AC RMS DMM tests

[Kleinstein]

The DACs are usually pretty fast settling. For the AD5791 they give 1 µs settling for a 10 V step. Part of this could already be the OP-amp speed. A slight problem could be the switching glitches. This can give some additional background of the DAC code is changing rather frequent. One may have to compromise with the sampling rate between the background from the glitches and good following the sine waveform.
With a DDS like generator the number of switching steps / gliches depend on the frequency in a not so predictable way. With a fixed set of samples and variable sampling rate the extra glitches would be proportional to the frequency.

For the filter performance one may also include scattering in the filter components. With no longer the ideal values the pass band ripple will be higher than in the ideal case.

[mawyatt]

I was thinking worst case at 1 kHz, so for instance an OP-07 only has an open loop gain of 60dB at 1 kHz, yielding 1000 ppm of error.  An OP-27 gets this down to 100 ppm.  There are faster precision operational amplifiers so this is handled.  I am cheap so would consider the OPA1611.

Yeah there's a number of Op-amps that should serve this purpose.

The DDS/DAC method seems promising.  I think accuracy will ultimately depend on the DAC, and there are some pretty good ones.  The problem here is that many of the best DACs lack AC specifications, so it is difficult to estimate the amplitude error when generating an AC signal.  Otherwise I might expect a total AC error below 10 ppm (6 digits and better) from something like a 20-bit AD5791.

Would think at 1kHz and below the AD5791 should perform quite well!!

I am not aware of anybody doing it this way.  Most people would rely on an AC calibration of the source, instead of designing it to require only a DC calibration.

6 digit accuracy seems reasonable, with 7 digits possible.  The unknown is the DAC's analog frequency response.

Agree, this whole concept of DC verifiable waveform creation for precision AC use seems completely missed. Remember way back when we did the CMOS Logic FF voltage divide by 2, even before that the CMOS Logic based precision triangle and trapezoidal waveform generation just seemed like a different way to do things rather than the "old school" tried and true methods.

Totally surprised that Keysight hasn't anything like this, they had custom DACs 2 decades ago like SiGe based Griffin that were ultra-precise into the GHz region and working on pure CMOS DACs that had over 100dB SFDR, far beyond anything ADI or TI had in the workings back then.

Anyway, seem like an interesting venture for someone

Best

[mawyatt]

The DACs are usually pretty fast settling. For the AD5791 they give 1 µs settling for a 10 V step. Part of this could already be the OP-amp speed. A slight problem could be the switching glitches. This can give some additional background of the DAC code is changing rather frequent. One may have to compromise with the sampling rate between the background from the glitches and good following the sine waveform.
With a DDS like generator the number of switching steps / gliches depend on the frequency in a not so predictable way. With a fixed set of samples and variable sampling rate the extra glitches would be proportional to the frequency.

For the filter performance one may also include scattering in the filter components. With no longer the ideal values the pass band ripple will be higher than in the ideal case.

The small ripple/peaking caused by an error in component values doesn't appear near the LPF origin but closer to the corner as the filter poles don't move much. The Butterworth is one of the least sensitive filters to component values and a simple sensitivity MC analysis/simulation will prove this. The resistors should be fine as they don't effect the DC gain with the Sallen-Key and why this type filter should be considered. The capacitors also are not very critical, the ratios are more important as they control the filter "Q" or peaking.

Since the corner frequency should be much higher than the sine-wave these filter components can likely be just 1% Resistors and even 5% capacitors (maybe ratio matched), again a simple sensitivity analysis or MC can verify this assumption.

Also, the DAC glitches shouldn't contribute much to the sine-wave RMS content, especially after passing thru the LPF, which could be preceded by a "glitch filter", see our old CMOS waveform generator, the 3rd Order Butterworth is adapted for glitch removal by the addition of a split RC filter for the filter input without significantly affective the Butterworth response. Of course this "glitch filter" if required needs to be placed well above the LPF corner so as not to affect the sine-wave amplitude. One of the nice features of the Sallen-Key 3rd Order LPF implemented as shown is the filter input is directly into the RC lowpass which will attenuate very high frequency (glitches) by nature without additional effort/components. This significantly attenuates high frequencies before the feedforward capacitor to the op-amp output which is a limiting factor in the ultimate stop band rejection (op amp output Z is not zero, or even close, and has an inductive reactance (rises with frequency). However we must remember the goal is not necessarily a "pure" sine-wave but a somewhat "RMS invariant" type sine-wave waveform, verifiable by design and DC measurement.

Anyway, everything seems to point at having a DC verified AC Reference, whether the simple proven Squarewave CMOS concept, or the more involved DAC based sine-wave source which might achieve 10ppm levels of low frequency performance outside the complex/expensive/bulky methods from yesteryear

Best

[mawyatt]

I was thinking worst case at 1 kHz, so for instance an OP-07 only has an open loop gain of 60dB at 1 kHz, yielding 1000 ppm of error.  An OP-27 gets this down to 100 ppm.  There are faster precision operational amplifiers so this is handled.  I am cheap so would consider the OPA1611.

Here's something that might reduce the op-amp gain frequency dependency, similar to the AN-107 you mentioned. With a dual op-amp just use the "extra" for the feedback in a unity gain configuration, where the extra is configured as a wired unity gain (Vo to Vin-) providing the feedback to the forward amp - input. My simple thinking is the feedback unity gain experiences the same gain dependent frequency reducing as the forward gain op-amp and thus the two just partially cancel. This converges toward unity faster than just a simple unity gain follower with finite frequency dependent gain.

