Transcript Resistor Combinations; Source Transformation (3-1 to 3-2)

Resistor Combinations;
Source Transformation
Dr. Holbert
February 4, 2008
Lect6
EEE 202
1
Introduction
• For analysis, series resistors/impedances
can be replaced by an equivalent resistor/
impedance
• Parallel resistors/impedances can be
replaced by an equivalent resistor/
impedance
• Complicated networks of resistors/
impedances can be replaced by a single
equivalent resistor/impedance
Lect6
EEE 202
2
Equivalent Resistance
• Req is equivalent to the resistor network on the
left in the sense that they have the same i-v
characteristics
i(t)
i(t)
+
+
v(t)
v(t)
Req
–
–
• The rest of the circuit cannot tell whether the
resistor network or the equivalent resistor is
connected to it
Lect6
EEE 202
3
Series Resistance
R1
R2
Req
R3
Req = R1 + R2 + R3
Lect6
EEE 202
4
Parallel Resistance
R1
R2
R3
Req
1
1
1
1
 

Req R1 R2 R3
Lect6
EEE 202
5
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
Lect6
EEE 202
6
A More Realistic Source Model
i(t)
Rs
vs(t)
+
–
+
The
v(t)
Circuit
–
The Source
Lect6
EEE 202
7
I-V Relationship
The I-V relationship for this source model is
v(t) = vs(t) – Rs i(t)
v(t)
i(t)
Lect6
EEE 202
8
Open Circuit Voltage
• If the current flowing from a source is zero,
then the source 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)
Lect6
EEE 202
9
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) equals
zero is called the short circuit current:
isc(t)
Lect6
EEE 202
10
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
Lect6
EEE 202
v(t)
voc(t)
isc(t)
i(t)
11
Equivalent Current Source
i(t)
+
The
is(t)
Rs
v(t)
Circuit
–
vs (t )
i s (t ) 
Rs
Lect6
EEE 202
12
Source Transformation
Rs
Vs
+
–
Is
Vs
Is 
Rs
V s  Rs I s
Lect6
Rs
EEE 202
13
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 of the same value
• A current source in parallel with a resistor
is transformed into a voltage source in
series with a resistor of the same value
Lect6
EEE 202
14
Averaging Circuit
1kW
1kW
+
V1
+
–
Vout
1kW
+
–
V2
–
How can source transformation make
analysis of this circuit easier?
Lect6
EEE 202
15
Source Transformations
1kW
1kW
+
V1
+
–
Vout
1kW
+
–
V2
–
Lect6
EEE 202
16
Source Transformations
1kW
V1 /1kW
+ 1kW
1kW
V2 /1kW
Vout
–
Which is a single node-pair circuit
that we can use current division on!
Lect6
EEE 202
17
Class Examples
• Drill Problems P3-1, P3-2, P3-3
Lect6
EEE 202
18