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THEVENIN’S THEOREM

Learn how Thevenin’s and Norton’s Theorems simplify complex circuits, stating that any linear circuit is equivalent to a single source with resistance. Explore the procedure for finding Thevenin and Norton equivalent circuits.

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THEVENIN’S THEOREM

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  1. THEVENIN’S THEOREM • Used to help simplify complex circuits • States that any linear circuit is equivalent to a single source in series with asingle resistance • No matter how complex the circuit and no matter how many voltage and current sources it contains, it is equivalent to a real voltage source • We have to replace all of the original circuit lying on one side or the other of a pair of terminals by its Thevenin equivalent circuit • The Thevenin equivalent circuit consists of the Thevenin equivalent voltage, ETH, in series with the Thevenin equivalent resistance, RTH • The terminals of this ETH and RTH combination coincide with the terminals of the portion of the circuit of the original circuit that was replaced Thevenin and Norton Equivalent Circuits

  2. THEVENIN EQUIVALENT CIRCUIT LAYOUTS Thevenin and Norton Equivalent Circuits

  3. PROCEDURE • Open-circuit the terminals with respect to which the Thevenin circuit is desired, i.e. remove all of the circuitry that will not be replaced by a Thevenin equivalent, leaving the terminals where it was connected open-circuited • The Thevenin equivalent resistance, RTH, is the total resistance at the open-circuited terminals when all voltage sources are replaced by short circuits and all current sources are replaced by open circuits • The Thevenin equivalent voltage, ETH, is the voltage across the open circuited terminals. We can use superposition to calculate this • Replace the original circuitry by its Thevenin equivalent circuit with the Thevenin terminals occupying the same position as the original terminals. The external circuitry that was removed in step 1 may now be reconnected. Be certain that the polarity of ETH is such that it produces current in the external circuitry in the same direction as the original circuit produced it Thevenin and Norton Equivalent Circuits

  4. NORTON’S THEOREM • States that any linear circuit is equivalent to a real current source at a selected set of terminals • Similar to Thevenin’s theorem, except that the voltage source is replaced by a current source • First find the Thevenin equivalent circuit, then convert it to an equivalent current source • The Norton equivalent resistanceRN = RTH • The Norton equivalent currentIN = ETH/RTH • IN is the current that flows in the short circuit connected across the terminals where the Norton equivalent circuit is desired Thevenin and Norton Equivalent Circuits

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