[SOLVED] Equations for Peak-to-Peak Output Voltages for Differentiator and Integrator

[pavan garate]

Hi...

I want to design the differentiator and integrator using OPAmp (IC 741) and verify it for the sine wave input and square wave input. I know the nature of the output waveforms.

Can anyone tell me the equations for peak-to-peak output voltages for differentiator and integrator when sine wave and square wave are applied as the inputs..???

 

[Audioguru]

The sine wave output signal level will be 0.707 times the unmodified input level when the differentiator or integrator are at the cutoff frequency.
The square wave will have a unique differerentiated or integrated appearance but I do not know the formula for the output level.

 

[barry]

Hi...

I want to design the differentiator and integrator using OPAmp (IC 741) and verify it for the sine wave input and square wave input. I know the nature of the output waveforms.

Can anyone tell me the equations for peak-to-peak output voltages for differentiator and integrator when sine wave and square wave are applied as the inputs..???

There is no valid equation for the differentiator for an IDEAL square wave, since the edges have a slope of +/- infinity, and the derivative of infinity is ...

But, if you model your input as a trapezoidal wave (which is what it really is), you can develop equations.

 

[THINKER_KAM_MAN]

The sine wave output signal level will be 0.707 times the unmodified input level when the differentiator or integrator are at the cutoff frequency.
The square wave will have a unique differerentiated or integrated appearance but I do not know the formula for the output level.

i think for the case of the sq wave it will be
a 0.577 Pk as sq wave would be triangle.

 

[pavan garate]

The sine wave output signal level will be 0.707 times the unmodified input level when the differentiator or integrator are at the cutoff frequency.
The square wave will have a unique differerentiated or integrated appearance but I do not know the formula for the output level.

I know that-
1) For sine wave input- Both the integrator and differentiator will give the cosine wave at output.
2) For square wave input- Integrator will give the triangular wave and differentiator will give the spikes at the output.

I want to know the theoretical formulae for calculating the peak-to-peak voltage for all these four outputs. I have designed and simulated these circuits using OrCAD. I want to check whether I'm getting the correct outputs or not. Merely getting the correct shapes of output waveforms does not mean that I'm getting the correct results. There must be some formulae to find the peak-to-peak voltage for such outputs.

Thanks...

 

[THINKER_KAM_MAN]

I know that-
1) For sine wave input- Both the integrator and differentiator will give the cosine wave at output.
2) For square wave input- Integrator will give the triangular wave and differentiator will give the spikes at the output.

I want to know the theoretical formulae for calculating the peak-to-peak voltage for all these four outputs. I have designed and simulated these circuits using OrCAD. I want to check whether I'm getting the correct outputs or not. Merely getting the correct shapes of output waveforms does not mean that I'm getting the correct results. There must be some formulae to find the peak-to-peak voltage for such outputs.

Thanks...

RMS = PK* sq root(1/(mean value of the function))

for sinewave average=2, for triangle average = 3
clipped sine wave square sides = 1, sq wave (0-1-0) = 0.5, its the area under the curve. ∫(function)

triangle = dv/dt= back to sq wave