Download Thevenin resistance for a circuit containing a dependent source

Thevenin Equivalent of a circuit containing a
dependent source
a
R1
2kOhm
V
5V
I1
20 A/A
V2
3 V/V
R2
25 Ohm
b
VTh  vab  (20i)(25)  500i
5  3v
i
2000
ECE 201 Circuit Theory I
1
Solving for VTh
VTh  vab  (20i )(25)  500i
5  3v 5  3VTh
i

2000
2000
 5  3VTh 
VTh  500 

 2000 
3VTh  5
VTh 
4
VTh  5V
ECE 201 Circuit Theory I
2
Solving for Isc
a
20I
R1
Isc
2kOhm
V
5V
I
V2
3 V/V
I1
20 A/A
R2
25 Ohm
b
I sc  20 I
5
I
 2.5mA
2000
I sc  20(2.5)  50mA
ECE 201 Circuit Theory I
3
Calculate RTh
VTh
5V
RTh 

 100
I sc 50mA
ECE 201 Circuit Theory I
4
Thevenin Equivalent Circuit
R1
a
100 Ohm
VTh
5V
b
ECE 201 Circuit Theory I
5
Alternate Method
a
R1
2kOhm
V
5V
I1
20 A/A
V2
3 V/V
R2
25 Ohm
b
De-activate the independent voltage source and excite
the circuit from the a-b terminals with either a voltage or
current source.
Here, use a voltage source – then we will know the
dependent voltage and dependent current.
ECE 201 Circuit Theory I
6
Thevenin Resistance (continued)
a
IT
R1
2kOhm
I1
20 A/A
V2
3 V/V
VT
12 V
R2
25 Ohm
b
Apply voltage VT and determine the current IT.
The Thevenin Resistance will be RT = VT / IT.
ECE 201 Circuit Theory I
7
Thevenin Resistance (continued)
a
20I
R1
IT
2kOhm
I
V2
3 V/V
I1
20 A/A
VT
12 V
R2
25 Ohm
b
VT
+ 20I
25
3VT
I=2000
V
 3VT 
IT = T + 20  
25
 2000 
IT
1
6
1
=
=
 RTh =100Ω
VT 25 200 100
IT =
ECE 201 Circuit Theory I
8
Thevenin Equivalent Circuit
R1
a
100 Ohm
VTh
5V
b
ECE 201 Circuit Theory I
9