HP made a sampling AC voltmeter that was good to 1 GHz around 50 years ago. They abandoned it for some reason, like no customers? They also made a Thermal RF power meter with higher accuracy (a version is still in production for $20K +) which does still have customers.
Racal-Dana had one also. I have a couple of Tektronix 7S11 samplers so could put something with similar or better performance together in about 10 minutes with what I have on hand. Tektronix even published an application note showing how to do it.
The advantage of sampling measurement over linear measurement (for lack of a better term) is that the frequency response of the sampler can be calculated from the sampling gate width which can be measured with an unleveled RF source. So if you know the frequency components of the measured signal, which will often be the case with an RF sampling voltmeter measurement, a simple lookup will correct for the passband response. Racal-Dana included the correction curve for their sampling RMS voltmeter in their manual.
If I wanted to measure RMS with as much accuracy as possible, then I would use a high resolution sampling converter and calculate it directly. Such a sampling converter could be integrated, or if I thought I could get better performance, I might use a discrete high precision sampler in front of a slower but more accurate converter.
The most significant limitation to accuracy would be the passband response of the stages up to and including the sampler. If the frequency content can be known, then correction could be applied after conversion.
I think you underestimate the complexity of such systems.
Let's take the LTC1968. It will work to 500khz without too much trouble, costs 4 USD and it needs one capacitor (film preferably) and a slow 12-16 bit ADC to digitize it.
If you want to make a similar system with sampling, you have to make a DC ad AC accurate antialiasing filter,
Nope, one of the chief advantages of the sampling RMS measurement is that no antialiasing is required at all.
But what I was suggesting is either precision sampling followed by slow precision RMS conversion, or the direct computational approach where a high frequency high resolution sampling ADC is used for low frequency RMS conversion. I was told about 20 years ago that some multimeters had started using the later method in lieu of analog computation but have not been able to verify that.
The Racal-Dana and HP RF voltmeters mentioned above use the former method, and I am suggesting extending this idea to low frequency measurement.
Sample it with an ADC at least 1MSPS, but realistically, much higher, I would say 5MSPS. Then you have to make sure that your sampling frequency is not the multiple of the incoming signal, because then you sample it the same phase. Or you undersample it, and use an ADC with high input bandwidth. It will be a SAR ADC in either case, others will not have the sample rate.
The bandwidth is determined by the sampling gate width, which produces a non-linear passband response that can be easily calculated.
I suggested a simple system relying on a sampling ADC with high input bandwidth used at much lower frequencies, but an alternative is to implement a precision external sampler with a slower ADC. I messed around with the later many many years ago but not with this application in mind and I mostly learned what does not work for precision sampling.
Nevertheless, driving these is not trivial, needs a high bandwidth opamp, in the order of hundreds of MHz otherwise the input of the ADC will miss codes and all kinds of nastiness.
The chief advantage of the sampling method is that within the input signal range, no processing is required before sampling, removing those error contributions, which is the major reason to use it. I can design and fabricate a sampler or sampling system, but constructing a high accuracy thermal RMS converter would be much more difficult, at least for me.
Then we arrive at the microcontroller.
When you all verified the system, wrote the code, and finished it up... Sounds like a lot of work doesn't it? Could be more accurate? Yes, sure, but be ready to those debugging sessions, when "I wish I would have a 16 bit scope to see what my ADC driver is doing, and why do I have INL errors in my output code".
Calibration requires an unleveled RF source to measure the sampling gate width. If you are desperate, processing after sampling can be done with any low frequency RMS measuring tool. I could set something up which makes RMS measurements to GHz frequencies in about 10 minutes with what I have on hand, but it would not be real suitable for the low frequency high resolution measurements we are discussing, although it would work.