DC NETWORK THEOREMS – PART – 05 MILLMAN’S THEOREM

Millman’s theorem is a combination of Thevenin’s and Norton’s theorems.

Jacob Millman Born on 1911 in Ukraine, was a professor of Electrical Engineering Department at Columbia University. Millman received his Doctorate from MIT in 1935.

He joined Columbia University in 1951, and retired in 1975.

From 1941 to 1987, Millman wrote eight textbooks on electronics.

He received the IEEE Education Medal in 1970.

He left this planet on May 22, 1991 in Florida, USA.

Millman's Theorem (otherwise known as the Parallel generator theorem) is named after him.

He lived for 80 years in this planet and even today he lives in the form of his theorem in all electrical and electronics textbooks.

MILLMAN’S THEOREM

A number of current sources in parallel may be replaced by a single current source whose current strength is equivalent to algebraic sum of individual source currents and source resistance is equal to the parallel combination of individual source resistances.

PARALLEL CURRENT SOURCES

The current source that are directly connected in parallel can be replaced by a single equivalent current source.

PARALLEL VOLTAGE SOURCES

The voltage source that are directly connected in parallel can be replaced by a single equivalent voltage source.

VOLTAGE SOURCES AND CURRENT SOURCES IN PARALLEL

Each parallel-connected voltage source is converted to an equivalent current source and a set of parallel-connected current sources can be replaced into a single equivalent current source.

Each parallel-connected current source is converted to an equivalent voltage source and a set of parallel connected voltage sources can be replaced by an equivalent voltage source.

LIMITATION

This theorem is applicable only when the sources are connected directly in parallel without any resistance element between the sources.

APPLICATIONS

1. This theorem helps to combine a number of current sources operating in parallel and has the advantage of being easier to apply to some networks than mesh analysis, nodal analysis or superposition.

2. A voltage source can be converted into a current source. Thus it can also be applied to a circuit when both current and voltage sources are present.

3. This theorem is also applicable if the circuit has a mixture of parallel voltage and current sources.