Linear system and potential transformer

[rain2359]

Hi,

Does anyone knows how to prove that a potential transformer is a linear system or not? Can I use principle of superposition with time-domain impulse to prove it? Is there other ways other than the principle of superposition to prove linearity of a potential transformer? Is there a way to use the frequency domain response to prove? If yes, how should I go about doing it?

Thanks in advance.

 

[berkeman]

Superposition would normally be the way you would show that a system was linear.

 

[rbj]

Does anyone knows how to prove that a potential transformer is a linear system or not? Can I use principle of superposition with time-domain impulse to prove it? Is there other ways other than the principle of superposition to prove linearity of a potential transformer?

superposition is essentially synonymous with linearity. it's what linearity means.

but one problem with what you're saying is that for some system to be linear, superposition has to work with the sum of any pair of signals, not just impulses.

$$L\left\{ x_1(t) + x_2(t) \right\} = L\left\{ x_1(t) \right\} + L\left\{ x_2(t) \right\} \quad \forall x_1(t), x_2(t)$$

you don't get to pick the $x_1(t), x_2(t)$, the devil hands you a pair and you have to show the above equation is true no matter what he hands you.

Is there a way to use the frequency domain response to prove?

there really is no such concept of a single frequency domain response until you are already past the point of linear and time-invariant.

 

[rain2359]

Hi, thanks for the reply.

May I know, if I am working using the FFT, which means the z-domain, does it still holds that if my system is not linear, there will not be able to have any frequency domain response to describe my system?

Thanks.