11/9/2019 Physics Academy www.physicsacademy.org www.physicsacademy.org | Unit: 4 | Lecture: 19 www.hazemsakeek.net Circuit Theorems: Source Transformation | Sakeek Dr. Hazem Falah Sakeek Al-Azhar University of Gaza Falah Hazem Dr. 1 1 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 Hazem Dr. 2 2 1 11/9/2019 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 Hazem Dr. 3 3 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 Hazem Dr. for current source. Transformation of dependent sources 4 4 2 11/9/2019 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 6 3 11/9/2019 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 7 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 8 4 11/9/2019 Problems to Solve by yourself (1) Use source transformation to reduce (3) Use source transformation to find the the circuit to a single voltage source in voltage 푉푥 series with a single resistor. www.physicsacademy.org | www.hazemsakeek.net (2) Use source transformation to find 푖. | (4) Use source transformation to find 푖x. Sakeek Dr. Hazem Falah Hazem Dr. 9 9 5.