Hello ,I am use to see differentiator and iintegrator from a perspective of pulse input.
Integrator turns pulse into ramp because its accumilating.
differtiator turns pulse into two spike because its mathematics.
In the circuit below I have RC integrator and differentiators.
Is the some mathematical intution regarding the differentiator that could explain why given the following input I have such shape on output V(b)?
Thanks.
The "integrator" is not an integrator - there is a resistor across the capacitor.
The two resistors form s voltage divider of roughly 6:1 so the capacitor can never charge beyond roughly 1/7th the supply voltage.
Note that a passive R-C integrator will not give linear results as the rate of change varies with the existing capacitor voltage, for a fixed input voltage. You need to use an opamp based integrator for to work well.
The difference between a true P or I and a passive RC network is the bandwidth beyond where the phase shift = +/-45 deg for a 1st order filter.
When you see a pulse of fixed slope and duration, you are using a partial BW with limited upper and lower end.
Thus we call RC a "partial integrator or partial derivative" and the linear region of phase shift for a 1st order filter extends +/1 decade around the breakpoint, fo.
Thus the Q = fo/BW of your modulation may determine if a partial or passive partial D + I filter will be adequate.
We generally try to match the spectrum of the filter to the output signal depending on details of group delay flatness.