Norton's theorem

In the theory of linear electrical networks Norton theorem, named after Edward Lawry Norton and as Mayer Norton theorem states indicates that every possible combination of voltage sources, current sources and resistors with respect to two terminals electrically equivalent to a parallel circuit of a power source and a resistance R is. This equivalent circuit is called Norton or equivalent in German-speaking back-up power source.

Calculation of the Norton equivalent

Norton equivalent consisting of a resistor and a current source RNO INo. To determine the two unknowns RNO and INo, you need two equations. These equations can be created in various ways. Most often one uses, however, the following:

• The output current IAB determine at short circuit. This short circuit current is the Norton equivalent current INo.

To determine the Norton equivalent resistance RNO, there are various methods:

• Just replace all voltage sources by short circuits and cancels all power sources (ie, they are replaced by open circuits). Then we can calculate the equivalent resistance. This is equal to the Norton equivalent resistance.
• If you know the open circuit voltage UAB, you use Ohm's Law to determine RNO:

The proof of Norton 's theorem is based on the principle of superposition.

Conversion between Norton and Thevenin equivalent

A Norton equivalent can be converted to a Thévenin equivalent using the following equations:

Question on understanding

Question: "In two black casket a current source with a parallel resistor and a voltage source with series resistance were hidden, so that the above equations are satisfied. Can you determine from the outside, in which black casket is the Norton circuit? "

Answer: Yes! The little box with the Norton circuit is warmer because it removes permanently the power. The Thevenin circuit consumes no power, and is not, therefore, hotter. The equivalence is thus only with respect to the output terminals. Burdened to both Kistchen but with a short circuit, so does the little box with the Thévenin circuit performance, since now current flows through the Thevenin resistance. The Norton circuit, however, does not absorb any more power, because the Norton resistance is short-circuited. The power circuit receives the Norton the open case is the same size, as the power is absorbed by the Thevenin circuit in the short-circuited case.

This question proved to great lengths to clarify the limits of the theory of Norton and Thevenin equivalent in courses.

Extension for AC

The Norton 's theorem can be generalized to harmonic alternating current systems by impedances instead of ohmic resistors are used.

History

Norton 's theorem is an extension of the Thévenin 's theorem. It was discovered in 1926 simultaneously and independently by Hans Ferdinand Mayer ( 1895-1980 ) ( Siemens & Halske ) and Edward Lawry Norton ( 1898-1983 ) ( at Bell Labs). Mayer published his discovery in the journal telegraph and telephone technology, Norton published his discovery in an internal work report of Bell Labs. This theorem is used as a simplification of technology in the circuit analysis.