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Physics Academy
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Unit: 4 | Lecture: 19 www.hazemsakeek.net
Circuit Theorems: Source Transformation | Sakeek Dr. Hazem Falah Sakeek
Al-Azhar University of Gaza Falah Hazem Dr.
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Circuit Theorems www.physicsacademy.org
4.1 Introduction | 4.2 Linearity Property 4.3 Superposition
4.4 Source Transformation www.hazemsakeek.net 4.5 Thevenin’s Theorem |
4.6 Norton’s Theorem Sakeek
4.7 Maximum Power Transfer Dr. Hazem Falah Falah Hazem Dr.
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4.4 Source Transformation (1)
• Source transformation is another tool for simplifying circuits, based
on the concept of equivalence. www.physicsacademy.org | | • An equivalent circuit is one whose 푣-푖 characteristics are identical
with the original circuit. www.hazemsakeek.net
Source transformation is the process of replacing a voltage source | Sakeek vS in series with a resistor R by a current source iS in parallel with a
resistor R, or vice versa. Dr. Hazem Falah Falah Hazem Dr.
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4.4 Source Transformation (2)
The arrow of the
current source is www.physicsacademy.org directed toward | the positive terminal of the voltage source.
Transformation of independent sources www.hazemsakeek.net The source trans- |
formation is not Sakeek possible when R = 0 for voltage
source and R = ∞ Dr. Hazem Falah Falah Hazem Dr. for current source. Transformation of dependent sources 4
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4.4 Source Transformation (3)
The two circuits are equivalent, i.e. they have the
same voltage-current relation at terminals a-b.
www.physicsacademy.org | | If the sources are turned off, the equivalent resistance at terminals a-b in both circuits is R. (a)
When terminals a-b are short-circuited, the short- www.hazemsakeek.net
circuit current flowing from a to b is 풊풔풄 = 풗풔Τ푹 in |
the circuit (a) and 풊풔풄 = 풊풔 for the circuit (b). Sakeek
푣푠Τ푅 = 푖푠 Source transformation requires that 풗 Falah Hazem Dr. 풗 = 풊 푹 or 풊 = 풔 풔 풔 풔 푹 (b) 5 5
Example 4.6
Use source transformation to find 풗풐 Solution:
1. Transform the current and voltage www.physicsacademy.org | | sources, we get circuit (a). (a) 2. Combining the 2 & 4 = 6 3. Transform the 12 V source in circuit
(a) we get circuit (b). www.hazemsakeek.net
4. Combining the 6 & 3 in parallel | and the 2 A & 4 A current source, we (b)
get circuit (c). Sakeek Applying current division to get 2
푖 = 2 = 0.4 퐴 (c) Falah Hazem Dr. 2 + 8
∴ 푣표 = 8 푖 = 8 0.4 = 3.2 푉 6
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Example 4.7 (1)
Find 풗풙 using source transformation www.physicsacademy.org 1. Transform the 6 V source and the | dependent current source 0.25푣푥 we get circuit (a).
2. Combining the 2- & 2- in www.hazemsakeek.net
parallel to give 1-, which is in |
parallel with 3 A current source. (a) Sakeek 3. Transform the 3 A current source in circuit (a) we get circuit (b).
Notice that the terminals for are Falah Hazem Dr. intact. (b) 7
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Example 4.7 (2)
Applying KVL (1)
−3 + 5푖 + 푣푥 + 18 = 0 www.physicsacademy.org | | Applying KVL to the loop containing only the 3-V voltage source and 1 and 푣푥,we get
−3 + 1푖 + 푣푥 = 0 www.hazemsakeek.net ∴ 푣푥= 3 − 푖 (2) |
Substituting Eq. (2) in Eq. (1), we obtain Sakeek 15 + 5푖 + 3 − 푖 = 0
∴ 푖 = 4.5 퐴 Falah Hazem Dr.
∴ 푣푥= 3 − 푖 = 7.5 푉 8
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Problems to Solve by yourself
(1) Use source transformation to reduce (3) Use source transformatio