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Norton's Theorem




Norton's theorem is an extension of researcher Hans Ferdinand Mayer ( 1895 - 1980 ) and Bell Labs engineer Edward Lawry Norton ( 1898 - 1983 ). Mayer was the only one of the two who actually published on this topic, but Norton made known his finding through an internal technical report at Bell Labs.

containing only voltage sources, current sources, and resistors can be converted to a Norton equivalent circuit.]]


CALCULATION OF A NORTON EQUIVALENT CIRCUIT


To calculate the equivalent circuit:

# Calculate the output current, ''I''AB, when a Short Circuit is the Load (meaning 0 resistance between A and B). This is INo.
# Calculate the output voltage, ''V''AB, when in Open Circuit condition (no load resistor - meaning infinite resistance). RNo equals this VAB divided by INo.
  • The equivalent circuit is a current source with current ''I''No, in parallel with a resistance ''R''No.


Case 2 can also be thought of like this:
  • 2a. Now replace independent voltage sources with short circuits and independent current sources with open circuits.

  • 2b. For circuits without dependent sources ''R''No is the total resistance with the independent sources removed.---


  • Note: A more general method for determining the Norton Impedance is to connect a current source at the output terminals of the circuit with a value of 1 Ampere and calculate the voltage at its terminals; this voltage is equal to the impedance of the circuit. This method must be used if the circuit contains dependent sources. This method is not shown below in the diagrams.



CONVERSION TO A THéVENIN EQUIVALENT


To convert to a Thévenin equivalent circuit, one can use the following equations:
:R_{Th} = R_{No} \!
:V_{Th} = I_{No} R_{No} \!


EXAMPLE OF A NORTON EQUIVALENT CIRCUIT


In the example, the total current ''I''total is given by:

: