Lumped and Distributed elements

Lumped elements

In electrical circuits if the physical size of the element is negligibly small when compared with wave length of electromagnetic wave propagation then the element is modelled as lumped elements. The lumped element can be represented with its parameters like resistance or inductance with its total value at a place.

Examples: Resistors, inductors, capacitors.

Distributed elements

If the physical size of the element is comparable with wavelength of electromagnetic wave propagation then such an element is modelled as distributed element. In these elements resistance, inductance or capacitance are distributed and cannot be separated and modelled at a single point. These are distributed throughout the circuit.

Example: Long transmission lines-in which the resistance, capacitance and inductance are distributed throughout the line. Elements in high frequency electronic circuits.

Identifying a lumped element or distributed element

Energy transfer in electrical circuits takes place in the form of electromagnetic wave propagation. The velocity of electromagnetic wave is equal to the speed of light which is 3x10⁸ m/s.

The velocity is given by ν=λf

Where ν=velocity=3x10⁸ m/s

             λ=wave length of electromagnetic wave

             f=frequency electromagnetic wave (usually the supply frequency is 60 Hz or 50 Hz but varies for some circuits with high frequency)

The wave length of electromagnetic wave propagation for 60 Hz is given by,

λ=ν/f ⟹ λ=(3x10⁸ )/60= 5000000 m= 5000 km

Consider a transmission line of length of 50 Km.

When this line is operating at 60 Hz, the length of the line is very small in comparison with the wave length of electromagnetic wave as 50 Km << 5000 Km so it can be modelled as lumped element.

Consider the same line operating at 3 KHz,

Then the wave length of electromagnetic wave propagation is,

λ=ν/f ⟹ λ= (3x10⁸ )/(3x10³)= 100000m= 100km.

Though length = 50 km is less than the wave length λ=100 km, the length of the line is comparable is length to that of the wave length of electromagnetic propagation and it has to modelled as distributed element.

Thus the long transmission lines and elements in high frequency circuit are referred to as distributed elements. Kirchoff's laws (KVL and KCL) are applicable only to lumped elements and do not applicable to distributed elements.

Also Read

Classification of circuit elements
Active and passive elements
Linear and Non Linear elements
Unilateral and bilateral elements