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# integrator phase not reaching 90 degrees

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#### piers

##### Newbie level 3
integrator phase

Sorry if this question sounds simple. We all know that an ideal integrator has a phase of 90 degrees. Actual integrators are designed to be within a certain range from that angle. What are the problems if an integrator failed to achieve a phase close to 90 degrees? Thanks!

Re: integrator phase

piers said:
Sorry if this question sounds simple. We all know that an ideal integrator has a phase of 90 degrees. Actual integrators are designed to be within a certain range from that angle. What are the problems if an integrator failed to achieve a phase close to 90 degrees? Thanks!

It depends on your application.
It active filters, for example, some deviations from specified pole positions are to be expected. This also applies to oscillators (oscillating frequency).
For other applications (noise reduction) I expect no severe problems.

Added after 5 minutes:

Addendum: Your question is not simple or silly at all. Connected with your question is the following problem:

There is a double-integrator oscillator (e .g. with two Miller integrators and one inverter using "lousy" 741 amps). For higher frequencies each integrator has a phase error (deviation from 90 deg) of - let´s say - two degrees. As a consequence, the loop gain has a phase error of app. 4 degrees, resulting in a loop phase of -4 deg.
Nevertheless the circuit will oscillate at the desired frequency. WHY ???

Re: integrator phase

Thanks for the reply. My target application is for a delta-sigma ADC. What i know of is that if my integrator's phase is far from 90 degrees, if i input a square wave, i don't get the expected triangular wave. Surely there could be more problems? Or probably a more technical explanation.

Re: integrator phase

piers said:
............ if my integrator's phase is far from 90 degrees, ..........

What do you call "far from" ? A reasonable value for the phase error is app. 1 or 2 deg. (depending on the integration time constant and, of course, the opamp used).

Re: integrator phase

Far from like, more than 10 degrees off.

Addendum:
Some more details about my task. I am designing an OTA based gm-C integrator for a delta-sigma ADC to operate in 300kHz to 600kHz, and I am required to have its phase to within 10% error from 90 degrees in the operating frequencies. I am also asked what will happen if I fail to accomplish this requirement. So, yeah, what happens if I don't fulfill it?

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