For example a simple Unity gain Voltage Follower with an op-amp with A(f) = 100 has a gain of  100/101 or  0.99099 which is 0.991% low, while the method shown below utilizing another identical op-amp in the feedback has a gain of (100^2 + 100)/(100^2 + 100 + 1) or  10,100/(10,101) or 0.999901 which is 0.0099% low and improvement of 100!! Of course this configuration will need frequency compensation to be stable which will eat into this advantage.

Best,

[mawyatt]

Curiosity got the best of us, always does!! Here's a quick LTspice simulation of this Dual Op-Amp Precision Unity Gain Follower and modified Butterworth type 2nd Order LPF. The Dual Op-Amp Precision Follower has frequency compensation for a Phase Margin of ~56degrees based on the Open Loop Bode plot with OP-07.

The Standard op-amp follower shows an amplitude error (Vout-Vin) of -78.54dBV @ 100Hz or 1.18mVp for 10V peak input which agrees well with the transient plot, the Dual op-amp follower shows -124.85dBV, or 5.72uVp for 10V peak input which also agrees well with the transient plot. Both of these also agree well with the previous error analysis when the OP-07 gain is considered at 100Hz (78.6dB) as predicted by the OP-07 Spice model. 

The LPF has a RC "glitch pre-filter filter" mentioned earlier. This helps with fast glitches from the AD5790 type DACs which might present a problem with active filters, especially with 2nd Order Sallen-Key types. Note the improvement with the Dual Amp approach at the lower frequencies. These are all with just OP-07 Op-Amps, nothing special, and even works with the low end LM358!!!

Anyway, this is getting quite interesting indeed!!

Best

[David Hess]

Curiosity got the best of us, always does!! Here's a quick LTspice simulation of this Dual Op-Amp Precision Unity Gain Follower and modified Butterworth type 2nd Order LPF. The Dual Op-Amp Precision Follower has frequency compensation for a Phase Margin of ~56degrees based on the Open Loop Bode plot with OP-07.

Thank you for confirming the issue and finding a solution.

I have not seen this kind of compensation used but I suspect applications which require this level of AC precision without leveling are few and far between.

[mawyatt]

Curiosity got the best of us, always does!! Here's a quick LTspice simulation of this Dual Op-Amp Precision Unity Gain Follower and modified Butterworth type 2nd Order LPF. The Dual Op-Amp Precision Follower has frequency compensation for a Phase Margin of ~56degrees based on the Open Loop Bode plot with OP-07.

Thank you for confirming the issue and finding a solution.

I have not seen this kind of compensation used but I suspect applications which require this level of AC precision without leveling are few and far between.

Here's LTspice computational result for an input 10V since-wave @ 100Hz. This level of precision is taxing LTspice and can be seen in the previous Transient Sine-wave Response of the Vout-Vin Error for the Dual Amp Follower which shows a 0.6ppm error, and note the jittery error waveform an indication of numerical precision/convergence limits. This 0.6ppm level of error agrees with the AC linear analysis which is shown the AC Error plot as -124.85dBv which is 0.572ppm.

Agree, there's likely been little if any type of AC precision along these lines without some level of output sensing and feedback (leveling) and we wondered why this hasn't shown up in some Fluke or Keysight AC Calibration instruments. Don't know maybe it has, but we've never seen it, or maybe we're just fooling ourselves

Now we're trying to investigate the effects of DAC glitches on the RMS waveform content, in the interest of a somewhat RMS invariant solution. We've added a a plot showing a "20mV glitch" and the RMS result.

Best

[mawyatt]

Here we've added results with the lowly LM358 op-amp used as a simple Follower and Dual Amp Follower. The input signal is a 10V peak sine-wave @ 100Hz. We also used LTspice to estimate the total RMS difference between the input and output of the Follower (vo1) and Dual Amp Follower (vo2), note the improvement!!!

Also added the same with the OP-07. In actual use would expect the OP-07 version to perform better than the LM358 (has way better offset and bias current, but lower BW), however these results are limited by the fidelity of the Spice models and believe the OP-07 model we used (from LTspice library) represents the physical op-amp better than the simpler behavioral model used for the LM358.

BTW at low frequencies the dynamic Common Mode voltage for the Dual Amp is ~ the same for the forward follower amp and the feedback amp, as well as the inherent op-amp distortion levels, and should yield a level of improvement over the common op-amp unity gain follower.

Anyway, seems this Dual Op-Amp approach works well and provides a significant improvement in Voltage Follower Precision Unity Gain at low frequencies.

Edit: We should probably start a new thread on the Unity Gain Follower rather than clutter up this thread more.

https://www.eevblog.com/forum/projects/different-type-precision-unity-gain-follower/msg6191175/#msg6191175

Best

[David Hess]

Real world performance will be worse than the SPICE calculations suggest because the two operational amplifiers are not identical, but the performance improvement is still significant.  The operational amplifiers match better when duals and quads are used, and the results from the Analog Devices application note depend on this.

[mawyatt]

Real world performance will be worse than the SPICE calculations suggest because the two operational amplifiers are not identical, but the performance improvement is still significant.  The operational amplifiers match better when duals and quads are used, and the results from the Analog Devices application note depend on this.

There's more discussions on this over here.

https://www.eevblog.com/forum/projects/different-type-precision-unity-gain-follower/

Best