Superposition Theorem | Network Theory

by / Thursday, 15 June 2017 / Published in Blog

Superposition Principle:
Super position is only valid in linear circuits. So firstly discuss about linearity. Linearity is defined by two principles

  • Homogenity
  • Additivity

Homogenity

If input is scaled by some constant factor, then output should also be scaled by same constant factor. One more very important fact to justify the homogenity is., if input is not applied to the circuit, output must have to be zero.

Additivity
If we will add two inputs and feed to the circuits, then total output must have to be equal as the sum of individual output which will be produced by each source individually.
x(t)↔y(t)
ax(t)↔ay(t) bx(t)↔by(t) } Homogenity
(a+b)x(t)↔ay(t)+by(t)←Addivity
Superposition theorem
In any linear circuit, voltage across or current through an element is the algebraic sum of voltages across or current through that element due to each independent source acting alone, when remaining sources are replaced by their internal impedances.
null

Hence we have to determine (v’)
Active voltage source only and calculate v’; when current source is replaced by ideal independent source.
Voltage source→ideal impedance is zero Rs=0 ;(S/C)
Current source→ideal impedance is infinity Rs=∞ ;(O/C)

Limitation of Superposition principle

  • Power calculation cannot be done by superposition principle because power is not linear function of voltage or current.
  • Superposition is not applicable if any redundant source will present in the circuit.
  • Superposition is not applicable if any non-linear component is present in circuit.

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