BASICS OF ELECTRICAL CIRCUITS
EHB 211 E
Techniques of Circuit Analysis II
Asst. Prof. Onur Ferhanoğlu
1
Source Transformation
A useful method to simplify circuits
Find vs and is that satisfy the equivalence
Assume load resistance: RL is connected between a-b
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
2
Source Transformation - Exercise
Find the power associated with 6V source
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
3
Source Transformation
What if we have a parallel resistor with voltage source
& series resistor with a current source
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Has no effect
4
Source Transformation - Exercise
a) Find v0 b) Find P250V c) P8A
Get rid of 125 and
10 ohm resistances
P8A = 480W
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
5
Source Transformation - Exercise
Find v, P120V
48V, 374.4W
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
6
Thevenin & Norton Equivalent
Thevenin & Norton equivalent circuits are simplification techniques that focus on
terminal behaviour
Thevenin equivalent: Independent voltage source in series with a
resistor, which replaces an interconnection of sources and
resistors
• Open circuit voltage = VTh
• Short circuit current ->
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
7
Thevenin equivalent
Find thevenin equivalent
Open circuit voltage
Short circuit current
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
8
Thevenin equivalent
Find thevenin equivalent
Source transformation
Thevenin
Norton
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
9
Thevenin equivalent – Dependent source
Find thevenin equivalent
Short circuit current
OPEN circuit voltage
2 equations
2 unknowns
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Exercise
Find Norton equivalent
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Exercise
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Thevenin Equivalent – Deactivating sources
Deactivate independent sources -> voltage source: short circuit
current souce: open circuit
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Thevenin Equivalent – Test source
If the network contains dependent sources:
• deactivate all independent sources
• Apply a test source
Substitute second eq. into 1st
R = 100 ohms
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Maximum power transfer
Power transferred to load resistance
For a given circuit, VTh and RTh will be fixed
Derivative is 0 when
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Maximum power transfer - exercise
Find RL for maximum power transfer to RL
Calculate the max. power that can be delivered
Open circuit voltage:
Thevenin Resistance (eliminate source)
= RL
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Superposition
• Apply 1 source at a time
• Kill others
• Add results
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Superposition
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Superposition
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Superposition – Dependent sources
Find v0
Asst. Prof. Onur Ferhanoğlu
vΔ` = 10. 0.4 vΔ` -> vΔ` = 0
No current passing over 10 ohms
(open circuit)
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS
Superposition – Dependent sources
Find v0
Node a
Node b
Asst. Prof. Onur Ferhanoğlu
Techniques of Circuit Analysis II / BASICS OF ELECTRICAL CIRCUITS