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Basic Electric Circuits Session 12C
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Basic Electric Circuits Session 12C
1.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com
2.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 2 Session 12C: Focus Thévenin’s Theorem ◦ Example Problem 2 Norton’s Theorem Home Work problem
3.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 3 Example 2: Thévenin’s Theorem Find current through 2 Ω: 4 Ω 6 Ω 4 Ω 5 Ω 9 V 4 9 4+ 4 + 6 2.571 V 6 Ω 4 Ω 4 Ω 5 Ω 2.571 V 7.857 Ω 2 Ω voc = 2.571 V, RTH = 7.857 Ω I2Ω = 260.8 mA
4.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 4 A few Key Points: Thévenin Theorem The equivalent circuit that we have learnt to obtain, is completely independent of network B ◦ To which the network A is connected to The only restriction that we must impose on A or B is that all dependent sources in A have their control variables in A, and similarly for B. No restrictions are imposed on the complexity of A or B; either one may contain any combination of independent voltage or current sources, linear dependent voltage or current sources, resistors, or any other circuit elements which are linear. The dead network A can be represented by a single equivalent resistance RTH ◦ Which we will call the Thévenin equivalent resistance.
5.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com Norton’s Equivalent Circuit
6.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 6 Example 3: Thévenin and Nortan’s equivalent circuits Find the Thévenin and Nortan’s equivalent circuits: Applying Superposition to find Voc = 5 kΩ Voc o o
7.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 7 Example 3: Continued. RTH = 5 kΩ Voc = 8 V Isc = 1.6 mA Thévenin Equivalent circuit Norton Equivalent circuit
8.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 8 Norton’s Theorem 1. Given any linear circuit, rearrange it in the form of two networks, A and B, connected by two wires. ◦ Network A is the network to be simplified; B will be left untouched. As before, if either network contains a dependent source, its controlling variable must be in the same network. 2. Disconnect network B, and short the terminals of A. Define a current isc as the current now flowing through the shorted terminals of network A. 3. Turn off or “zero out” every independent source in network A to form an inactive network (RTh). Leave dependent sources unchanged.
9.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 9 Norton’s Theorem 4. Connect an independent current source with value isc in parallel with the inactive network. ◦ Do not complete the circuit; leave the two terminals disconnected. 5. Connect network B to the terminals of the new network A. ◦ All currents and voltages in B will remain unchanged.
10.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com Home Work Problem
11.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 11 HW1: Thévenin and Norton Equivalents Note: This is Practice 5.7 on page 147, Figure 5.30 in the Ref 1 book (by Hayt) voc = -7.86 V, RTH = 2.429 kΩ Isc = -3.235 mA Voc
12.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 12 Session 12C: Summary Thévenin’s and Norton’s Equivalent Circuit Thévenin’s Theorem ◦ Example Problem 2 Norton’s Theorem Home Work problem
13.
Basic Electric Circuits
– © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 13 References Ref 1 Ref 2