Measuring RMS voltage for PWM-like signals at 150 kHz - Page 1
Forum section: electronics / testgear

author: siealex
author_rank: Regular Contributor
timestamp: August 07, 2023, 09:58:11 pm
content: Can any "true RMS" multimeters measure, for example, the filament voltage coming from the voltage converter in a vintage VFD calculator? Typical characteristics of this voltage: 2.5 V RMS (in some models 3.15 V), no DC component (directly from a transformer), 80..150 kHz, pulsed PWM-like shape. My new ZT-702s displays something only in scope mode, the "true RMS" multimeter mode shows all zeros. And even the scope mode displays 3.3 V RMS, a voltage that would burn the VFD filament in a couple of minutes, on a perfectly working VFD with 2.5 V filament voltage.

author: bdunham7
author_rank: Super Contributor
timestamp: August 07, 2023, 10:11:12 pm
content: Scopes are a good way to get RMS readings on higher-BW AC, but you need to have a decent scope and know how the gating works--it isn't hard to get a wrong result. As far as DMMs, better bench meters might be able to get you a good enough reading on a signal like this. The only ones I have that I'm reasonably confident would be pretty accurate are very old, the Fluke 8506A Thermal RMS and the 8505A (regular) RMS but with a 1MHz BW. Analog meters like the HP3400B would work too.

author: TimFox
author_rank: Super Contributor
timestamp: August 07, 2023, 11:04:38 pm
content: The -hp- 3400 (analog readout) and 3403 (digital readout) true-RMS meters have sufficient bandwidth for your measurement.Note that the input connector for each one is a BNC with grounded shell.If you worry about crest factor (peak divided by RMS), you can always set the meter to a higher full-scale input value to see that the reading remains the same.The 3400A is good up to 10 MHz, only AC-coupled (above 10 Hz).The 3403C is good up to 100 MHz, and can be AC or DC-coupled (to include the DC component in true power) by switch selection.I like the 3403 series for noise measurements, since it has fast or slow averaging modes (inside the RMS averaging).

author: gnuarm
author_rank: Super Contributor
timestamp: August 08, 2023, 05:55:58 am
content: Quote from: siealex on August 07, 2023, 09:58:11 pmIf the Vmax and Vpp values are correct, I can tell you the Vrms will be greater than 3.0V. Vpp - Vmax = ~3.0V. Ignoring the brief time in the transition and the duty cycle, the minimum possible Vrms would be 3.04V and the max possible would be 6.7V.The voltage is at 6.7V about 20% of the time. Considering that the impact is relative to the square of the voltage, this will have about the same impact as being at -3.04V 80% of the time. My seat of the pants guesstimate is about 4.5Vrms.

author: bdunham7
author_rank: Super Contributor
timestamp: August 08, 2023, 02:39:24 pm
content: As the saying goes "You might be an engineer if you debate something for an hour when a 5-minute experiment would resolve the issue". Or something like that.I think the OPs scope is reasonably close to the truth. I tried to replicate that signal with an AWG, I used +6V and -2V with a 25% duty cycle, a fast rise and a 1µs fall time. This resulted in a balanced signal that looks pretty much the same with DC or AC coupling. This gives me ~3.23VRMSon the scope, as shown.As for what meters can read this directly, I tried some.HP 34401A: 3.28xx V (this meter is a bit 'peaky' at higher bandwidths, meaning it is in spec but the error is to the high side at first, then drops later)Fluke 8842A: 2.98xx V (only specified to 100kHz)Fluke 8808A: 3.18xx VFluke 189: 2.55xx VFluke 289: 2.64xx VFluke 8505A: 3.204 VFluke 8506A: 3.202934 V (this is probably as good as it gets and the output of the AWG isn't nearly stable enough for this resolution)

author: gnuarm
author_rank: Super Contributor
timestamp: August 08, 2023, 06:01:20 pm
content: Quote from: bdunham7 on August 08, 2023, 02:39:24 pmNice experiment. You took seven measurements and got seven wrong answers.

