1. TECHNIQUES OF DC CIRCUIT ANALYSIS: SKEE 1023
Superposition Principle
Source Transformation
Thevenin’s Theorem
Norton’s Theorem
Maximum Power Transfer
SKEE 1023

2. What do we mean by a linear relationship?
Applies only for LINEAR CIRCUIT
Circuit containing only linear circuit elements
A LINEAR relationship between voltage and current
What do we mean by a linear relationship?

3. What do we mean by a linear relationship?
When the relationship fulfilled 2 properties:
Homogeneity (scaling)
f(x) = y  f(kx) = ky = kf(x)
Additivity
f(x) = y  f(x1 + x2) = f(x1) + f(x2) = y1 + y2
What do we mean by a linear relationship?

4. Superposition Principle: The voltage across an element ( or the current through an element) of a linear circuit containing more than one independent source, is the algebraic sum the voltage across that element (or the current through that element) due to each independent source acting alone.
All other independent sources are deactivated
voltage sources are shorted
current sources are opened
Note that dependent sources CANNOT be deactivated !

5. Superposition Principle: The voltage across an element ( or the current through an element) of a linear circuit containing more than one independent source, is the algebraic sum the voltage across that element (or the current through that element) due to each independent source acting alone.

6. Superposition Principle: The voltage across an element ( or the current through an element) of a linear circuit containing more than one independent source, is the algebraic sum the voltage across that element (or the current through that element) due to each independent source acting alone.
may involve MORE work
cannot be applied to power calculation – find i or v first (using superposition) before calculating power !
most suitably used when involved with sources of different properties or types, e.g. different frequencies, mixture of DC and AC, etc.

7. Source Transformation: A tool used to simplify circuit; a process of replacing a voltage source in series with a resistor by a current source in parallel with a resistor or vice versa vs R a b is R a b
voc = isR
isc = is
voc = vs
isc = vs/R
If the circuit is equivalent at terminal a-b, their open-circuit and short-circuit characteristics are similar

8. Source Transformation: A tool used to simplify circuit; a process of replacing a voltage source in series with a resistor by a current source in parallel with a resistor or vice versa vs R a b is R a b
voc = isR
isc = is
voc = vs
isc = vs/R

9. VTh= ? RTh= ? In 1883, M.L. Thevenin proposed a theorem …….
Thevenin’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor
Linear two-terminal
circuit
Load + V  I + V 
Load
VTh
RTh I
VTh= ?
RTh= ?

10. Thevenin’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor
To determine VTh =
VTh
RTh
Load
Linear two-terminal
circuit
Load

11. Thevenin’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor
To determine VTh
RTh
Load
open circuit voltage = Voc + 
VTh
= VTh
Load
Linear two-terminal
circuit

12. Thevenin’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor
To determine VTh
RTh
open circuit voltage = Voc + 
VTh
= VTh
Load
Linear two-terminal
circuit
open circuit voltage = Voc + 

13. Thevenin’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor
To determine VTh
Linear two-terminal
circuit
VTh
RTh
open circuit voltage = Voc + 
= VTh
VTh = Voc = Open circuit voltage
= VTh (Since the circuit is equivalent)

14. Thevenin’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor
To determine RTh - Method 1
Linear two-terminal
circuit
VTh
RTh
isc a b
Short circuit current, isc =

15. Thevenin’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor
To determine RTh – Method 2
Pre-requisite: circuit with NO dependent sources
Deactivate all the independent sources
Linear circuit – independent sources killed
Rin = RTh
Rin = RTh

16. Thevenin’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor
To determine RTh – Method 3
Deactivate all the independent sources - dependent sources stay as they are
Linear
Circuit – ONLY dependent sources killed vo io + -
RTh is calculated as:
Introduce a voltage (or current) source.

17. IN= ? RN= ? 43 years later, E.L. Norton proposed a similar theorem. ….
Norton’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source in parallel with a resistor
43 years later, E.L. Norton proposed a similar theorem. ….
Linear two-terminal
circuit
Load + V  I
IN= ? + V  I
Load IN RN
RN= ?

18. Norton’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source in parallel with a resistor
To determine IN IN RN
Linear circuit

19. Norton’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source in parallel with a resistor
To determine IN IN
IN= Short circuit current RN
Linear circuit
Short circuit current
= IN

20. Norton’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source in parallel with a resistor
To determine IN
IN= Short circuit current IN RN
Linear circuit
Short circuit current
= IN
IN = Isc = Short circuit current

21. SIMILAR METHOD AS HOW TO OBTAIN RTh
Norton’s Theorem: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source in parallel with a resistor
To determine RN
SIMILAR METHOD AS HOW TO OBTAIN RTh
RN = RTh

22. Relationship between Norton’s and Thevenin’s equivalentsRN b a
Linear two-terminal
circuit b a OR
VTh
RTh b a

23. Since both circuits are equivalent, voc must be the same
Relationship between Norton’s and Thevenin’s equivalents IN RN b a
VTh
RTh + 
Since both circuits are equivalent, voc must be the same + 

24. Maximum Power Transfer
Linear circuit RL
What would be the value of RL for power delivered to it become MAXIMUM?

25. Maximum Power Transfer
VTh
RTh
Linear circuit RL
What would be the value of RL for power delivered to it become MAXIMUM?

26. Maximum Power TransferRL p
Maximum power
Rl=linspace(1,60,500);
Vth=10;
Rth=12;
p=((Vth./(Rl+Rth)).^2).*Rl;
plot(Rl,p,'r');
grid;
RL = 12 

27. Maximum Power Transfer
Mathematically, we evaluate RL when

28. Using PSpice to verify Norton’s and Thevenin’s Theorems
Find Thevenin equivalent at terminals a-b

29. Using PSpice to verify Norton’s and Thevenin’s Theorems

30. Using PSpice to verify Norton’s and Thevenin’s Theorems

31. Using PSpice to verify Norton’s and Thevenin’s Theorems

32. Using PSpice to verify Norton’s and Thevenin’s Theorems

33. Using PSpice to verify Norton’s and Thevenin’s Theorems
RTh = 6/1 = 6

34. Using PSpice to verify Norton’s and Thevenin’s Theorems
VTh = 20V