continuous-time sigma delta ADC

[kuohsi]

continuous-time sigma-delta adc

Why the best performances of lowpass CT sigma-delta modulators have been
achieved using an RC integrator in the first stage and Gm-C integrators for the subsequent stages.

And what are the advantages of ALL Gm-C sigma-delta?

thanks!

 

[tsb_nph]

continuous time sigma delta adc

Why the best performances of lowpass CT sigma-delta modulators have been
achieved using an RC integrator in the first stage and Gm-C integrators for the subsequent stages.

And what are the advantages of ALL Gm-C sigma-delta?

thanks!

Active RC integrator has an amplifier in feedback loop and gives better linearity performance than a gm-C integrator. In a gm-C integrator, the transconductor is in open loop and hence you would expect lower linearity than an amplifier operating in a feedback loop.

In a CT sigma-delta (or for that matter any sigma-delta), the linearity of the overall system is limited by the linearity of the first stage and the linearity of the DAC connected to the first stage (higher OSR helps to suppress this requirement to some extent). The linearity of the subsequent stages are masked by the loop gain upto that stage, so the 2nd and 3rd stage do not have very stringent linearity requirements. Because of this reason, it is preferable to have active-RC integrator as first stage.
The main disadvantage of active-RC is that the amplifier bandwidth has to be high enough to operate in feedback configuration. In addition, it needs to have enough gain in the signal bandwidth to provide good linearity (linearity is related to gain at that frequency, higher the amplifier gain at the signal frequency, better is the linearity). The gm of gm-C integrator has lower gain bandwidth requirement since it operates in open loop and hence can consume lower power.
So in terms of power optimization, first stage has active-RC (higher power) and subsequent stages have gm-C (lower power). Overall, this arrangement gives best performance @ optimum power consumption.
However, linearity of the DAC connected to the first stage shoudl be >= linearity of the first stage active-RC integrator.

Advantage of an all-GmC would be lower power at the cost of lower linearity. Input referred noise comparison cannot be generalized as it depends on the value of R in the active-RC integrator, but the R values can be adjusted such that input referred noise of active-RC integrator can be made lower than the gm-C integrator, which implies a higher dynamic range if active-RC integrator is used as the first stage.

 

[kuohsi]

Why the gm-C integrator has lower gain bandwidth requirement as it operates in open loop?

And what is the effect of finite DC gain of gm in sigma-delta?

Thanks!