Skip to main content
Engineering LibreTexts

4.5: Norton's Theorem

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    Norton's theorem is credited to Edward Lawry Norton. In a nutshell, Norton's theorem is the current source version of Thévenin's theorem. That is, a single port DC network can be reduced to a single current source, \(I_N\), with parallel internal resistance, \(R_N\). Indeed, once you understand one of them, the other is but a minor extension, so we will not need to spend a great deal of time here once the basics are outlined sufficiently.

    The process of determining the Norton equivalent current and resistance is very similar to that employed for the Thévenin equivalent. First, the Norton resistance is found the same way as is the Thévenin resistance: replace all sources with their ideal internal resistance and then perform appropriate series and parallel combinations to reduce this to a single resistance value. Consequently, the Norton and Thévenin resistance values are identical, \(R_N = R_{th}\). Second, instead of finding the open circuit output voltage, we find the short circuit output current. This is the Norton current. Instead of thinking in terms of a voltmeter at the opened load, we think in terms of connecting a shorting ammeter across the load. Either way, we're looking for the maximum value that can be obtained.

    Perhaps the most useful thing to remember here is that if we can create a Thévenin equivalent for a network then it must be possible to create a Norton equivalent. Indeed, once a Thévenin equivalent is found, a source conversion can be performed on it to yield the Norton equivalent! The opposite, of course, is also true.

    4.5: Norton's Theorem is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by James M. Fiore.

    • Was this article helpful?