Special Techniques
• Superposition Theorem
• Thevenin’s Theorem
• Norton’s Theorem
• Source Transformation
Linearity Characteristic
RL
6Ω
42V
4Ω
10V
IL+
VRL
-
If RL change its value , how will it effect the current and voltage across it?
I
VVOC
ISC
For any circuit constructed from only linear components
Not just RL, all resistors have this property.
Voc = Voltage open-circuit Isc = Current short-circuit
Thevenin’s TheoremWhen we are interested in current and voltage across RL, we can simplify other parts in the circuit.
RL
6Ω
42V
4Ω
10V
RL
RTH
VTH
Equivalent circuit
RL
6Ω
42V
4Ω
10V
RL
RTH
VTH
I
V
VOC
ISC
Voc = Voltage open-circuitIsc = Current short-circuitR = R equivalent
Slope = 1/R
Thevenin’s Equivalent Circuit
RL
RTH
VTH
Thevenin’sequivalentcircuit
VTH = Voc (by removing RL and find the voltage difference between 2 pins)
RTH (by looking into the opened connections that we remove RL, see how much resistance from the connections. If we see a voltage source, we short circuit. If we see a current source, we open circuit.)
Why do we needequivalent circuit?
• To analyze a circuit with several values of RL
• For circuit simplification (source transformation)
• To find RL that gives maximum power (maximum power transfer theorem)
Procedure
1. Remove RL from the circuit
2. Find voltage difference of the 2 opened connections. Let it equal VTH.
3. From step 2 find RTH by3.1 short-circuit voltage sources3.2 open-circuit current sources3.3 Look into the 2 opened connections. Find equivalent resistance.
Example
3Ω
2Ω
10V
10Ω
RL
2Ω
Find Thevenin’s equivalent circuitand find the current that passes through RL when RL = 1Ω
Special Techniques
• Superposition Theorem
• Thevenin’s Theorem
• Norton’s Theorem
• Source Transformation
Norton’s Equivalent Circuit
RLRNIN
In= Isc from replacing RL with an electric wire (resistance = 0) and find the currentRn = RTH (by looking into the opened connections that we remove RL, see how much resistance from the connections. If we see a voltage source, we short circuit. If we see a current source, we open circuit.)
Example
3Ω
2Ω
10V
10Ω
RL
2Ω
Find Norton’s equivalent circuitand find the current that passes through RL when RL = 1Ω
3Ω
2Ω
10V
10Ω
2Ω
Isc
Find In
Find R total
Find I total
Current divider
4.4123
1232)210(||32
AR
VI 27.2
4.4
10
AISC 45.027.2123
3
RL13.20.45
Norton’s equivalent circuit
13.2
6V RL
Thevenin’s equivalent circuit
Same R value
2.1345.06 THNTH
NTH
RIV
RR
Equivalent Circuits withDependent Sources
We cannot find Rth in circuits with dependent sources usingthe total resistance method.
But we can use
SC
OCTH I
VR
1V 4K
2K
80
250
+Vx- -
+ 100Vx
+
-
Find Voc
I1 I2
12400014250
0)21(400012501
II
IIIKVLloop1
024060801404000
)21(4000
010028022000)12(4000
II
IIVx
VxIIIIKVLloop2
1V 4K
2K
80
250
+Vx- -
+ 100Vx
+
-
I1 I2
Solve equations
I1 = 3.697mA I2 = 3.678mA
V
mA
IIIVxIVOC
3.7
)678.3697.3(400000)678.3(80
)21(400000280100280
1V 4K
2K
80
250
+Vx- -
+ 100Vx
Isc
Find Isc
I1 I2 I3
12400014250
0)21(400012501
II
IIIKVLloop1
038024060801404000
)21(4000
0100)32(8022000)12(4000
III
IIVx
VxIIIIIKVLloop2
KVLloop3
038024000801400000
0100)23(80
III
VxII
1V 4K
2K
80
250
+Vx- -
+ 100Vx
Isc
Find Isc
I1 I2 I3
I1 = 0.632mAI2 = 0.421mAI3 = -1.052 A
Isc = I3 = -1.052 A