DC NETWORK THEOREMS – PART – 06 – TELLEGEN’S THEOREM

BERNARD D.H. TELLEGEN a Dutch electrical engineering and inventor of the pentode and the gyrator. He is also known for a theorem in circuit theory, viz. Tellegen’s theorem

Born on 24^th June 1900 in Netherland, he obtained his master’s degree in electrical engineering from Delft University.

In 1923 he joined the Philips Physics Laboratory.

In 1926 he invented the pentode vacuum tube.

Tellegen was an adjunct professor of circuit theory at the University of Delft from 1946 to 1966.

The gyrator was invented by him around 1948.

The gyrator was useful to simulate the effect of an inductor without using a coil.

He held 41 US patents.

In 1970 the University of Delft conferred him the doctor honoris causa degree.

He won the IEEE Edison Medal in 1973 for a creative career of significant achievement in electrical circuit theory, including the gyrator.

Died on 30^th August 1990. He lived for 90 years in this planet and even today he lives in all electrical and electronics textbooks in the form of his theorem.

TELLEGEN’S THEOREM

This theorem is based on Kirchhoff’s laws, but not the type of circuit element.

This theorem states that in an arbitrary lumped network, the algebraic sum of the powers in all branches at any instant is zero.

                                                [OR]

Algebraic sum of the powers delivered by all the sources is equal to the algebraic sum of the powers absorbed by all elements.

[All branch currents and voltages in that network must satisfy Kirchhoff’s laws]

LIMITATION

This theorem can be used for any lumped network which may be linear or nonlinear, passive or active, time-varying or time-invariant.

LUMPED NETWORK

A lumped network is usually a simplification of a distributed network, such as a transmission line. A transmission line has built in resistance, inductance and capacitance, for every tiny fraction of its length]