Download THEVENIN-NORTON THEOREM Definitions and Keywords

THEVENIN-NORTON THEOREM
Definitions and Keywords
Thevenin Theorem : Any two terminals of a network composed of linear
passive and active circuit elements may be replaced by an equivalent
voltage source and an equivalent series resistance. The voltage source is
equal to the potential difference between the two terminals connected to
these terminals. The series resistance is the equivalent resistance looking
into the two terminal ports with all the power sources within the terminal
pair inactive.
Norton Theorem : Any two terminals of a network composed of linear
passive and active circuit elements may be replaced by an equivalent
current source and a parallel resistance. The current of the source is the
current measured in the short circuit placed across the terminal-pair. The
parallel resistance is the equivalent resistance looking into the terminalpair with all the independent power sources inactive.
CALCULATING THE THEVENIN EQUIVALENT
To calculate the equivalent circuit, the resistance and voltage are needed, so
two equations are required. These two equations are usually obtained by
using the following steps, but any conditions placed on the terminals of the
circuit should also work:
1. Calculate the output voltage, VAB, when in open circuit condition (no load
resistor -meaning infinite resistance). This is VTh.
2.(a) Now replace voltage sources with short circuits and current sources with
open circuits.
(b) Replace the load circuit with an imaginary ohmmeter and measure the
total resistance, R, "looking back" into the circuit. This is RTh.
CALCULATING THE NORTON EQUIVALENT
To calculate the equivalent circuit, the resistance and voltage are needed, so
two equations are required. These two equations are usually obtained by using
the following steps, but any conditions placed on the terminals of the circuit
should also work:
1. Find the Norton current INo. Calculate the output current, IAB, with a short circuit as
the load (meaning 0 resistance between A and B). This is INo.
2. Find the Norton resistance RNo. When there are no dependent sources (i.e., all
current and voltage sources are independent), there are two methods of
determining the Norton impedance RNo.
Calculate the output voltage, VAB, when in open circuit condition (i.e., no load
resistor — meaning infinite load resistance). RNo equals this VAB divided by INo.
or Replace independent voltage sources with short circuits and independent current
sources with open circuits. The total resistance across the output port is the Norton
impedance Rno .
Concept details
Step
number
Details of the step
A typical Circuit diagram.
1
2
3
Image / Diagram
Text to be
displayed
The circuit consists of
resistors and a voltage
source. Terminals A and
B are the terminals
across which Thevenin
equivalent circuit is to be
determined.
The diagram will be morphed
into the next equivalent circuit
diagram which is the circuit for
calculating the equivalent
output voltage.
Current, using an arrow tip, will
be circulated across the loop as
well as voltage drop across
each resistor will be displayed
in parallelism. After 1 complete
circulation it’s value will be
determined and from there the
voltage across terminals A and
B.
Equivalent circuit for determining
equivalent output voltage.
Equivalent circuit for determining
equivalent resistance.
Action / Motion in
the step
Req=R1+[(R2+R3)||R4]
The previous circuit will be
morphed into the circuit for
determining equivalent
resistance. Next the voltage
source will be converted into a
short. And, equivalent
resistance will be calculated
using the formula provided.
Step
number
4
Details of the step
The final equivalent circuit of the
original circuit.
A typical Circuit diagram.
5
6
Equivalent circuit for determining
equivalent output voltage.
Image / Diagram
Text to be
displayed
Action / Motion in
the step
The Thevenin
equivalent circuit.
The previous circuit will be
morphed into original circuit .
Next, all the resistances will be
combined together and the
equivalent resistance will be
displayed in parallelism of
changing the value of 15V to
7.5V .
The circuit consists of
resistors and a voltage
source. Terminals A and
B are the terminals
across which Norton
equivalent circuit is to be
determined.
The diagram will be morphed
into the next equivalent circuit
diagram which is the circuit for
calculating the equivalent
output voltage.
Itotal
Itotal will be calculated using
Kirchhoff's laws . And, finally
using the current divider rule I
will be calculated.
=V1/[R4+{R1||(R2+R3)}]
Using current divider rule:
I=[(R2+R3)/(R1+R2+R3)]*
Itotal
Step
number
Details of the step
Image / Diagram
Text to be
displayed
Req= R1+R4||(R2+R3)
7
8
Equivalent circuit for determining
equivalent resistance.
The final equivalent circuit of the
original circuit.
The Norton
equivalent circuit.
Action / Motion in
the step
The previous circuit will be
morphed into the circuit for
determining equivalent
resistance. Next the voltage
source will be converted into a
short. And, equivalent
resistance will be calculated
using the formula provided.
The previous circuit will be
morphed into original circuit .
Next, all the resistances will be
combined together and the
equivalent resistance will be
displayed in parallelism of
changing the value of voltage
source from 15V to current
source of 3.75mA .
Interactivity and Boundary limits
While determining the
Thevenin equivalent of a
given circuit the user can
alter the value of
resistances and sources and
observe the changes.
While determining the
Thevenin equivalent of a
given circuit the user can
alter the value of
resistances and sources and
observe the changes.
Changing the values of the
inputs changes the
equivalent outputs.
None of the resistances
or sources should be
zero or infinity.
Changing the values of the
inputs changes the
equivalent outputs.
None of the resistances
or sources should be
zero or infinity.
Questionnaire
1. The relation between Thevenin equivalent resistance(RTH) and that of
Norton’s (RN) is given by:
Answers: a) RTH>RN
b) RTH=RN
c)RTH<RN
d)RTH>>RN
2.In the Thevenin equivalent circuit, the equivalent voltage
source is _______ with the equivalent Thevenin resistance.
Answer: a)in Parallel
b)not connected.
c)in series.
d)None of them.
3.In the Norton equivalent circuit, the equivalent Norton
resistance is _______ with the equivalent Norton current
source.
Answer: a)in Parallel
b)not connected.
c)in series.
d)None of them.
4.A network has the configuration shown in the figure. All
resistance values are expressed in ohms. Find the current
through RL when it takes on values of 10, 50 and 200 ohms.
Answer: a)0.324A, 0.481A and 0.146A respectively
b)0.481A, 0.146A and 0.324A respectively
c)0.481A, 0.324A and 0.146A respectively
d)None of these.
5.The small signal equivalent of a vacuum-tube amplifier has the
configuration depicted in the figure. The indicated circuit
parameters have the following values: µ=99, R1=147,000 ohms
,rp =66,000 ohms and R2 =100,000 ohms. Find the value of the
voltage for Eg=0.4 volt.
Answer: a)1.872V
b)18.72V
c)11.42V
d)15.78V
Links for further reading
[1] “Electrical Engineering Fundamentals”, by Vincent Del Toro, Prentice-hall
Of India Pvt. Ltd.
[2] “Basic Electrical Engineering”, by D.P. Kothari and I.J. Nagrath, Tata
McGraw-Hill Publishing Pvt. Ltd.
Thank you
Made by:- Rutesh Chavda