Basic Experiment and Design of Electronics
E
C
Ho Kyung Kim, Ph.D.
hokyung@pusan.ac.kr
School of Mechanical Engineering
Pusan National University

•
Superposition theorem
•
Thévenin’s and Norton’s theorem
•
Maximum power transfer theorem
•
Wheatstone bridge
2

•
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
B 1
 v
B 2

Ri

0 i
 v
B 1
 v
B 2
R
 v
B 1
R
 v
B 2
R
 i
B 1
 i
B 2

– 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

•
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 v
T in series with an equivalent resistance
R
T
.
① find the equivalent resistance presented by the circuit at its terminal
② compute the Thévenin voltage

•
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 i
N in parallel with an equivalent resistance
R
N
.
① find the equivalent resistance presented by the circuit at its terminal
② compute the Norton current

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.
R
T

R
1
|| R
2

R
3

• The equivalent (Thévenin) source voltage is equal to the terminals (with the load removed).
open-circuit voltage at the load
① remove the load, leaving the load terminals open -circuited
② define the open-circuit voltage v
OC
③ solve for v
OC
④ Thévenin voltage, v
T
= v
OC across the open load terminals v
S
R
1
R
3
R
2
+ 0 V -
+ v
OC
-
+ v
OC
i
L
R
L v
OC
 v
R 2
 v
S
R
1
R
2

R
2

i
L

R
T v
T

R
L


( R
1
||
R
2 v
S
R
2
R
1
)


R
2
R
3


R
L

• The Norton equivalent current is equal to the load were replaced by a short circuit.
short-circuit current that would flow if the
① replace the load with a short circuit
② define the short-circuit current i
SC
③ solve for i
SC
④ Norton current, i
N
= i
SC to be the Norton equivalent current v
S

R
1 v
 v
R
2
 v
R
3 v
 v
S
R
1
R
3
R
2
R
3

R
2
R
3

R
1
R
2 i
N
 i
SC
 v
R
3
 v
S
R
1
R
3
R
2

R
2
R
3

R
1
R
2

• 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?

Then, we have;
P
L
 v
T
2
( R
T

R
L
)
2
R
L
Maximum P
L can be obtained when

P
L

R
L

0

P
L

R
L
 v
T
2
( R
T

R
L
)
2
( R
T


2 v
T
2
R
L
)
R
L
4
( R
T

R
L
)

0
R
L
= R
T
Power absorbed by the load,
R
L
;
P
L
 i
L
2
R
L
Load current, i
L
; i
L

R
T v
T

R
L

• 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
R
1
R
2

R
2 and v bd
 v
S
R
3
R x

R x v ab
 v ad
 v bd
 v
S


R
1
R
2

R
2

R
3
R x

R x



•
Rizzoni (5 th ed.), Ch. 3
–
51, 52, 53, 54, 56, 58, 59, 60, 73, 75
14