# Linear system and potential transformer

• rain2359
In summary: No, the frequency domain response would still be possible, but it would be more difficult to measure.
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?

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

rain2359 said:
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.

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.

## What is a linear system?

A linear system is a mathematical model that describes a relationship between two or more variables in a form of linear equations. It follows the principle of superposition, where the output is directly proportional to the input.

## What is a potential transformer?

A potential transformer is a type of instrument transformer that is used to measure the voltage in high voltage transmission systems. It works by stepping down the voltage to a manageable level for measurement and protection purposes.

## How does a linear system work?

A linear system works by using linear equations to represent the relationship between the input and output variables. The equations can be solved using algebraic methods to determine the values of the variables.

## What is the purpose of a potential transformer?

The purpose of a potential transformer is to accurately measure and monitor the voltage in high voltage systems without causing any disruption or damage. It also helps in providing isolation and protection to the measuring instruments and personnel.

## What are some applications of linear systems and potential transformers?

Linear systems and potential transformers have various applications in different fields, such as electrical engineering, control systems, signal processing, and physics. They are used for measuring, controlling, and analyzing the behavior of systems and circuits.

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