B.D.H.
Tellegen
Image Source: edubilla.com
Image Source: edubilla.com
Tellegen’s Theorem is the very first theorem that initiates
the journey of EEE. In 1952, Dutch engineer B.D.H. Tellegen proposed this
theorem which goes something like this,
‘‘In
any electrical network, the summation of instantaneous
power in all the branches is equal to zero provided that the network
power in all the branches is equal to zero provided that the network
satisfies Kirchhoff’s Laws’’
Eventually this theorem has become an important circuit analysis
tool. But what is so special in this theorem? It simply looks like another form
of energy conservation law, isn’t it?
Power Is Everything
Engineers throughout the world are much more concerned about power. Why? Let us take a device (electrical or mechanical) for example. You will see we never care about the voltage or current specifications of the device while buying. Rather we want to know the power rating or how efficient the device is. So power is an important term to define the sustainability of a system and it requires to measure power associated with each element of an electrical system.
Engineers throughout the world are much more concerned about power. Why? Let us take a device (electrical or mechanical) for example. You will see we never care about the voltage or current specifications of the device while buying. Rather we want to know the power rating or how efficient the device is. So power is an important term to define the sustainability of a system and it requires to measure power associated with each element of an electrical system.
Absorbed
or Supplied?
The theorem clearly says that absorbed power has to be equal to supplied power. Here we encounter some facts;
· How to find out which element is supplying power and which one is absorbing? Is it always the source (voltage/current) that supplies power?
· How to differentiate between the absorbed power and the supplied power?
The theorem clearly says that absorbed power has to be equal to supplied power. Here we encounter some facts;
· How to find out which element is supplying power and which one is absorbing? Is it always the source (voltage/current) that supplies power?
· How to differentiate between the absorbed power and the supplied power?
Sign Convention
It’s a general convention that current comes out from the positive terminal of active components (battery and discharging capacitor) , flows through the passive component and flows back into the negative terminal of the active component.
It’s a general convention that current comes out from the positive terminal of active components (battery and discharging capacitor) , flows through the passive component and flows back into the negative terminal of the active component.
A simple
circuit
Image credit: Engineer’s Articles
Image credit: Engineer’s Articles
Following this convention we have,
Active Sign Convention states
that if current comes out from the positive terminal of an active
element, power is being supplied to the network and it has a negative
sign.
Passive Sign Convention states
that if current enters into the positive terminal of a passive
element, power is being absorbed by that element and it has a positive
sign.
Sign
Convention
Image Source: Basic Engineering Circuit Analysis by J.D. Irwin
Image Source: Basic Engineering Circuit Analysis by J.D. Irwin
Throughout the calculation, sign of power will vary
according to the current direction and the sign of the component’s terminal.
But the question is, does a passive element (i.e. resistor) have specified
positive or negative terminals? Think it
yourself.
Network Solving
It is very simple to solve electrical network using Tellegen’s Theorem. We just need to find the values of branch voltages and current through the element. Using appropriate sign of powers, this theorem can be verified and circuit can be solved for unknown parameters.
It is very simple to solve electrical network using Tellegen’s Theorem. We just need to find the values of branch voltages and current through the element. Using appropriate sign of powers, this theorem can be verified and circuit can be solved for unknown parameters.
Another question remains; why is this theorem so important?
Apart from solving electrical networks, Tellegen’s theorem is used for filter
designing in digital signal processing; in areas of biological & chemical
processes; in determining the stability of complex systems.
