# RMS value of fundamental harmonic vs RMS of third harmonic

If we have a periodic signal (square wave) with amplitude of 100V. Then what would the RMS value of the fundamental harmonic be compared to the RMS value of the third harmonic?

Am I correct?

• It depends on the shape (instantaneous amplitude profile) of the waveform. – Andy aka Sep 19 '19 at 11:28
• The third harmonic of a triangle wave has another RMS value than the third harmonic of a square wave. The shape is extremely important. – Harry Svensson Sep 19 '19 at 12:40
• @Andyaka I edited my question in order to be more precise. Thanks for pointing it out – maverick98 Sep 19 '19 at 13:42
• 100 Volt per period? So after more periods have passed, the amplitude gets larger? The amplitude is just 100V, period. Not per period. – Bart Sep 19 '19 at 13:47

Depends on what kind of periodic signal it is. As @Andy Aka mentioned: "Amplitude Profile" or How its amplitude changes with time (Triangular, Square or others ?).

Whatever be the complex periodic wave you have (say amplitude =$$\ V_o \$$ , Period = $$\T = 2\pi/\omega\$$), it can be represented as sum of fundamental frequency and its harmonics.

$$V(t) = V_f(t) + V_2(t)+V_3(t).....V_n(t)$$ where fundemental frequency component is -

$$V_f(t) = V_osin(\omega t)$$

Harmonics are - $$V_2(t) = V_2sin(2\omega t)$$ $$V_3(t) = V_3sin(3\omega t)$$ $$.$$ $$V_n(t) = V_nsin(n\omega t)$$ So, the nth harmonic's RMS value would be: $$V_{n(rms)} = \sqrt{\frac{1}{T}\int_0^TV_n^2sin^2(n\omega t)dt}$$

The amplitude of the wave $$\V_0\$$ is not enough information to determine what would be the amplitude of the nth harmonic ie., $$\V_n\$$ . So you cannot formulate a direct relation between rms value of the fundamental wave and its nth harmonic just with that information.

• What happened to the odd harmonics? – Andy aka Sep 19 '19 at 12:12
• oh ya good catch :D – Mitu Raj Sep 19 '19 at 12:15
• @Μitu Raj if it is a square wave, can we know then? – maverick98 Sep 19 '19 at 12:19
• You can expand its fourier series and find it. – Mitu Raj Sep 19 '19 at 12:24
• check out fourier analysis section here: en.wikipedia.org/wiki/Square_wave @maverick – Mitu Raj Sep 19 '19 at 12:30