author: TimFox
author_rank: Super Contributor
timestamp: August 08, 2023, 06:55:55 pm
content: bdunham7:Did you try increasing the full-scale voltage one notch on the DVMs to see if you had any crest-factor problems?

author: bdunham7
author_rank: Super Contributor
timestamp: August 08, 2023, 08:01:34 pm
content: Quote from: TimFox on August 08, 2023, 06:55:55 pmExcellent point--I did on the bench meters and had some slight variations either way, except for the 8506A which can handle insane crest factors without any issue. With all the other ones it was difficult to discern the difference between CF and BW variations between ranges. Using autorange, these are the ranges that the meters settled into.8506A: "3V" range, full-scale of 4.000000V, full rated accuracy with up to 8:1 CF, peaks less than 16V and HF components all less than 10MHz.8505A: 10V range, CF <7.8842A: 20v range34401A: 10V range, 12V full scale8808A: 20V range.So you can see those should have no issues with peaks going out of range and the CF is actually less than 2 for this waveform. However, the handhelds showed a little improvement and both read a bit over 3.0V on their 50V ranges. Still some of this is BW (both meters are only specified to 100kHz) and some is CF (specified as <3.0 at FS). To sort that out I tried slowing the waveform down to 12kHz and then I got:Fluke 289 (5V range) 3.16xx V (50V range) 3.206 VFluke 189 (5V range) 3.17xx V (50V range) 3.211 VThose readings are within the specified tolerances for both of those ranges once you do the math. So the issue with the handhelds and the 120kHz signal seems to be mostly BW or perhaps some combination.

author: bdunham7
author_rank: Super Contributor
timestamp: August 08, 2023, 08:36:44 pm
content: Quote from: gnuarm on August 08, 2023, 06:01:20 pmHow 'right' do you expect them to be? The meters that are specified to handle this signal got it right, the others took a swing with varying results. The ones with suboptimal results simply don't have the BW. The OP's question was "Can any "true RMS" multimeters measure..." I think I've shown two that can, some that sort-of almost can and some that can't.You could calculate the RMS from what I specified but you'd still have some small error due to the AWG not being perfect. Or, if you like, I can pick a different waveform that will be easier to calculate. I think 1% is good enough for the OP's purpose and I'm confident the two large meters are within that. And the scope is right there as well, within reasonable expectations anyhow.

author: Someone
author_rank: Super Contributor
timestamp: August 08, 2023, 10:47:17 pm
content: Quote from: bdunham7 on August 08, 2023, 08:36:44 pmQuantifying the accuracy is the important part here, as the data sheets for multimeters put the limit somewhere (for example 1% for a 200kHz sine wave) but they may well produce acceptable results beyond those "limits" particularly if the user accepts reduced performance or manual calibration/comparison.

author: siealex
author_rank: Regular Contributor
timestamp: August 08, 2023, 11:20:27 pm
content: Quote from: gnuarm on August 08, 2023, 05:55:58 am3.0 V would kill a VFD designed for 2.4 V +/- 10% in a couple of hours. And it operates perfectly. How?

author: bdunham7
author_rank: Super Contributor
timestamp: August 08, 2023, 11:35:39 pm
content: Quote from: siealex on August 08, 2023, 11:20:27 pmAre you assuming that it would burn out that quickly or have you done actual tests? If you are convinced that there has to be a discrepancy somewhere, tell us exactly how you are measuring this voltage, which I presume and hope is directly across the VFD.As for theories, perhaps the VFD filament is a bit inductive and would burn out on 3.3VDC, but at this frequency the current is a bit less. That's a stretch, but I can't think of anything else offhand.

