SOURCE TRANSFORMATION 1 Source Transformation An equivalent circuit

SOURCE TRANSFORMATION 1

Source Transformation • • An equivalent circuit is one whose v-i characteristics are identical with the original circuit. It is the process of replacing a voltage source v. S in series with a resistor R by a current source i. S in parallel with a resistor R, or vice versa. 2

Source Transformation (a) Independent source transform (b) Dependent source transform • The arrow of the current source is directed toward the positive terminal of the voltage source. • The source transformation is not possible when R = 0 for voltage source and R = ∞ for current source. 3

Source Transformation Example 4. 6 Use source transformation to find v 0 4

Source Transformation 5

Source Transformation Example 4. 7 Find vx using Source Transformation 6

Source Transformation 7

Source Transformation Practice Problem 4. 6 Find i 0 in the circuit below using source transformation 8

Source Transformation Practice Problem 4. 7 Find ix in the circuit below using source transformation 9

THEVENIN’S THEOREM 10

Thevenin’s Theorem It states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTH in series with a resistor RTH, 11

Thevenin’s Theorem • VTH is the open-circuit voltage at the terminals. • RTH is the input or equivalent resistance at the terminals when the independent sources are turned off. 12

Thevenin’s Theorem Finding Thevenin resistance, RTH: CASE 1 (If network has NO dependent sources) • Turn off all independent sources. RTH is the input resistance of the network looking between its two terminals 13

Thevenin’s Theorem Finding Thevenin resistance, RTH: CASE 2 (If network has dependent sources) • • Turn off all independent sources BUT leave dependent sources intact (similar to superposition theorem) Two approaches: ü Approach 1 – Apply a voltage source v 0 at the terminals and determine the resulting current i 0. Then RTH = v 0/i 0 (figure a) ü Approach 2 – Insert a current source i 0 at the network terminal and find the terminal voltage v 0 (figure b) 14

Thevenin’s Theorem A Thevenin-equivalent circuit is a simple voltage divider, VL by mere inspection 15

Thevenin’s Theorem Example 4. 8 Find the Thevenin equivalent circuit of the circuit below to the left of the terminals a-b. Also find the current when RL is 6, 16 and 36 ohms. 16

Thevenin’s Theorem Example 4. 8 17

Thevenin’s Theorem Example 4. 9 Find the Thevenin equivalent circuit of the circuit below at terminals a-b. 18

Thevenin’s Theorem Example 4. 9 19

Thevenin’s Theorem Practice Problem 4. 8 Using Thevenin’s Theorem, find the equivalent circuit to the left of the terminals in the circuit below. Then find I 20

Thevenin’s Theorem Practice Problem 4. 9 Find the Thevenin equivalent circuit of the circuit below 21

Thevenin’s Theorem Practice Problem 4. 10 Using Thevenin’s Theorem, find the equivalent circuit to the left of the terminals in the circuit below 22

Tutorial (Source Transformation) Problem 4. 27 Apply source transformation to find vx in the circuit below 23

Tutorial (Source Transformation) Problem 4. 32 Use source transformation to find ix in the circuit below 24

Tutorial (Thevenin’s Theorem) Problem 4. 33 Determine RTH and VTH at terminals 1 -2 of each of the circuit below: 25

Tutorial (Thevenin’s Theorem) Problem 4. 38 Apply thevenin’s theorem to find Vo in the circuit below: 26

Tutorial (Thevenin’s Theorem) Problem 4. 39 Obtain thevenin equivalent at terminals a-b of the circuit below: 27

Tutorial (Thevenin’s Theorem) Problem 4. 44 For the circuit below, obtain thevenin’s equivalent as seen from terminals (a) a-b (b) b-c 28

Tutorial (Thevenin’s Theorem) Problem 4. 40 Find thevenin equivalent at terminals a-b of the circuit below: 29

Homework (Thevenin’s Theorem) Problem 4. 42 Find thevenin equivalent between terminals a-b of the circuit below: 30

Homework (Thevenin’s Theorem) Problem 4. 43 Find thevenin equivalent looking into terminals a-b of the circuit below: 31

Homework (Thevenin’s Theorem) Problem 4. 36 Solve for the current i in the circuit below (Hint: find thevenin equivalent seen by the 12 ohm resistor) 32

NORTON’S THEOREM 33

Norton’s Theorem It states that a linear two-terminal circuit can be replaced by an equivalent circuit of a current source IN in parallel with a resistor RN, Thevenin’s and Norton equivalent circuits are related by a source transformation. 34

Norton’s Theorem Where IN is the short circuit current through the terminals. RN is the input or equivalent resistance at the terminals when the independent sources are turned off. 35

Relationship between Thevenin’s Theorem and Norton’s Theorem 36

Norton’s Theorem Example 4. 11 Find the Norton equivalent of the circuit in the figure below 37

Norton’s Theorem 1 st approach 38

Norton’s Theorem 2 nd approach 39

Norton’s Theorem Example 4. 12 Find the Norton equivalent of the circuit at terminals a-b in the figure below 40

Norton’s Theorem 41

Norton’s Theorem Practice Problem 4. 11 Find the Norton equivalent of the circuit at terminals a-b in the figure below 42

Norton’s Theorem Practice Problem 4. 12 Find the Norton equivalent of the circuit at terminals a-b in the figure below 43

Tutorial (Norton’s Theorem) Problem 4. 50 Obtain the Norton equivalent of the circuit below to the left of the terminals a-b. Use the result to find current i 44

Tutorial (Norton’s Theorem) Problem 4. 51 Obtain the norton equivalent as viewed from terminals: a) a-b b) c-d 45

Tutorial (Norton’s Theorem) Problem 4. 53 Find the Norton equivalent at terminals a-b of the circuit below: 46

Tutorial (Norton’s Theorem) Try these problems: 1. Problem 4. 57, ans: RTH = 10 ohm, VTH = 166. 67 V, IN = 16. 667 A 2. Problem 4. 56, ans: V 0 = -2. 857 V 47