Doubt: before I thought I had understood the transfer function, now, I realize that I did not understand what transfer function is it on a structural level , that is how it 'makes a circuit' or is manifested or implemented concretely because I see a translation motion here where function is integrated when a Shift Operator is provided or better, is induced by control system or still better, technically we have a a differential operator of an electric field (a complex field C)
In mathematics, and in particular functional analysis, the shift operator also known as translation operator is an operator that takes a function x ↦ f(x) to its translation x ↦ f(x + a)
In mathematics, a fixed point (sometimes called an invariant point) of a function is an element of the function's domain that is mapped to itself by the function
I know that the amplifier amplifies in the sense of 'gain', but the gain depends, and I do not understand here, how the transfer function is defined (is just a calculation or it is reflected by a shift operator ? This is not very clear)
What I do not understand is if the transfer function, concretely, can be calculated by an operational amplifier in the physically operative sense of the term because to do this we need to have an linear functional because we need to have a current not a physical movement because we talk about of trasfer function, not about information extraction !
Basically, current doesn’t flow because current is just measurement. It is developed by flow of electrons. Current is rate of flow of charge.
But this flow of charge how is determinated in relation of transfer function ?
A flow formalizes the idea of the motion of current because the direction of current flow is opposite to the direction of electron flow.
The related question is about the 'information nature' of transfer function: is this a signal action like a 'function' (and therefore I ask how it is done) or, if the function, here, is to be calculated in another meaning, that is, something that is extracted or indirectly calculated as a 'behavior' of the circuit, an impulsive response, etc. but.. in this case we should, mathematically speaking, talk about of image function
an image is the subset of a function's codomain which is the output of the function from a subset of its domain
Definition of transfer function is instead
It is often represented as a graph, called a transfer curve or characteristic curve. The transfer function provides information which specifies the behavior of the component in a system
What type of function is this curve ? Exponential, logarithmic.. ? Because if it provide information you need a function to do that, maybe a constant function ?
I find that is method of characteristics for solving partial differential equations, so this is the 'function' of transfer function ? But is not clear if I want to induce a transfer function (Current–voltage characteristic) I need a Semiconductor curve tracer