This article is written thanks to our student Siddharth Mohan
Siddharth is a very knowledgeable R&D Hardware Engineer and his bio is provided on his LinkedIn address above
Linear systems have a property where the relationship between the input and output can be expressed by a straight line for example V versus I relationship of a resistor.
We can define a non-linear system y as a function of x as per the equations indicated below :
Non-Linearity : the output has linear part but there are many more extra terms which cause non-linearity like the 2nd order, 3rd order and so on… The higher order terms are very small comparatively hence can be ignored unless sensitivity is very critical.
Y = a1x+a2x^2+a3^3
For example the MOS based differential pair the relationship between Vout and Vin is a non-linear one with the 3rd order term as non-zero. The 2nd order term is zero though (a2=0) for differential systems.
Y = a1x+a3x^3
Suppose X -> 0 is very small then we can ignore even the 2nd & 3rd order terms in which case we can say that for very small values of X the system is linear. Or in other terms in non-linear systems the value of X is relatively big.
When calculating the gain of circuit we assume small signal analysis in which the input is assumed to be very small. Hence Vout = gmRd*Vin
If the amplitude of Vin increases the system starts to behave non-linearly.
Problems due to non-linear system.
Suppose we have an input Acoswt and we have a no-linear system. Lets see what happens to the output. We can replace the input x = Acoswt
Using trigonometry we can express output y as :
y(t) = a2A2/2 …
y(t) has a DC value as well as a linear part coming from the fundamental frequency. So non-linear systems produce harmonics apart from the fundamental which distorts the expected output. Instead of the just the fundamental term we have many more terms corrupting the output.