Download Thevenin resistance for a circuit containing a dependent source

Thevenin Equivalent for a circuit containing
a dependent source
R1
a
2kOhm
V
5V
V2
3 V/V
I1
20 A/A
R2
25 Ohm
b
ECE 201 Circuit Theory I
1
Determine the Thevenin voltage VTh
R1
a
2kOhm
V
5V
+
I
V2
3 V/V
I1
20 A/A
20 I
R2
25 Ohm
VTh
b
VTh = -20I(25) = -500I
5 - 3V 5 - 3VTh 5 - 3(-500I)
=
=
2000
2000
2000
5
1
I=
=
500 100
VTh = -500I = -5Volts
I=
ECE 201 Circuit Theory I
2
Determine the Thevenin resistance RTh
R1
a
2kOhm
V
5V
V2
3 V/V
I1
20 A/A
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
3
Thevenin Resistance (continued)
R1
a
2kOhm
V2
3 V/V
I1
20 A/A
R2
25 Ohm
IT
VT
12 V
b
Apply voltage VT and determine the current IT.
The Thevenin Resistance will be RTh = VT / IT.
ECE 201 Circuit Theory I
4
Thevenin Resistance (continued)
R1
a
2kOhm
I
V2
3 V/V
I1
20 A/A
R2
25 Ohm
IT
VT
12 V
20 I
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
5
The Thevenin Equivalent Circuit
Rth
a
100 Ohm
Vth
5V
b
ECE 201 Circuit Theory I
6