Drill Problems P3-3 and P3-4
16