True RMS
With measuring instruments we can often come across the term True RMS. What it means when and where it is used and when it is important for your measuring device to be marked with this magic name is in this article.
With this concept we encounter in the measuring technique where the voltage is measured, the current in the area of AC therefore alternating course. This is a way of measuring the effective value of these quantities but let’s start nicely from the beginning.
Effective value
For a start, let’s imagine sinus voltage an effective value of 230V 50Hz. Do we have to start by asking ourselves what is the effective value of voltage? The effective ac voltage value is a number that tells us how much the DC voltage value would have to be to give rise to the same thermal effect as the ac voltage mentioned above. In our case, this means that if we were to join, for example the heating element on this AC voltage source the same thermal effect would also give us a DC voltage source of 230V. So in the case of an effective value, we always talk about some kind of relationship versus DC’s tension to the thermal effect it would perform. In addition to the effective value, we still know other things, such as the peak, average etc.
Peak value
The peak value of the AC voltage (in our sinus course example) is the max value achieved by the AC course. In the case of a purely sinus course, this can also be defined mathematically as the second root of the number 2 multiplied by the effective value. So if we label the effective voltage value as Urms and peak as Upk then we get the formula:
Upk = √2 . Urms
In our example, it will be approximately 325V, but caution !!! this applies only if the course is purely sinus.
Mean
The mean voltage is essentially the arithmetic mean theoretically infinite of virtually a large number of measured samples of a given course. It doesn’t matter if it’s a purely sinus signal or some other course. With a high number of measured samples, we get a figure that is very close to the actual mean value. If we labeled it as Uav so:
Uav = (U1 + U2 + …. + Un) / n
in the case of a sinus course, the mean value can also be expressed as:
Uav = 0.637 . Upk
In our example, it is approximately 207 V
We can therefore measure the peak value by some absolute-shaped maximum detector. Mean value as the arithmetic mean of the individual measurements which, if they are in sufficient numbers (the sampling frequency will be sufficient given the accuracy we require). However, the effective value is problematic in that its definition is about the thermal effect. If we are sure that we will always measure the sinus or quasi-sinus course, we will need a methodology for measuring the mean (arithmetic mean) that we multiply by a constant that corresponds to the effective value of the sinus voltage. Since we can calculate the peak value, and we can also calculate the effective one from the peak, we will get a constant that will be sufficient to calculate from the mean value effective. On this principle, most of the cheap multimeters work which we can trust in the sinusoias of the measured signal.
What about the non sinus course?
If the measured signal is different from pure sinus (triac regulators, PWM signals, etc.) we get to a situation where cheap multimeters respectively. those who cannot boast a magic True RMS formula convey a false figure to us and therefore cannot use them in these cases !!! On the contrary, measuring instruments labelled true RMS will measure the correct effective value even in the case of non-sinus progressions and thus in cases where the signal shape is different from the sinus or we are not sure what it is in reality, we should always use a measuring instrument labelled True RMS.
So what is “True RMS”?
We already know that measuring instruments with this marking can convey a true indication of the magnitude of the effective value of the measured quantity even in the case of a non-sinusoio course, but what it really means and on what principle it works we will say right now.
We have already explained the difference between the mean value and the effective value of any course. First, we need to ask ourselves what relationship is warm to tension or current. Heat as a loss-long power can be expressed as a product of voltage and current (in case we consider only a purely resinal load ie. pure ohmic resistance with zero reactance). If we mark the voltage as U current as I and heat as P then:
P = U . I
The volt-ampere characteristic of the resistive load is linear i.e. if we increase the n-fold voltage, the current flowing through this load will increase, so that in the event of a 2-fold increase in voltage, the flowing current will also be doubled and thus the thermal loss power increases 4x. It’s better to see if we’re going to put in a formula under OHM’s law, for example. instead of current, the resdetectable load value. Ohm’s Law says:
I = U / R
so after the commissioning we receive :
P= U . U/R
after a little adjustment we get
P = U²/R
It is already clear here that power grows with the square
If we go back to that efficiency, we said at the beginning that it was a value that corresponds to the same thermal effect of DC voltage. In the case of AC course, it is therefore a kind of average similar to the mean, but in this case it will not be an arithmetic average but a square. Ideally, this would be the proportional mean of the infinite number of measured samples. In the real world, it will be as many samples as possible or which will be the accuracy of the measurement that we require. The square average is also called Root Mean Square i.e. RMS.
Urms =√( (U1² + U2² + … + Un²) / n)
The principle difference in measurement by a common and True RMS measuring instrument thus consists in the fact that the ordinary multimeter uses an arithmetic mean for this measurement which adjusts by multiplying a certain compensatory constant to achieve relatively good accuracy in the sinus flow area, wherethe True RMS multimeter uses the calculation in the form of a square diameter when measured, thus reaching a level of good accuracy for almost any shape of the measured signal.
In conclusion, the
The issue of measuring effective value is, of course, expressed mathematically mainly in the field of integration and derivation, but in this post it was about showing it in a simpler form based not so much on mathematics as on logic and logical determination. If you want to verify this post experimentally, you can do so e.g. on the triak light regulator where if you set the control value to 1/3 max. level and you will load it and measure the output voltage with two multimeters of output voltage, one of which will be ordinary and the other will measure True RMS, you will surely see the difference in measured values. In this case, trust the measuring instrument with the True RMS method of measuring AC ranges.
OM4IK Igor