When I went through EMC testing of some electronic boards, I observed that the frequencies of the EM waves generated by the boards are at the fundamental frequency with multiples of some whole number. For example, I have an oscillator that produces a 25 MHz square wave. The EM waves generated are like 125 MHz, 175 MHz, 250 MHz, and so on. I found that these are all because of the harmonics. But I can't get why harmonics occur only in whole number multiples. Why not 11.3 times the fundamental frequency ? What's the physics behind this, or is it just a theoretical representation ? Can anyone provide some direction for understanding these things ?

To add more details, the oscillator I used is a MEMS type oscillator. The part number is "ASDMB-25.000MHZ-LC-T".

  • \$\begingroup\$ The two answers provided assume that your 25 MHz oscillator is producing a square wave? Is this really the case, because an ideal sinusoidal oscillator would only have a single frequency component, at the fundamental. \$\endgroup\$
    – SteveSh
    Feb 25, 2022 at 14:24
  • \$\begingroup\$ Yes, @SteveSh, the oscillator is producing square waves. \$\endgroup\$
    – Vignesh C
    Feb 28, 2022 at 6:33

3 Answers 3


An ideal square wave with a 50% duty is a sum of sine waves with a base frequency and only odd harmonics.

If the edges of the square wave do not trigger another system to resonate (such as parasitic LC components) then it won't resonate at non-integer multiples.

But it is of course possible that for example a 100 kHz square wave triggers a resonant frequency at 3.141592 MHz in some circuit too so there may be bursts of 3.141592 MHz bursts at a rate of 100 kHz.

  • \$\begingroup\$ Thanks for your response. BTW, Do you mean , the MEMS oscillator produces the square wave by summing different sine waves ? \$\endgroup\$
    – Vignesh C
    Feb 28, 2022 at 7:07
  • \$\begingroup\$ @VigneshC No I don't mean that, I have not said such a thing. Those are two completely unrelated concepts. What matters is that you have something that outputs a logic level square wave signal, never mind what it is that outputs square wave logic level signal. \$\endgroup\$
    – Justme
    Feb 28, 2022 at 8:11

If you construct a square wave from sinusoidal components you will find that it takes certain multiples of the base frequency to generate a signal of that shape. Odd positive integers with a 50 % duty cycle. You can perform a FFT analysis on a square wave or any other wave type to find it's approximate components.

In EMC tests you'll find which of these components find anything resembling an antenna to that specific harmonic frequency to radiate from. It usually doesn't take much.

Spread spectrum oscillators are devices that periodically change the base frequency, thus changing the harmonic frequencies too, which reduces the radiated power on a certain frequency, making it easier to pass EMC tests.

Waves propagate in a manner where electic and magnetic field intensities change over time is sinusoidal. Any other wave type than sinusoidal cannot be transmitted as a "radio wave" (it can surely be transmitted, especially over short distances if required). That is why measurement instruments are chosen to display what they do.


In order to add sine waves into the shape of a square pulse, all the sine waves must rise fall together at the edges observed with identical polarity. i.e. it must be synchronous to create the same wave for each cycle. That means it must be an integer multiple of the fundamental.

If signal was not filtered, and the pulse is narrow, then all the harmonics contribute in gradual declining amount with the harmonic until nearly a null or missing harmonic exists. This corresponds to the frequency that fits a full cycle within the 50% amplitude pulse width or "PW50". This pattern is recursive with repeating notches again at integer harmonics of that PW50 frequency.

When this occurs on a perfect square wave, that null harmonic is 2f and all the even harmonics.

However the parasitic resonance effects of LC or 1/4 wavelength structures tend to leak amplified high impedance harmonics.

You can select a square wave here and log scale with phase for the Fourier properties and hand draw any repetitive wave or change spectral amplitudes.

enter image description here

  • \$\begingroup\$ If the PW50 is not a perfect 1/n duty cycle , then the corresponding f will not be perfectly nulled and phase will not be synchronous, but shifted \$\endgroup\$ Feb 25, 2022 at 20:46
  • \$\begingroup\$ Hey Tony, you can synthesize a square wave using an infinite sum of sinusoids (cosines) with different frequencies (harmonics) right? If you send a square wave through an op-amp with a high THD what will happen? Will the signal get ruined? Hopefully my question is clear. \$\endgroup\$
    – Carl
    Feb 25, 2022 at 20:56
  • \$\begingroup\$ Why don't you be the judge and use the link and listen \$\endgroup\$ Feb 25, 2022 at 21:19
  • \$\begingroup\$ Thanks Tony. It does make a huge difference. Btw, I didn't know that Falstad also included audio in their simulations but apparently they do! \$\endgroup\$
    – Carl
    Feb 25, 2022 at 21:23

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