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Encyclopedia > Norton's theorem

Norton's theorem for electrical networks states that any collection of voltage sources and resistors with two terminals is electrically equivalent to an ideal current source, I, in parallel with a single resistor, R. For single-frequency AC systems the theorem can also be applied to general impedances, not just resistors. The Norton equivalent is used to represent any network of linear sources and impedances, at a given frequency. The circuit consists of an ideal current source in parallel with an ideal impedance (or resistor for non-reactive circuits). An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, and switches. ... now. ... Resistor symbols (US and Japan) Resistor symbols (Europe, IEC) A pack of resistors A resistor is a two-terminal electrical or electronic component that resists an electric current by producing a voltage drop between its terminals in accordance with Ohms law. ... An ideal current source, I, driving a resistor, R, and creating a voltage V A current source is an electrical or electronic device that delivers or absorbs electric current. ... In electrical engineering, Impedance is a measure of opposition to a sinusoidal electric current. ...


Norton's theorem is an extension of Thévenin's theorem and was introduced in 1926 separately by two people: Hause-Siemens 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. In electrical circuit theory, Thévenins theorem for electrical networks states that any combination of voltage sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. For single frequency AC systems the theorem can also be applied to... 1926 (MCMXXVI) was a common year starting on Friday (link will take you to calendar). ... 1895 (MDCCCXCV) was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar (or a common year starting on Thursday of the 12-day-slower Julian calendar). ... 1980 (MCMLXXX) was a leap year starting on Tuesday. ... Bell Laboratories (also known as Bell Labs and formerly known as AT&T Bell Laboratories and Bell Telephone Laboratories) was the main research and development arm of the United States Bell System. ... Edward Lawry Norton (1898 - 1983) was an accomplished Bell Labs engineer famous for developing the concept of the Norton equivalent circuit. ... 1898 (MDCCCXCVIII) was a common year starting on Saturday (see link for calendar) of the Gregorian calendar (or a common year starting on Monday of the 12-day-slower Julian calendar). ... 1983 (MCMLXXXIII) was a common year starting on Saturday of the Gregorian calendar. ...

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

Contents

Image File history File links Norton_equivelant. ... This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...

Calculation of a Norton equivalent circuit

To calculate the equivalent circuit:

  1. Calculate the output current, IAB, when a short circuit is the load (meaning 0 resistance between A and B). This is INo.
  2. Calculate the output voltage, VAB, 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 INo, in parallel with a resistance RNo.

Case 2 can also be thought of like this: For alternate meanings see Short circuit (disambiguation) A short circuit (sometimes known as simply a short) is a fault whereby electricity moves through a circuit in an unintended path, usually due to a connection forming where none was expected. ... Open circuit can mean:- In electronics, where there is nothing connected to a load and no current can flow. ...

  • 2a. Now replace independent voltage sources with short circuits and independent current sources with open circuits.
  • 2b. For circuits without dependent sources RNo 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 follow the following equations: Image File history File links Thevenin_to_Norton. ...

R_{Th} = R_{No} !
V_{Th} = I_{No} R_{No} !

Example of a Norton equivalent circuit

Step 0: The original circuit
Step 0: The original circuit
Step 1: Calculating the equivalent output current
Step 1: Calculating the equivalent output current
Step 2: Calculating the equivalent resistance
Step 2: Calculating the equivalent resistance
Step 3: The equivalent circuit
Step 3: The equivalent circuit

In the example, the total current Itotal is given by: Wikipedia does not have an article with this exact name. ... Image File history File links Norton_step_2. ... Wikipedia does not have an article with this exact name. ... Image File history File links Norton_step_4. ...

I_mathrm{total} = {15 mathrm{V} over 2,mathrm{k}Omega + 1,mathrm{k}Omega | (1,mathrm{k}Omega + 1,mathrm{k}Omega)} = 5.625 mathrm{mA}

The current through the load is then:

I = {1,mathrm{k}Omega + 1,mathrm{k}Omega over (1,mathrm{k}Omega + 1,mathrm{k}Omega + 1,mathrm{k}Omega)} cdot I_mathrm{total}
= 2/3 cdot 5.625 mathrm{mA} = 3.75 mathrm{mA}

And the equivalent resistance looking back into the circuit is:

R = 1,mathrm{k}Omega + 2,mathrm{k}Omega | (1,mathrm{k}Omega + 1,mathrm{k}Omega) = 2,mathrm{k}Omega

So the equivalent circuit is a 3.75 mA current source in parallel with a 2 kΩ resistor.


In popular culture

While one might doubt that there is any popular culture around electrical theorems, both Norton's theorem and Thévenin's theorem feature in the 4th and 10th of May 2006 Doonesbury comic strip panels [1], [2]. Doonesbury was featured on the cover of the Feb. ...


See also

  • Thévenin's theorem

In electrical circuit theory, Thévenins theorem for electrical networks states that any combination of voltage sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. For single frequency AC systems the theorem can also be applied to...

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