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

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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.

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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.

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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.

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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.

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

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

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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.

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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.

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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. R th is then that equivalent resistance and V th is just the voltage that you found.

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

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

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

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Norton Example Find the Norton Equiv. Circuit

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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.

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

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Maximum Power Transfer When does the load receive maximum power? – see notes When R L = R th

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

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