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Basic Experiment and Design of Electronics
EQUIVALENT CIRCUITS
Ho Kyung Kim, Ph.D.
[email protected]
School of Mechanical Engineering
Pusan National University
Outline
•
Superposition theorem
•
Thévenin’s and Norton’s theorem
•
Maximum power transfer theorem
•
Wheatstone bridge
2
Superposition theorem
•
In any linear circuit containing multiple independent sources, the current or voltage at
any point in the network may be calculated as the algebraic sum of the individual
contributions of each source acting alone.
v B1  v B 2  Ri  0
i
v B1  v B 2 v B1 v B 2


 i B1  i B 2
R
R
R
–
in order to set a voltage source equal to zero, replace it with a short circuit
–
in order to set a current source equal to zero, replace it with an open circuit
Thévenin's theorem
•
When viewed from the load, any network composed of ideal voltage and current sources,
and of linear resistors, may be represented by an equivalent circuit consisting of an ideal
voltage source vT in series with an equivalent resistance RT.
① find the equivalent resistance presented by the circuit at its terminal
② compute the Thévenin voltage
Norton's theorem
•
When viewed from the load, any network composed of ideal voltage and current sources,
and of linear resistors, may be represented by an equivalent circuit consisting of an ideal
current source iN in parallel with an equivalent resistance RN.
① find the equivalent resistance presented by the circuit at its terminal
② compute the Norton current
Determination of equivalent resistance
① remove the load
② zero all independent voltage and current sources
③ compute the total resistance between load terminals
Note that the computed resistance is equivalent to that which would be
encountered by a current source connected to the circuit in place of the load.
RT  R1 || R2  R3
Computing the Thévenin voltage
•
The equivalent (Thévenin) source voltage is equal to the open-circuit voltage at the load
terminals (with the load removed).
①
②
③
④
remove the load, leaving the load terminals open-circuited
define the open-circuit voltage vOC across the open load terminals
solve for vOC
Thévenin voltage, vT = vOC
R1
vS
R3
R2
+0V- +
+
vOC
vOC
-
iL
RL
vOC  v R 2  v S
R2
R1  R2
R2
vT
R1  R2
iL 

RT  R L ( R1 || R2 )  R3   R L
vS
Computing the Norton current
•
The Norton equivalent current is equal to the short-circuit current that would flow if the
load were replaced by a short circuit.
①
②
③
④
replace the load with a short circuit
define the short-circuit current iSC to be the Norton equivalent current
solve for iSC
Norton current, iN = iSC
vS  v
v
v


R1
R2 R3
v  vS
R2 R3
R1 R3  R2 R3  R1 R2
i N  i SC 
R2
v
 vS
R3
R1 R3  R2 R3  R1 R2
Maximum power transfer theorem
•
The Thévenin and Norton models imply that some of the power generated by the source
will necessarily be dissipated by the internal circuits within the source.
Thévenin equivalent
•
Then, how much power can be transferred to the load from the source under the most
ideal conditions?
Power absorbed by the load, RL;
PL  i L2 RL
Load current, iL;
iL 
Then, we have;
PL 
vT2
( RT  R L ) 2
RL
Maximum PL can be obtained when
PL
0
R L
PL vT2 ( RT  R L ) 2  2vT2 R L ( RT  R L )

0
R L
( RT  R L ) 4
RL = RT
vT
RT  R L
Wheatstone bridge
•
•
a resistive circuit
widely used as measurement circuit
The source voltage divides between each resistor pair according to the voltage divider rule;
v ad  v S
R2
R1  R2
and
vbd  v S
Rx
R3  R x
 R2
Rx

v ab  v ad  vbd  v S 
 R1  R2 R3  R x




Self-assigned HW
•
Rizzoni (5th ed.), Ch. 3
–
51, 52, 53, 54, 56, 58, 59, 60, 73, 75
14