EEEB113 Circuit Analysis 1 Chapter 4 Circuit Theorems By : Nur Fadilah Ab Aziz Email :
[email protected] Room : BN-1-031
OVERVIEW 1. Sup Superp erposi ositio tion n Theo Theorem rem 2. Sou Source rce Tran Transfo sforma rmatio tion n Theorem Theorem 3. Thevenin’s Theorem 4. Norton’s Theorem 5. Max Maximu imum m Power Tran Transfe sferr Theorem Theorem
1. SUPERPOSITION THEOREM Definition:
The superposition states that: the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through) that element due to EACH independent source acting alone. alone.
* Another approach to determine voltage/current if a circuit has two or more independent sources
1. SUPERPOSITION THEOREM The
principle of superposition helps us to analyze a linear circuit with more than one independent source by calculating the contribution of each independent source separately and then adding them up.
Example:
The total value of v is obtained by considering the contribution from 6 V and 3 A one by one, and then add the two contribution from the two sources together for together for the final value.
1. SUPERPOSITION THEOREM When
applying superposition, keep in mind that:
1. Only one independent source at a time and the other independent source are made 0 (turn off): i. Voltage source 0 V (short circuit) ii. Current source 0 A (open circuit) 2. Dependent sources are left intact because they are controlled by circuit variables.
1. SUPERPOSITION THEOREM - St Steps eps to app apply ly the the theor theorem em
1. SUPERPOSITION THEOREM - Ex Exam ample ple 1 (E. (E. 4.3 4.3))
1. SUPERPOSITION THEOREM - Ex Examp ample le 1 (St (Step ep 1 & Step Step 2) 2)
1. SUPERPOSITION THEOREM - Ex Exam ample ple 1 (St (Step 3) 3)
1. SUPERPOSITION THEOREM - Example 2 (P.P (P.P.. 4.3)
1. SUPERPOSITION THEOREM - Ex Exam ample ple 2 (So (Solut lutio ion) n)
1. SUPERPOSITION THEOREM - Exer Exercise cise 1 (P.P (P.P.. 4.4)
1. SUPERPOSITION THEOREM - Exer Exercise cise 2 (P.P (P.P.. 4.5)
2. SOURCE TRANSFORMATION THEOREM Another
tool to simplify circuit
the concept of equivalent circuits – circuits – the v-i characteristics are identical with the original circuit
Use
Transformation is the process of replacing a voltage Source Transformation source in series with a resistor with resistor with a current source parallel with the resistor or resistor or vice versa.
2. SOURCE TRANSFORMATION THEOREM An
resistor,, R can be ideal voltage source, V s in series with resistor transformed into an ideal current source, I in parallel with resistor, R using the relation V s = I sR and vice versa.s
a)
Independent So Source Tr Transformation
SOURCE TRANSFORMA TION THEOREM TRANSFORMATION
b)
Dependent So Source Tr Transformation
NOTES:
1.
The arrow of the I source is directed towards the positive terminal of the V source. source.
2.
NOT possible when:
a) R = 0 (voltage sorce)
b)
R
= ∞ (current source)
2. SOURCE TRANSFORMATION THEOREM - Example 1 (P.P (P.P.. 4.6)
2. SOURCE TRANSFORMATION THEOREM - Ex Exam ample ple 1 (So (Solut lutio ion) n)
2. SOURCE TRANSFORMATION THEOREM - Ex Exam ample ple 1 (So (Solut lutio ion) n)
2. SOURCE TRANSFORMATION THEOREM - Ex Exam ample ple 1 (So (Solut lutio ion) n)
2. SOURCE TRANSFORMATION THEOREM - Ex Exam ample ple 1 (So (Solut lutio ion) n)
2. SOURCE TRANSFORMATION THEOREM - Ex Exer erci cise se 1
i = 7.059 mA
i x
7.059 mA
2. SOURCE TRANSFORMATION THEOREM - Ex Exer erci cise se 2
THEVENIN’s AND NORTON’s
THEOREM
Both theorems help to simplify complex circuit to a simpler equivalent circuit.
Complicated circuit
Simpler circuit
We are interested on the value of V and I across and through the load
THEVENIN’s AND NORTON’s
THEOREM
3. THEVENIN’ s THEOREM THEVENIN’s Definition:
Thevenin’s Theorem states that: A that: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source, V Th in series with a resistor , R Th. V Th = open circuit voltage at the terminals R Th = input or equivalent resistance at the terminal when the independent sources are turned off.
3. THEVENIN’ s THEOREM THEVENIN’s
3. THEVENIN’s THEOREM Th and RTh - St Step epss to to fin find d V Th 1. The termin terminal al are made made open open circuited circuited by removing removing the load load and determ determine ine the the V oc across the terminal, where V oc = V Th.
