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Maximum dV by dT a RC filter can follow
Although this is a very simple and well known circuit some interesting questions here and results here that we derive here is
- What happens when
$V_i$ is a ramp rather than a step.
- How does the output voltage behave different ramp slopes
Why are those important? If we know how soon the output catches up to a ramp and what is the voltage lag we can determine the RC values that give the desired response to a ramp input encountered so often in circuits.
where M is the ramp slope and t is time so we have:
Solving this differential equation for
by multiplying with
and integrating we get:
is the integration constant which can be solved by the initial condition at t=0
So we have:
So now lets look at
after certain number of time constants say K i.e.
so we have:
Here we can write
therefore we have:
Therefore the output would start tracking after a couple of time constants and the difference (voltage lag) between the output and the input is approximately MRC.
An amplitude limited ramp is given as
$$\table V_i, = ,Mt , t<t_F; ,=, Mt_F, t≥t_F$$
To make a good ramp follower RC circuit the time
so that it starts following the ramp much before the ramp reaches its limit