Tellegen's Theorem

B.D.H. Tellegen

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 

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 measuring 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?

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.

A simple circuit

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

Throughout the calculation, signs 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 the electrical network using Tellegen’s Theorem. We just need to find the values of branch voltages and current through the element. Using the appropriate sign of powers, this theorem can be verified and the 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.

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