# How to do analysis and comparison of Analog Integrator vs. Digital Integrator

1. ## How to do analysis and comparison of Analog Integrator vs. Digital Integrator

I found a good article in 'analog dialog' from 1967 discussing the various errors and design issues with a Operational Amplifier Integrator circuit.

But what about the Digital Integrator. What would be the errors involved with a Forward Euler vs. Runge-Kutta etc..

---------- Post added at 10:22 ---------- Previous post was at 10:21 ----------

This integrator will be measuring a di/dt to compute current.

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2. ## Re: How to do analysis and comparison of Analog Integrator vs. Digital Integrator

There are no errors added after the signal has been transfered to the digital domain. Errors of the analog input signal (offset, noise) are supplemented by quantization errors and ADC non-linearity.

I guess, you are talking about a di/dt current sensor (Rogowski coil) interface?

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3. ## Re: How to do analysis and comparison of Analog Integrator vs. Digital Integrator

Originally Posted by FvM

I guess, you are talking about a di/dt current sensor (Rogowski coil) interface?
Yes.

Originally Posted by FvM
There are no errors added after the signal has been transfered to the digital domain. Errors of the analog input signal (offset, noise) are supplemented by quantization errors and ADC non-linearity.
If no errors in digital domain, then why do people goto the trouble of doing more advanced 4th order integrators like Runge-Kutta? Why not just do simple Forward Euler and be done with it?

---------- Post added at 11:14 ---------- Previous post was at 10:47 ----------

I would think that since the step size is not infinitely small, every step some error is produced.

4. ## Re: How to do analysis and comparison of Analog Integrator vs. Digital Integrator

Runge Kutta is for solving differential equations, which is a completely different problem than calculating the integral of a sampled waveform. Provided that the requirements of the sampling theorem are fulfilled (no spectral components of the signal higher than 1/2 of sampling frequency), the time-discrete signal processing operations can be exactly described by z-transformations.

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5. ## Re: How to do analysis and comparison of Analog Integrator vs. Digital Integrator

Ok. So i do need to just make sure my maximum step size is small enough to do this integration correctly?

6. ## Re: How to do analysis and comparison of Analog Integrator vs. Digital Integrator

So i do need to just make sure my maximum step size is small enough to do this integration correctly?
In a short, yes. You can review the datasheets of energy measurement chips, e.g. from Analog, that are all providing digital integrators for di/dt sensors and check the implementation parameters.

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7. ## Re: How to do analysis and comparison of Analog Integrator vs. Digital Integrator

Originally Posted by FvM
Runge Kutta is for solving differential equations, which is a completely different problem than calculating the integral of a sampled waveform.
Can you explain further? I dont see how integration is different in applying to a di/dt waveform vs. being used to reduce derivatives in a differential equation?

8. ## Re: How to do analysis and comparison of Analog Integrator vs. Digital Integrator

The difference is in the band limited nature of the signals (if applicable). They can be completely represented by just the sampling points.

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9. ## Re: How to do analysis and comparison of Analog Integrator vs. Digital Integrator

I know this is a loaded question, but what do you think would be the smallest acceptable voltage level for di/dt out of the rowgoski coil to accuratley measure? (whether going into a Analog integrator or sampled and into Digital Integrator)

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10. ## Re: How to do analysis and comparison of Analog Integrator vs. Digital Integrator

Provided you provide sufficient ADC resolution, the minimal voltage is mainly limited by input amplifier noise. It's reasonable to use lowest noise amplifiers for sensitive Rogowski coil measurements. All practical integrators will implement at least one zero respectively place a highpass in front of the integrator. The noise of the integrator output (current signal) depdends strongly on the high pass cut-off frequency. uV resolution and mV full scale order of magnitudes are achievable.

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