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 24th 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 30th 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]
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.
He
was a German Jewish engineer and physicist worked in Russia. Brother of Carl
Gustav Jacob Jacobi was a German mathematician, who made fundamental
contributions in elliptic functions, dynamics and differential equations.
He
was born on 21st September 1801 in the Kingdom of Prussia.
In
1834 he began to study magnetic motors.
In
1835 he moved to Dorpat to lecture at Dorpat University.
He
moved to Saint Petersburg in 1837 to take up research in the usage of
electromagnetic forces for moving machines for Russian Academy of Sciences.
He
investigated the power of an electromagnet in motors and generators. While
studying the transfer of power from a battery to an electric motor, he deduced
the maximum power theorem.
Jacobi
tested motors output by determining the amount of zinc consumed by the battery.
Jacobi constructed a 28 foot electric motor boat powered by battery cells in
1839. The boat carried 14 passengers on Neva River against the current. The
boat fared at the speed of three miles per hour.
He
left this planet on 10th March-1874.
He
lived for 72 years in this planet and even today he lives in the form of his
theorem in all electrical electronics text books.
Maximum
power transfer theorem is useful to determine the value of load resistance for
which there would be maximum amount of power transfer from source to load.
MAXIMUM
POWER TRANSFER THEOREM
A
network delivers maximum power to a load when the load resistance is equal to
the output resistance of the network as seen from the load terminals.
[OR]
A
resistive load connected to a DC network receives maximum power when the load
resistance is equal to the internal resistance of the source network as seen
from load terminals.
APPLICATIONS
1.
In Electronics and telecommunication circuits, resistance matching is
important. These circuits have high output resistance and it is desirable to
adjust the load resistance to get maximum output power irrespective of the
efficiency value.
2.
In power systems, batteries and other sources resistance is so low that the
device would be overloaded if load resistance is made so low as to match the
source resistance. Power system is desirable to keep the losses low and
efficiency high.
In
the circuit given in figure, find the value of R and the current flowing
through it, if current through branch OA is zero.
PROBLEM
– 02
In
the circuit shown in figure, use mesh analysis to find out the power delivered
to the 4Ω resistor. To what voltage should the 100 V battery should be changed
so that no power is delivered to the 4Ω resistor?
PROBLEM
– 03
In
the circuit shown in figure, find the voltage across A & B.
PROBLEM
– 04
Calculate
the current supplied by the batteries and the potential difference between A
& B.
PROBLEM
– 05
In
the circuit shown in figure, find the current flowing through all the branches.
A
Bell labs engineer and scientist famous for developing the concept of the
Norton equivalent circuit was born on July 29, 1898 in USA.
He
served as a radio operator in the US Navy between 1917 and 1919 and he received
his electrical engineering degree from M.I.T in 1922 and his master’s degree
from Columbia University in 1925.
He
remained with Bell Labs throughout his career, retiring in 1963. He wrote three
technical papers, obtained 18 patents and he wrote 92 technical reports during
his career.
Norton
was one of the legendary figure in network theory, who brought out a prodigious
number of designs armed only with a slide rule and his intuition.
He
applied his deep knowledge of circuit analysis in many fields, and after World
War II, he worked on Nike missile guidance systems.
He
died on January 28, 1983 at the King James Nursing Home in Chatham, New Jersey.
He
lived for 85 years in this planet and even today he lives in the form of his
theorem in basic electrical and electronics textbooks.
Norton's Theorem is the converse of Thevenin's theorem. It consists of an equivalent current source in parallel to the internal resistance of the network. NORTON’S
THEOREM
Any
two linear active bilateral networks can be replaced by an equivalent current
source in parallel to a resistance. The current source being the short
circuited current through the load terminals and the resistance being the
internal resistance of the source network looking through the open circuited
load terminals.
[OR]
Any
two terminal linear network containing independent voltage and current sources,
may be replaced by a constant current source IN in parallel with a resistance
RN where IN is the current flowing through a short circuit placed across the
terminals and RN is the equivalent resistance of the network as seen from the
two terminals with all sources replaced by their internal resistances.
