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# Thévénin Equivalent Circuit

Original Circuit Prior to the Thévénin Equivalent

Thévénin Equivalent

The Thévénin voltage is the open circuit voltage at the output. calculation is straightforward node or loop circuit analysis. Using loop analysis:

Voc:  [8 * I1] + [(8+2+6) * I2] - [6 * I3] = 1 A

I2 = ½A ==> Voc = ½A * 6

Ω= 3 V = Vth

Calculate the Thévénin resistance from the open circuit voltage and the short circuit current

(set RL = 0 and solve for I3) using Ohm's Law.

Rth = Voc / Isc = 3 V / [(4/9) A] = 27 / 4 Ω = Rth

The Thévénin Equivalent of a circuit consists of a Thévénin voltage source in series with a Thévénin resistor and is valid for any load. In AC circuits a Thévénin equivalent circuit is valid for a single frequency.

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Thévénin's Theorem

Thévénin's Theorem is a fundamental concept in electrical engineering that simplifies complex linear electrical networks into simpler, equivalent circuits. It's named after the French engineer Léon Charles Thévénin, who formulated the theorem. Thévénin's Theorem is particularly useful for analyzing and solving circuits with multiple components and sources.

The theorem states that any linear electrical network with multiple sources and resistive elements can be replaced by a single voltage source (Thévénin voltage) in series with a single resistor (Thévénin resistance). This simplified equivalent circuit is called the Thévénin equivalent circuit.

Here are the key components of the Thévénin equivalent circuit:

• Thévénin Voltage (Vth): The Thévénin voltage (Vth) is the open-circuit voltage measured across the two terminals of interest in the original circuit after all the independent voltage sources have been replaced with short circuits and all the independent current sources have been replaced with open circuits. In other words, Vth is the voltage you would measure between the two terminals when no load is connected.
• Thévénin Resistance (Rth): The Thévénin resistance (Rth) is the equivalent resistance measured across the same two terminals in the original circuit, again with all independent sources turned off (replaced with their internal resistances, if any). To calculate Rth, you remove the sources and determine the equivalent resistance seen from the terminals.

The Thévénin equivalent circuit consists of a single voltage source Vth in series with a single resistor Rth. This equivalent circuit can accurately represent the behavior of the original circuit as seen from the terminals of interest, making it easier to analyze and solve complex circuits. It is especially valuable when you want to determine how a particular load will affect the voltage and current at the terminals without delving into the entire circuit.

To find the Thévénin voltage and resistance, you typically follow these steps:

• Turn off all independent voltage sources (replace with short circuits) and all independent current sources (replace with open circuits).
• Calculate the voltage across the two terminals of interest (Vth) in the simplified circuit.
• Calculate the equivalent resistance (Rth) between the two terminals.
• Construct the Thévénin equivalent circuit with Vth and Rth in series.

Once you have the Thévénin equivalent circuit, you can use it to analyze the behavior of the original circuit when connected to various loads or to simplify circuit analysis for complex networks.

Posted September 8, 2023
(updated from original post on 6/30/2001)