21-11-2012, 06:53 AM
Thanks for the paper, Keith - lots of good stuff in there.
One small question/issue, if I may... You mention about some meters having an "RMS" setting and you warn that this is typically limited by frequency. However, there is a hidden issue with RMS measurements on most meters.
By definition, the RMS value of a waveform is the DC equivalent constant voltage or current that would cause the same heating effect in a purely resistive (not reactive) load over the sample period. For a steady-state DC system this is simply P = I * V; with varying values this becomes Prms = Irms * Vrms. "RMS" stands for "Root Mean Square" - the so-called "quadratic mean" value - it turns out that the True RMS value of a signal as computed by the quadratic mean is identical to the DC equivalent voltage of the waveform - Google for the first-principles maths if you need that.
The original analogue meters that measured RMS current values did indeed use a pure resistive load with a thermocouple that measured the temperature rise and displayed the RMS power via that - as we shall see, this was a far "truer" RMS reading than most digital RMS or "True RMS" meters give.
For a pure sine wave, Vrms = Vpeak / squareroot(2) and likewise Irms = Ipeak / squareroot(2).
There are two points here - the first is that pretty much every cheapo meter does indeed assume a sine wave for AC, and thus the "RMS" I or V value is normally an estimate calculated from the above equations.
A "True RMS" meter does (or should!) not assume a pure sine wave or a periodic waveform at all - it should be waveform independent and should sample at a far higher frequency than its specified highest frequency - using the Nyquist criteria, this should be at least twice the peak frequency, but for a good meter, at least 4 times or higher (e.g. 10x). The value displayed should be the true RMS value calculated between display updates (the square root of the arithmetic mean of the squares of the sample values taken during the interval).
Herein lies the problem. Nearly EVERY so-called "True RMS" meter I've seen is AC coupled on the RMS settings. This means that any DC component (aka "offset") in the signal under test (SIT) is ignored - this flies in the face of the definition of an RMS value and I'm not just being picky and a purist here - this can be important.
You can easily check if your meter handles or ignores any DC component by setting it to measure RMS volts and applying a DC voltage. If it reads 0, then the RMS scale is AC coupled and the meter is giving incorrect results - think about it - the RMS value of a steady-state DC voltage should be the same as that DC voltage.
Some meters - e.g. I have a Tektronix DMM 916 - are genuinely "True RMS" as they are DC coupled and can accurately measure real RMS values for current & voltage - in the case of the DMM 916, up to 2MHz - what's more, for compatibility with most engineers' incorrect expectations of RMS, the DMM 916 has an AC-coupled True RMS setting too, but at least it makes that explicit !
Most meters when measuring RMS or True RMS lie to you as either they assume a pure sine wave and estimate the result and/or are AC coupled so that any DC offset is incorrectly ignored. Its a convenience & cost saving for the meter manufacturer as the resulting signal is centred around zero meaning a simple peak measurement and maths can give a sort-of RMS-ish value.
Note that the old "heat a resistor and measure the power it gives off" method is, assuming you can measure the resultant power accurately, by definition the most accurate way of doing this as the resistor's thermal lag integrates any signal nicely.... also, note that for small signals, unless the meter uses an ideal precision rectifier, small signal RMS AC values may have a large error component.
Cheers
One small question/issue, if I may... You mention about some meters having an "RMS" setting and you warn that this is typically limited by frequency. However, there is a hidden issue with RMS measurements on most meters.
By definition, the RMS value of a waveform is the DC equivalent constant voltage or current that would cause the same heating effect in a purely resistive (not reactive) load over the sample period. For a steady-state DC system this is simply P = I * V; with varying values this becomes Prms = Irms * Vrms. "RMS" stands for "Root Mean Square" - the so-called "quadratic mean" value - it turns out that the True RMS value of a signal as computed by the quadratic mean is identical to the DC equivalent voltage of the waveform - Google for the first-principles maths if you need that.
The original analogue meters that measured RMS current values did indeed use a pure resistive load with a thermocouple that measured the temperature rise and displayed the RMS power via that - as we shall see, this was a far "truer" RMS reading than most digital RMS or "True RMS" meters give.
For a pure sine wave, Vrms = Vpeak / squareroot(2) and likewise Irms = Ipeak / squareroot(2).
There are two points here - the first is that pretty much every cheapo meter does indeed assume a sine wave for AC, and thus the "RMS" I or V value is normally an estimate calculated from the above equations.
A "True RMS" meter does (or should!) not assume a pure sine wave or a periodic waveform at all - it should be waveform independent and should sample at a far higher frequency than its specified highest frequency - using the Nyquist criteria, this should be at least twice the peak frequency, but for a good meter, at least 4 times or higher (e.g. 10x). The value displayed should be the true RMS value calculated between display updates (the square root of the arithmetic mean of the squares of the sample values taken during the interval).
Herein lies the problem. Nearly EVERY so-called "True RMS" meter I've seen is AC coupled on the RMS settings. This means that any DC component (aka "offset") in the signal under test (SIT) is ignored - this flies in the face of the definition of an RMS value and I'm not just being picky and a purist here - this can be important.
You can easily check if your meter handles or ignores any DC component by setting it to measure RMS volts and applying a DC voltage. If it reads 0, then the RMS scale is AC coupled and the meter is giving incorrect results - think about it - the RMS value of a steady-state DC voltage should be the same as that DC voltage.
Some meters - e.g. I have a Tektronix DMM 916 - are genuinely "True RMS" as they are DC coupled and can accurately measure real RMS values for current & voltage - in the case of the DMM 916, up to 2MHz - what's more, for compatibility with most engineers' incorrect expectations of RMS, the DMM 916 has an AC-coupled True RMS setting too, but at least it makes that explicit !
Most meters when measuring RMS or True RMS lie to you as either they assume a pure sine wave and estimate the result and/or are AC coupled so that any DC offset is incorrectly ignored. Its a convenience & cost saving for the meter manufacturer as the resulting signal is centred around zero meaning a simple peak measurement and maths can give a sort-of RMS-ish value.
Note that the old "heat a resistor and measure the power it gives off" method is, assuming you can measure the resultant power accurately, by definition the most accurate way of doing this as the resistor's thermal lag integrates any signal nicely.... also, note that for small signals, unless the meter uses an ideal precision rectifier, small signal RMS AC values may have a large error component.
Cheers
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