shape logic of analog differeratiator and integrator

[yefj]

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.

--- Updated Thursday at 11:12 AM ---

update:
V(A) is a integrator.the input is a ramp .integrator result always rises as the input non zero. why the integrator result of V(a) gets platoe?

 

[G4BCH]

Hint what is the output voltage of R5 & R20?

 

[barry]

voltage didvider?

 

[FvM]

The circuits are high- and low-passes, not differentiators and integrators.

 

[D.A.(Tony)Stewart]

The only difference between passive and active "differentiators and integrators" is the BW limitiation.

So we often call HPF/LPF as "partial differentiators / integrators"

The active types have gain which may extend or limit the BW depending on the breakpoint and GBW ofthe amplifier. BW = GBW / G.

--- Updated Thursday at 7:50 PM ---

The negative feedback extends the freq. range over this mathematical property.

By increasing the BW to 100 MHz on the dv/dt circuit aka Kd component of a PID compensator extends the accuracy and freq. range above -3dB. Otherwise it is almost identical below -3dB.

Below is the passive then active version with pole=zero at 10 kHz. in the passive version, while the active version extends the BW with gain >0 while the passive "partial" filter is confined to 1 freq. decade yet both are interactive multiple pole/zeros R1C1 : R2C2 and compromised.

Then parallel ID only, again with pole=zero and extend GBW of Differentiator to 100 MHz
Notice this also creates the 10kHz bridge-T notch filter, to generate the integrator at -90 deg then the differentiator at + 90 deg . These are the properties of perfectly matched RC gains.

--- Updated Thursday at 8:04 PM ---

Link to filter sim and time domain

 

[danadakk]

Minor changes, you get differentiator and integrating behavior :

 

[D.A.(Tony)Stewart]

Minor changes, you get differentiator and integrating behavior :

This is an example with zero = 100 x pole with the sq.wave in the middle of the +/- 1/2 decade region of BW and also when combined becomes the twin-T notch

With a different mix ratio in time domain

 

[FvM]

The question in post #1 was, why the "integrator" response has a plateau, and the answer is, because it's no actual integrator...

 

[danadakk]

Is the some mathematical intution regarding the differentiator that could explain why given the following input I have such shape on output V(b)?

I thought OP original question was why differentiator output not as expected....?

And then at bottom raises the plateau question of integrator is added.

 

[D.A.(Tony)Stewart]

The question in post #1 was, why the "integrator" response has a plateau, and the answer is, because it's no actual integrator...

It is a partial integrator if and only if the spectrum BW was below the -3dB to -6dB implying the max pulse width < 1/2 of Tau.

 

[FvM]

It is a partial integrator if and only if the spectrum BW was below the -3dB to -6dB implying the max pulse width < 1/2 of Tau.

Post #1 input signal has infinite duration, in so far there's no pulse width involved. In this case RC time constant must be at least double the observation interval to get integral behaviour.

 

[D.A.(Tony)Stewart]

Post #1 input signal has infinite duration, in so far there's no pulse width involved. In this case RC time constant must be at least double the observation interval to get integral behaviour.

View attachment 198033

Thanks for confirming what I said with PW50 <= 1/2 of Tau=RC