Hi Electrician,
That's not really true is it?
When I said "...which works only with RMS values. ", I meant it in the most general sense. When combining quantities RMS wise (square root of the sum of the squares), and if said quantities are not all sinusoidal (or possessed of some other shared waveshape) such that the ratio of peak to RMS is the same for each of the individual quantities, then one must combine RMS wise using the RMS values of the quantities, not their peak values.
If one had a peak value for the sum of several harmonics and then wanted to add another harmonic to the mix, adding (RMS wise) the peak value of the next single harmonic to the peak value of the previously existing sum of several harmonics won't necessarily give the peak value of the total. This is because, of course, the ratio of peak to RMS (crest factor) for a sum of several harmonics is not necessarily the same as the crest factor for a single sinusoid.
In the particular case where the individual components to be added together are all sinusoidal and are to be combined all at once then each component may be multiplied by any constant (such as peak to RMS) and then combined RMS wise. But this only works if all the components have the same crest factor.
Using the RMS wise addition of RMS components always works to give an RMS sum no matter what the waveshape of the components. It's better to get in the habit of using the RMS value of individual components when combining RMS wise.
Hmm; I was always taught that 1 + 1 = 2.
1 + 1 does equal 2 when you use the right point of view.
When RMS quantities are used, the underlying consideration is
power. That is the rationale for using RMS quantities in the first place. The RMS value (voltage perhaps) of a complex waveform is that voltage which would dissipate the same power in a resistor as a DC voltage of that same value.
So, when you have a waveform consisting of a fundamental of 10 volts and a second harmonic of 10 volts, the RMS value of the combination is 14.14 volts. Notice that the fundamental and second harmonic, individually would each dissipate 1 watt in a 100 ohm resistor. The combination of fundamental and second harmonic has an RMS value of 14.14 volts, which would dissipate 2 watts in a 100 ohm resistor; this is double the power dissipated by the fundamental alone.
The distortion using the second (the audio version) distortion definition for this waveform would be 70.7%; this is a ratio of RMS voltages. This says that the power dissipated in a resistor by the harmonics (in this case, only a second harmonic of the same value as the fundamental) would be 1/2 the power dissipated by the total waveform (fundamental and second harmonic). In other words (using the second definition), the distortion
power is proportional to the square of the distortion percentage (taken as a fraction) because the power a voltage E dissipates in a resistor R is given by (E^2)/R.