author: bdunham7
author_rank: Super Contributor
timestamp: August 09, 2023, 12:38:59 am
content: Quote from: Someone on August 08, 2023, 10:47:17 pmTrue, but that's a tricky area and requires specific characterization. For example you might find that a meter has better-than-advertised half-scale CF capability at half of specified BW and better than advertised sine wave BW, say 1% at twice the specified maximum. However, if you tried to measure something with both of those over spec you it might not work well due to slew rate limitations since slew rate is one possible limiting factor for both parameters. Also, meters that use the AD63x and AD73x TRMS converter chips seem tocover upincorporate its various nonlinearities, slew rate and other limitations into one single accuracy specification. It might seem better than advertised on some signals, but that spec is there because they know full well it won't be as good on others.I think the best and most obvious solution for most users is simply a decent 10-bit or 12-bit DSO. If you calibrate it with a sine wave, you can be pretty sure it isn't going to suffer from any of the issues that a TRMS converter chip has and will give you a reasonable result as long as you keep the signal on screen and watch the gating, sample rate, etc.

author: gnuarm
author_rank: Super Contributor
timestamp: August 09, 2023, 01:19:24 am
content: Quote from: bdunham7 on August 08, 2023, 08:36:44 pmNone these measurements are close to the actual value. You can piecewise integrate this by hand to find a number that is much closer to 4V. The voltage is around -3V for more than half the time, then spends over 20% of the time at over 6V. Given the square involved, this 20% will be a large part of the result, pushing it to closer to 4V.That's why all the measurements are wrong.

author: bdunham7
author_rank: Super Contributor
timestamp: August 09, 2023, 02:12:37 am
content: Quote from: gnuarm on August 09, 2023, 01:19:24 amAre you referring to the OP's waveform or my example? Clearly I can't measure the OP's signal from here.... If you are using the displayed values of -3.04V and +6.70V, then you're not reading the scope properly--the top is less than 6.00V and the bottom is just a bit less than -2.00V. Those peak numbers are noise and overshoot. I think his scope display is about right but I didn't set out to prove that.Now if you doubt my measurements onmytest signal, I have a simpler example with easy math. Instead of replicating the long fall time, I just used a top of 6.00V, a bottom of -2.00V, a duty cycle of 25% and rise/fall times of 8.4ns--the minimum for the AWG. So if you ignore the rise/fall altogether, you'll get an RMS value of √12, or about 3.464V.In fact, the 8506A measured that as 3.438xxx volts and the scope measured it as 3.45xxxx volts. The scope seems to be about 0.4% higher than the meter on all signals including sine if I engage the 20MHz BW limiter, which seems reasonable to me. So I'm pretty sure the actual voltage in this case is 3.438 and the 0.7% discrepancy between that and the calculated value is about what you get from the seemingly miniscule 8.4ns rise/fall times.

author: gnuarm
author_rank: Super Contributor
timestamp: August 09, 2023, 03:55:30 am
content: Quote from: bdunham7 on August 09, 2023, 02:12:37 amOk, you got me. I made a stupid assumption you were trying to approximate the OP's waveform, so I used his values. With -2V for the low end, I suppose you would get a much lower value. But to what end?QuoteWhy -2 and 6, instead of values more like the OP's? What does your emulation tell us?QuoteI don't know what "case" you are talking about.

author: bdunham7
author_rank: Super Contributor
timestamp: August 09, 2023, 04:11:16 am
content: Quote from: gnuarm on August 09, 2023, 03:55:30 amI picked -2 and 6 because the OP's values are close to -2 and 6. My emulation tells us which multimeters are capable of accurately measuring such a signal and which ones don't do as well. That was the OP's actual question. To do that I generated a signal with a more or less known RMS value and compared.QuoteThe case where I simplified the RMS calculations by eliminating the 1µs fall time. With this signal it can be easily calculated that the actual RMS value is very close to √12. It's still similar enough to the OP's waveform that it would be valid for determining what type of meters could accurately measure this type of signal.

author: sonpul
author_rank: Regular Contributor
timestamp: August 09, 2023, 04:49:35 am
content: On one of the forums I saw a discussion of this issue. In it, someone made a simulation in Micro-Cap by digitizing the graph. The calculation showed that the green RMS line tends to 3.34V RMS.

author: gnuarm
author_rank: Super Contributor
timestamp: August 09, 2023, 05:45:16 am
content: Quote from: bdunham7 on August 09, 2023, 04:11:16 amOk, looking at it more closely, I realize the scope reported values were pretty far off. So -2V and 6V are better estimates.