Why would I ask mysefl that, then look at a bode plot of a high-pass filter? Here is a real bode of a diffeentiator.
Read Differentiator Bode
Hello,
The perfect differentiator is simply "s" alone, but we dont always need a perfect "s"
in real life circuits.
The thing that you are missing is not that "s" is different than "s/(s+a)", we know that,
but that "s/(s+a)" can be made to look like "s" over the range of frequencies of interest
simply by making 'a' large enough so that it swamps out the denominator 's' term.
What we end up with is a slope that looks exactly like "s" divided by a constant gain
up until a certain frequency is reached when it flattens out and possibly also rolls off.
The gain can be made up for later.
All you need to do is compare frequency plots of "s" and "s/(s+a)" when 'a' is somewhat
largish and see that they behave almost the same up to a certain point, keeping in mind
that we usually also have control over the gain too.
BTW, for the sake of the OP...
One circuit that is often overlooked is the simple RC passive circuit. That's with C in
series with R and the output is taken across R. It doesnt have the problems that op
amps sometimes bring either, but if gain is needed it can be added in the next stage.