Lesson 6:
Current Sources
Source Conversion
Learning Objectives
Analyze a circuit consisting of a current
source, voltage source and resistors.
 Convert a current source and a resister into
an equivalent circuit consisting of a voltage
source and a resistor.
 Evaluate a circuit that contains several
current sources in parallel

Ideal sources

An ideal source is an active element that
provides a specified voltage or current that is
completely independent of other circuit
elements.
DC Voltage
Source
DC current
source
CURRENT SOURCES
In general, a current source determines
the direction and magnitude of the
current in the branch where it is
located.
 Furthermore, the magnitude and the
polarity of the voltage across a current
source are each a function of the
network to which the voltage is applied.

Constant Current Sources
 Maintains
same current in branch of
circuit
Doesn’t matter how components
are connected external to the
source
 Direction of current source indicates
direction of current flow in branch
Constant Current Sources

Series circuit
 Current

Current source in a series circuit
 Value

must be same everywhere in circuit
of the current for that circuit
For the circuit shown
I
= 2 mA
Constant Current Sources
KVL  Vs  1000   0.002 A   10V  (2000 )(0.002 A) = 0
Vs  2V  10V  4V  0
Constant Current Sources
The voltage across the current source (VS) is dependant on
how other components are connected to it.
Changing R2 from 2kΩ to 6kΩ causes the voltage across
the current source to change polarity.
Current source voltage polarity does NOT have to follow the
current source’s arrow!
Practical voltage sources

A real or practical source supplies its rated
voltage when its terminals are not connected to
a load (open-circuited) but its voltage drops off
as the current it supplies increases.
Practical voltage source

We can model a practical voltage source using
an ideal source vs in series with an internal
resistance Rs.
Practical current source


A practical current source supplies its rated
current when its terminals are short-circuited but
its current drops off as the load resistance
increases.
We can model a practical current source using
an ideal current source is in parallel with an
internal resistance Rs.
Source transformation

Replace a voltage source vs in series with a
resistor R by a current source is in parallel with
the SAME resistor R.
SOURCE CONVERSIONS
FIG. 8.6 Source
conversion.
Source transformation

How do you calculate the new current source
value?
v 100V
 Just apply Ohm’s Law: i  s 
 2A
s
R 50
Example Problem 1
Use source transformation to determine vo.
Source transformation Part II

Replace a current source is in parallel with a
resistor R by a voltage source vs in series with
the SAME resistor R.
Source transformation

How do you calculate the new voltage source
value?
 Just apply Ohm’s Law: vs  is R   2 A 50  100V
Example Problem 2
Use source transformation to determine vo.
CURRENT SOURCES IN PARALLEL

We found that voltage sources of different
terminal voltages cannot be placed in
parallel because of a violation of
Kirchhoff’s voltage law.
 Similarly,
current sources of different
values cannot be placed in series due to a
violation of Kirchhoff’s current law.
Current Sources in Series
CURRENT SOURCES IN PARALLEL

However, current sources can be placed in
parallel just as voltage sources can be placed in
series.
 In
general, two or more current sources in parallel
can be replaced by a single current source having
a magnitude determined by the difference of the
sum of the currents in one direction and the sum
in the opposite direction. The new parallel internal
resistance is the total resistance of the resulting
parallel resistive elements.
Parallel Current Sources

Parallel current sources simply add
together, and can be simplified by a single
current source.
IT  I1  I 2  I 3  I 4
 2  (7)  5  3
 3A
Example Problem 3
Use source transformation and parallel current
source rule to simplify the circuit and determine vo.
Example Problem 4
Use source transformation to determine V0
ONLY one source transformation is possible!
And it doesn’t help you solve the problem….
Example Problem 5
Determine I2 and V3.