Thevenin's Theorem

Thevenin's Theorem states that any circuit, no matter how complex, acts as if it were a single voltage source and a single impedance in series with that voltage source (for now, an impedance is a resistor, it impedes the flow of electrical current). The Thevenin equivalent circuit can be determined by dividing the open circuit voltage by the closed circuit current. This can be illustrated by looking at the example circuit in Series-Parallel Circuits above. By choosing two points on the circuit (denoted by the circles in the diagrams below) you can determine the Thevenin equivalent circuit as seen at those points, by measuring the open circuit voltage and the closed circuit current at those points.

As already determined above, there is a 30 volt drop across the 10 ohm resistor, leaving 30 volts across the 15 ohm and 30 ohm resistors. Open Circuit voltage
Open circuit voltage
Placing a current meter across the 15 ohm and 30 ohm resistors creates a short circuit (a current meter has nearly 0 ohms). This eliminates those two resistors from the circuit,[1] placing the entire 60 volts from the battery across the 10 ohm resistor. The result is a current of 6 amps through the circuit. Short Circuit Current
Short circuit current
Therefore, looking at the points shown, with an open circuit voltage of 30 volts and a short circuit current of 6 amperes, the circuit acts exactly the same as a single 5 ohm resistor in series with a 30 volt battery. Thevenin Equivalent Circuit
Thevenin equivalent circuit

Output impedance

Any component or circuit has a Thevenin equivalent circuit. Particularly, any component or circuit that produces voltage, regardless of the actual complexity, will act as if it were a single voltage source in series with a single resistor (as per Thevenin's theorem). This is true for batteries, dynamic microphones (which are essentially sound-powered AC generators), radio-receiving antennas or anything else that converts non-electrical energy to electrical energy. Likewise, any circuit that delivers a voltage or current to another circuit can be reduced to a Thevenin equivalent circuit. The Thevenin equivalent resistance (properly called Thevenin equivalent impedance) has different names for different situations. For example, the Thevenin equivalent impedance of a battery is called its "internal resistance". However, for most circuits and components the Thevenin equivalent impedance is called "output impedance." [2]

                          Internal Resistance
Battery and Thevenin Equivalent
Battery                             Equivalent Circuit
                         Output Impedance
Microphone and Thevenin Equivalent
Microphone                      Equivalent Circuit

Thevenin equivalent circuits for a battery and a microphone. Each consists of a voltage source with a resistor in series. The voltage source for the battery is DC and is symbolized by a battery where the voltage source for the microphone is symbolized by an AC generator.

Input impedance

An electronic circuit consists of electronic components or subcircuits connected together. A typical arrangement is a public address system. Here you have a microphone that connects to a preamplifier, which connects to a power amplifier, which connects to a loudspeaker. Energy is passed from one stage to the next until the ultimate function of the circuit is performed.

At the beginning of the public address system, the microphone connects to a preamplifier. The input of the preamplifier exhibits some opposition to electrical current flow (impedance) as does any circuit. The impedance seen at the input of a circuit is called input impedance. Just as the output impedance of the microphone can be represented by a resistor, the input impedance of the preamplifier can also be represented by a resistor. Therefore, the part of the system that consists of the microphone and the input of the preamplifier can be represented with the Thevenin equivalent circuit of the microphone connected to a resistor that represents the input impedance of the amplifier.

Complete Equivalent Circuit
Equivalent circuits showing a microphone connected to the input of a preamplifier. The entire preamplifier is represented by a resistor with a value equal to the preamplifier's input impedance.

No matter how complex the actual circuits may be, they can be represented by the simple series circuit above.

Thevenin's Theorem, Output Impedance and Input Impedance
1When resistors are in parallel the total resistance will be lower than the lowest individual resistor. The current meter has zero ohms. Placing this in parallel with the other two resistors gives us 30 ohms, 15 ohms and 0 ohms in parallel. The total resistance must be lower than the lowest resistor, which is 0 ohms. Of course you can't get a resistance lower than zero ohms so the total resistance in the parallel part of the circuit is zero ohms.  With the 15 ohm and 30 ohm resistors shorted we end up with a total of 10 ohms.
2In AC circuits the Thevenin impedance is actually more complex than a resistor. AC impedance will be discussed in AC circuits.