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Superposition, Thevenin / Norton Equivalents, Maximum Power Transfer

Superposition, Thevenin / Norton Equivalents, Maximum Power Transfer. Circuits 1 Fall 2005 Harding University Jonathan White. Outline – Ch. 4. Superposition

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Superposition, Thevenin / Norton Equivalents, Maximum Power Transfer

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  1. Superposition, Thevenin / Norton Equivalents, Maximum Power Transfer Circuits 1 Fall 2005 Harding University Jonathan White

  2. Outline – Ch. 4 • Superposition • Method of analyzing a circuit by turning off all sources but 1 and then finding their contributions individually. End by summing up all the contributions. • Thevenin Equivalent Circuits • A circuit at a given 2 terminals can be replaced by a voltage source with a resistor in series. • Norton Equivalent Circuits • A circuit at a given 2 terminals can also be replaced with a current source and a parallel resistor. • Maximum Power Transfer • When you have a load, when does it receive the maximum power? We’ve already answered this in lab.

  3. Superposition • Resistors are linear elements, meaning that the output is linearly related to the input. • Voltages around a loop can simply be added up – no non linear math is required. • Instead of analyzing circuits like we did in Ch. 2 and Ch. 3, we can analyze them using Superposition. • Definition: The voltage across (or current through) a resistor is the algebraic sum of all the contributions due to each source acting alone. • So, another way to analyze a circuit is to find the contribution of each source individually and them add them up at the end to get the total.

  4. Superposition 2 • We only consider 1 independent source at a time when we use superposition. This means that we: • Replace voltage sources with a wire (0 V). • Replace current sources with an open circuit (no current can flow). • Dependent sources are left intact since they are controlled by circuit variables.

  5. Superposition 3 • To solve a circuit using superposition: • Turn off all independent sources but 1. Use the techniques of Ch. 2 and Ch. 3 to solve for the desired voltage or current. • Repeat for each independent source. • Find the total voltage or contribution by taking the algebraic sum.

  6. Superposition – Exp. 1 Find the voltage over the 2 Ohm resistor using superposition.

  7. Superposition Exp. 2 Find the voltage over the 5 ohm resistor using superposition. + V -

  8. Equivalent Circuits • A model of the real thing. • Used to capture only the necessary details of a potentially complex circuit. • Examples of various models: • Battery • OSI network layer • Function calls • You (as a user), don’t really care how the function operates, just that it does.

  9. Thevenin Equivalent Circuits • Consists of a voltage source and a resistor in series. • Used to provide a “black box” picture from the view of a load. The load, looking back in to the circuit, only wants to know the voltage and current that is provided to it.

  10. Finding a TEC • Steps: • Find the open circuit voltage – disconnect the load from the circuit and calculate the voltage looking in to the circuit. • Find the open circuit equivalent resistance looking back in to the circuit • Remove all independent current sources • Replace all independent voltage sources with wires. • Rth is then that equivalent resistance and Vth is just the voltage that you found.

  11. TEC Example - 1 Find the Thevenin Equivalent Circuit: a b

  12. TEC Example - 2 Find the Thevenin Equivalent Circuit: a b

  13. Norton Equivalent Circuits • Consists of a current source with a resistor in parallel. • Electrically equivalent to the Thevenin model • Rth is the same • In is equal to Vth / Rth • When finding Norton equivalents, I often recommend just finding the Thevenin equivalent and then just switch at the end.

  14. Norton Example Find the Norton Equiv. Circuit

  15. Source Transformations • Like the Wye-Delta transformation, we can transform a voltage source with a resistor in series into a current source with a resistor in parallel without changing the rest of the circuit and vice versa. • Like superposition, however, this is often more work than just using mesh currents to solve the problem.

  16. Source Transformation Exp. Find i0 and the voltage over the 3 ohm resistor using source transformations. i0 + V -

  17. Maximum Power Transfer • When does the load receive maximum power? – see notes • When RL = Rth

  18. Maximum Power Example Find the RL that achieves maximum power transfer. Find the power it absorbs. Note: You must find Vth to calculate the power.

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