1 ECE 3336 Introduction to Circuits & Electronics Note Set
#6 Thvenin's and Nortons Theorems Spring 2015, TUE&TH 5:30-7:00
pm Dr. Wanda Wosik Slide 2 2 Equivalent Circuits Here, equivalent
circuits are used to simplify circuit interaction with the load
(ex. another circuit, resistors, other passive elements etc.) An
equivalent circuit is used to simplify the original circuit
however, at the terminals, it maintains the exact same parameters:
ex. voltage and current. Thevenin Equivalent Norton Equivalent
Slide 3 3 Equivalent Circuits Reminder: The same circuit but
different equivalent circuit at different points A B i0i0 VDVD }
This part of the circuit must not notice any change on the right. D
iDiD VDVD } Equivalent circuit All elements to the right of V S2
are replaced by equivalent circuit D. Currents i 0 =i D are the
same Voltages V 2 &V 3 lost their meanings but V D is the same.
Slide 4 4 Thvenins Theorem Thvenins Theorem: any circuit built of
sources and resistors can be represented by one voltage source
(Thevenin Voltage) and a resistance in series (Thevenin
Resistance). The voltage source is equal to the open-circuit
voltage v oc =v T The resistance is equal to the equivalent
resistance R T of the circuit. Source Circuit drives Load Circuit
Slide 5 5 Thevenin Equivalent Voltage V TH and Resistance R TH To
find v oc we have to first disconnect the load. R load Thevenin
equivalent is obtained by finding v oc and R TH R load Now, we can
calculate power delivered to the load, voltage, current. v OC =v TH
Slide 6 6 Polarity of the voltage source The polarities the
Thevenin voltage source must be the same as open circuit voltage v
OC. No load here Thevenin equivalent will have identical properties
as the original circuit, when we connect the load R load R load
Slide 7 7 Zeroing Current and Voltage Sources This is Source
Deactivation Slide 8 8 Equivalent resistance R TH Equivalent
Resistance: it is in series with the Thevenin voltage source in the
equivalent circuit. Set independent sources equal to zero. Any
dependent sources are left in place. R TH Disconnect the load
Shorted source Slide 9 Short Circuit Current i SC HERE: i sc zero ~
i sc v TH ~ v OC R TH ~ R EQ Open Circuit voltage Short Circuit
current It is not Ohms Law The polarities of the short circuit
current as in Ohms Law Slide 10 10 Finding the Thvenin Equivalent
To find the Thvenin equivalent of a circuit by finding any two of
the following three things: 1)the open circuit voltage, v OC, 2)the
short-circuit current, i SC, and 3)the equivalent resistance, R EQ.
Once we find any two, we can find the third by using this equation.
v OC = v TH, and R EQ = R TH. If you change the signs Slide 11 11
Example #1 Find Thvenin equivalent of the circuit below, as seen
from terminals A and B (R L will be connected there later). Use
Node Voltage Method v OC +-+- +-+- vCvC Slide 12 12 Find Thevenin
Voltage For Thvenin equivalent having found v C we will find v OC
from the voltage divider rule v OC +-+- vCvC +-+- Slide 13 13 Find
Thevenin Resistance Independent sources are deactivated i.e. equal
to zero. Resistance seen from the output terminals (A & B) is
calculated Slide 14 14 Thevenin Equivalent Found Now, Short Circuit
Current We can also find i sc Slide 15 15 Short-circuit current in
the original circuit node voltage IS CHANGED. vDvD +-+- i sc Find
Short Circuit Current (compare) The same value as from V TH and R
TH Slide 16 16 Nortons Theorem Nortons Theorem: any circuit built
of sources and resistors can be represented by one current source
(Thevenin Current ) and a resistance in parallel (Thevenin
Resistance). The current source is equal to the short circuit
current i sc =i N The resistance R N is equal to the equivalent
resistance R T of the circuit. Source Circuit drives Load Circuit
Slide 17 17 R load To find i SC we have to first disconnect the
load Norton equivalent is obtained by finding i sc and R TH Nortons
Theorem i SC i N Norton Current i SC We can also find i SC from the
i RN =0 Slide 18 18 Finding the Norton Equivalent We can find the
Norton equivalent of a circuit by finding any two of the following
three things: 1) the open circuit voltage, v OC, 2) the
short-circuit current, i SC, and 3) the equivalent resistance, R
EQ. Once we find any two, we can find the third by using this
equation, v OC =v TH i SC = i N R EQ = R N. Slide 19 19 Norton
Equivalent - equivalent Behavior Dependent sources in the circuit
do not change the validity of the theorem. These sources cannot be
deactivated though. + v OC - i SC Polarity of current i N
important; as in Ohms Law It is NOT Ohms Law (different circuit)
Pick polarity Slide 20 20 Example #1 Find the Norton equivalent of
the circuit below, as seen from terminals A and B (here the load
will be connected). All resistors belong to the circuit. Use NVM to
find v OC. + v OC - Slide 21 21 Equivalent Resistance R N To find
the equivalent resistance, R EQ we deactivate all sources= set them
to zero. The voltage source becomes a short circuit, and the
current source becomes an open circuit. Slide 22 22 Norton
Equivalent Found The complete Norton s equivalent, seen from
terminals A and B has i N and R N Slide 23 23 Find the
short-circuit current in the original circuit directly not though v
TH. Norton Equivalent: i SC i R3 =0 i (R4+R5) =0 Slide 24 24 Redraw
the Circuit Calculate i SC from the modified circuit Norton
Equivalent Slide 25 Figur e 3.67 Measurement of open-circuit
voltage and short-circuit current Slide 26 26 Simplification of R2R
ladder circuit Copyright 2005 by Pearson Education, Inc. Upper
Saddle River, New Jersey 07458 All rights reserved. Slide 27 27
Source transformation Slide 28 28 Source transformation Norton
equivalent circuit Slide 29 29 Summary 1.Thevenin and Norton
equivalents of any circuit made up of voltage sources, current
sources, and resistors are very important in complicated circuits.
2.We can find the values of the these equivalents by finding two of
three parameters: the open-circuit voltage, short-circuit current
or equivalent resistance. The reference polarities of these
quantities are important. 3.To find the equivalent resistance, we
need to set the independent sources equal to zero. However, the
dependent sources will remain. Slide 30 30 Superposition Principle
The total current (through) or total voltage (across) any part of a
linear circuit is the algebraic sum of all currents/voltages
produced by each source acting separately. Slide 31 31 All
independent sources must be deactivated i.e. zeroed: V=0 (short),
I=0 (open) except for ONE. Do not turn off dependent sources Repeat
calculations for every independent source in the circuit Add all
obtained values of currents and voltages to find their total
values. Superposition Principle
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/suppos.html#c2