3. THEVENIN’s THEOREM Th and RTh - St Step epss to to fin find d V Th 2. Tu Turn rn off off all all the inde independ pendent ent source sources s and and find find the resis resistance tance,, R Th ‘looking in’ at the terminals
To Determine R Th (Case 1: NO Depen Dependent dent Source Sources) s)
Turn off all independent sources. Find R Th where it is the equivalent resistance at point ‘a’ and ‘b’ terminals.
3. THEVENIN’s THEOREM
- St Step epss to to fin find d V Th Th and RTh To Determine
R Th
(Case 2: 2: Circuit Circuit HAS Depen Dependent dent Sources) Sources)
Turn off all independent sources but dependent sources REMAIN as they are. Introduce a voltage (or current) source across the ‘a’ and ‘b’ terminals.
For Case 2: a) a) Any value for canV be Any assumed o and I o (usually V o =1V and I o =1A =1A)) b) =
c) R Th < 0 implies that circuit is supplying power (possible in a circuit WITH dependent source)
3. THEVENIN’s THEOREM
- St Step epss to to fin find d V Th Th and RTh 3.
Determine the current through the load, load, I L and voltage across the load, load, V L using the Thevenin Thev enin equi equivalen valentt circui circuit. t.
3. THEVENIN’s THEOREM
- Ex. 1, P.P 4.8 4.8 (NO depe depende ndent nt sou sourrces ces))
3. THEVENIN’s THEOREM
- Exa Example mple 1, P.P 4.8 (Step (Step 1)
3. THEVENIN’s THEOREM
- Exa Example mple 1, P.P 4.8 (Step (Step 1)
3. THEVENIN’s THEOREM
- Exa Example mple 1, P.P 4.8 (Step (Step 2)
3. THEVENIN’s THEOREM
- Exa Example mple 1, P.P 4.8 (Step (Step 3)
3. THEVENIN’s THEOREM
- Ex Exer erci cise se 1
I = 0.482 A
3. THEVENIN’s THEOREM
- Ex Exer erci cise se 2
3. THEVENIN’s THEOREM
- Ex. 2, P.P 4.9 4.9 (HAS (HAS dep depende endent nt sou sourrces ces))
3. THEVENIN’s THEOREM
- Exa Example mple 2, P.P 4.9 (Step (Step 1)
3. THEVENIN’s THEOREM
- Exa Example mple 2, P.P 4.9 (Step (Step 2)
3. THEVENIN’s THEOREM
- Ex Exer erci cise se 3
. NORTON’s THEOREM
4 Definition:
Norton’s Theorem states that: A that: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source, I N in parallel with a resistor, R N. I N = short circuit current through the terminals R = R , input or equivalent resistance at the terminal Th
Th
when the independent sources are turned off.
. NORTON’s THEOREM
4
4. NORTON’s THEOREM - St Step epss to to fin find d RN and I N
4. NORTON’s THEOREM - St Step epss to to fin find d RN and I N
4. NORTON’s THEOREM
- Ex Ex.. 1, 1, E. E. 4.1 4.11 1 (NO (NO dep depen ende dent nt so sour urce ces) s)
4. NORTON’s THEOREM
- Ex Examp ample le 1, 1, E. 4.11 4.11 (St (Step ep 1) 1)
4. NORTON’s THEOREM
- Ex Examp ample le 1, 1, E. 4.11 4.11 (St (Step ep 2) 2)
4. NORTON’s THEOREM
- Ex Examp ample le 1, 1, E. 4.11 4.11 (St (Step ep 2) 2)
4. NORTON’s THEOREM
- Ex Examp ample le 1, 1, E. 4.11 4.11 (St (Step ep 2) 2)
4. NORTON’s THEOREM
- Ex Exercise ercise 1, P.P P.P.. 4.11
4. NORTON’s THEOREM
- Ex Exer erci cise se 2
4. NORTON’s THEOREM
- Ex Ex.. 2, 2, E. E. 4.1 4.12 2 (HA (HAS S de depe pende ndent nt so sour urce ces) s)
4. NORTON’s THEOREM
- Ex Examp ample le 2, 2, E. 4.12 4.12 (St (Step ep 1) 1)
4. NORTON’s THEOREM
- Ex Examp ample le 2, 2, E. 4.12 4.12 (St (Step ep 2) 2)
4. NORTON’s THEOREM
- Ex Exercise ercise 3, P.P P.P.. 4.12
5. MAXIMUM POWER TRANSFER
5. MAXIMUM POWER TRANSFER - Ex Exam ample ple 1, E. 4. 4.13 13
5. MAXIMUM POWER TRANSFER - Ex Examp ample le 1, 1, E. 4.13 4.13 (Sol (Soluti ution) on)
5. MAXIMUM POWER TRANSFER - Ex Exer erci cise se 1, 1, E. 4.1 4.13 3
