Millman's theorem

The set of Millman is within the electrical circuitry a in network analysis -applied practical method to the sum voltage of several parallel -connected voltage and current sources to determine in a linear network. The procedure is based on the general " Kirchhoff rules ". It is named after Jacob Millman , who wrote several well-known textbooks on this subject in the English-speaking world.

description

Circuit diagram for Millman's Theorem

If several voltage and current sources are connected in parallel, as shown in the sketch opposite for two voltage sources and with the respective internal resistances and and a current source with internal resistance , the resulting voltage results from Millman's theorem: ${\displaystyle U_{1}}$ ${\displaystyle U_{2}}$ ${\displaystyle R_{1}}$ ${\displaystyle R_{2}}$ ${\displaystyle I_{1}}$ ${\displaystyle R_{3}}$ ${\displaystyle U_{\text{s}}}$

${\displaystyle U_{\text{s}}={\frac {{\frac {U_{1}}{R_{1}}}+{\frac {U_{2}}{R_{2}}}+I_{1}}{{\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+{\frac {1}{R_{3}}}}}}$

This means that the resulting total voltage can be expressed directly as the sum of the individual partial currents divided by the sum of the conductance values ​​of the internal resistances of the individual sources. In general terms with voltage sources connected in parallel and current sources connected in parallel, Millman's theorem is: ${\displaystyle m}$ ${\displaystyle n}$

${\displaystyle U_{s}={\frac {\sum _{i=1}^{m}{\frac {U_{i}}{R_{i}}}+\sum _{i=1}^{n}I_{i}}{\sum _{i=1}^{m}{\frac {1}{R_{i}}}+\sum _{i=1}^{n}{\frac {1}{R_{i}}}}}}$

Web links

• Millman's theorem. Retrieved October 9, 2014 . 
• Network Analysis X, Millman's Theorem Analysis. Retrieved October 9, 2014 . 

literature

• DC Kulshreshtha: Basic Electrical Engineering . Tata McGraw-Hill Education, 2009, ISBN 978-0-07-014100-1 , pp. 116 .
• Mohammed Arshad: Network Analysis and Synthesis . Firewall Media, 2006, ISBN 978-81-7008-959-9 , pp. 201-206 .
• Jacob Millman, Herbert Taub: Pulse and Digital Circuits . McGraw-Hill, 1956 ( online ).

Individual evidence

1. ^ Samuel Derman: Millman and Taub's Pulse and Digital Circuits - A Pioneer Text in Its Field . Volume E-27, No. 4 . IEEE Transactions on Education, 1984 ( Online [PDF]).