Independent Sources
Voltage and Current Sources
A source is a voltage or current generator capable of supplying energy to a circuit.
A voltage source could be a battery, Generator
Current source could be a solar cell
Independent Sources Dependent Sources
Voltage Current
Source Source
Voltage Voltage Current Current
Controlled Controlled Controlled Controlled
Voltage Current Voltage Current
Source Source Source Source
(VCVS) (VCCS) (CCVS) (CCCS)
Voltage and Current Sources
Independent Independent
Voltage Sources Current Sources
An independent An independent
voltage source provides current source
a specified voltage provides a current
independent of the independent of the
current through it and is voltage across the
independent of source element and is
any other circuit independent of any
variable other circuit variable
Symbols of Independent Sources
Independent Independent
Voltage Sources Current Sources
vs is
Independent Voltage Source
It is an Ideal Voltage Source
Although it does not represent a real device, it
is can fairly approximate voltage sources
Rs = 0
I Vout
V
Vout
V
0
I
Independent Current Source
It is an Ideal Current Source
Iout
Iout
I I
Rs = Vout
0
Vout
Ideal vs Practical Voltage Source
Ideal
Voltage
Source
Practical
Voltage
Source
Ideal vs Practical Current Source
Ideal
Current
Source
Practical
Current
Source
Dependent Sources
Dependent Dependent
Voltage Sources Current Sources
K vx r ix g vx K ix
Voltage Current Voltage Current
Controlled Controlled Controlled Controlled
Voltage Source Voltage Source Current Source Current Source
(VCVS) (CCVS) (VCCS) (CCCS)
Example of circuits containing
Dependent Sources
Current Voltage
Controlled Controlled
r ix Voltage Source g vx Current Source
(CCVS) (VCCS)
Svoboda and Dorf, 2001
Example of circuits containing
Dependent Sources
Operational amplifier which is a voltage
controlled voltage source (VCVS)
Svoboda and Dorf, 2001
Connections of Voltage Sources
Voltage Sources in Series Voltage Sources in Parallel
v1 v1
V1 V2
v2
= v2
=
v1 + v2 + v3 v1 - v2 + v3
v3 v3
Not allowed
unless V1 = V2
Connections of Current Sources
Current Sources in Series Current Sources in Parallel
I1 i1 i2 i1 + i 2
I2
Not allowed
i1 i2 i1 - i2
unless I1 = I2
Source Transformation
Source Transformation Example
www.mit.edu Spring 2006, Chaniotakis and Cory
Source Transformation Example
i = 0.5 A
www.mit.edu Spring 2006, Chaniotakis and Cory
