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
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
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
Note that the final Thevenin equivalent circuit is reminiscent of Georg Ohm's
voltage source, with the resistance applied in series with the source of
electromotive force. We will visit this in a moment after discussing output
impedance.
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
Equivalent Circuit
Output Impedance
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.
Note again that the battery's internal resistance is applied in series with
the voltage source. Likewise, the output impedance of the microphone is applied
in series with the AC voltage source. This clarifies a common mistake made by
new students. Let's say you have a 10-volt battery with a known internal
resistance of one ohm. If you apply 10 volts across one ohm, according to Ohm's
Law, you should get 10 amperes of current. Why doesn't the battery discharge
through its own internal resistance? The internal resistance must be applied in series
with the source of electromotive force. Therefore, there is no path for current unless the
battery terminals are connected together. Whenever you have a source of
electromotive force, any inherent impedance in that source must be applied in
series with the source. Some influencers have tried to invalidate Ohm's Law and
Kirchhoff's Voltage Law not understanding this principle. Don't fall into that
trap.
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.
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
Battery
Equivalent Circuit
