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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 source | Sakeek vS in series with a R by a 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 .

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