# Electromagnetic radiation from spark gap

I am an electrical college student.

I learned from some papers, sites online, including this forum that lightning discharge or any electrical arc emits wideband radio frequency because the odd integer harmonics of a square wave and an electrical arc is similar to a square wave. (Correct me if I am wrong, please)

Today I tried to generate an impulse voltage with a multistage impulse generator.

Here is the picture of the waveform from the oscilloscope:

• White: impulse voltage without air breakdown.
• Yellow: impulse voltage with air breakdown (electrical arc occurred on the sphere gap)

When I generate the impulse voltage with air breakdown, it creates an arc on the sphere gap. Can I get the frequency domain from this yellow wave with fourier transform? I do not really understand it yet, but since this is a non-periodic wave, can I get the frequency spectrum?

I want to know what exactly the electrical arc creates electromagnetic waves on a very wide frequency really means, and how.

• The Fourier transform works on any input signal. Try it and see! Dec 16, 2020 at 4:58
• An EM wave is "constructed" by both voltage and current and also how these signal events "couple" into the impedance of space in the far field. The near-field analysis is largely irrelevant for predicting the amplitude or spectral content of a far-field EM wave. Dec 16, 2020 at 10:53
• @Andyaka how can i determine the far-field from a spark? i only found about how to determine it with an antenna transmitter far field, but how i suppose to do it with a spark gap? Dec 20, 2020 at 5:43
• I'm unsure how to move this one forward @RamandaNvl Dec 20, 2020 at 10:22
• FWIW, the actual discharge is probably much faster then 3us or whatever you have up there. Dec 24, 2020 at 0:18

Spark in a gap means that the current starts. There's often some light because the air in the gap is violently disturbed and the electrons in molecules get short term excitation. But the start of the current is the actual radiowave maker. The spectrum of the radiowave depends in a complex way on the waveform (=how fast the current starts) and the dimensions of the area where the current starts. That's because antenna theory shows the radiation intensity with a certain current strength and waveform depends on the dimensions of the area where the current occurs.

Unfortunately also the wires and the edges of the gap are a part of the system where the current suddenly starts. They can as well radiate. They also have capacitance and inductance which radically affect what's the actual waveform of the starting current. Early radio makers especially tried to initiate narrow band oscillations with sparks to get as sinusoidal radiation as possible. It helped to get design problems manageable.

People can present objections when I didn't mention voltage. It has as big role as current. In a gap generally the voltage collapses because the air becomes very conductive. But actually the interesting voltage is what's induced by the accelerating current. Static nor linearly growing current do not radiate.

Unfortunately there's no easy way to calculate the caused radiation, one must solve ultra complex space vector field differential equations. Antenna designers use either numerical methods or make approximations by dividing the current area to elementary dipoles. If you want to learn it prepare to study say one full days university level math to be able to understand it.

Your Oscilloscope image doesn't give any possibilities to even guess the generated radiation after assuming a certain gap because the interesting part - the rise of the current - is out of the resolution, it looks vertical. You have used far too slow equipment.

If your gap is the open end of a 2 parallel wire transmission line which is fed by a properly terminated voltage source you have a theoretical possibility to get radiation only from the gap with no resonances of the wires, but only in the usable frequency range of that transmission line. That radiation could be in theory be measured with a measurement antenna and spectrum analyzer.

Prepare to some real work because the receiver must be far away and its antenna must be small to prevent any phase difference problems due the distance differences between the parts of the gap and the parts of the receiving antenna. You must do a long integration to pull the noise levels down. You need non-echoing room.

"Can I get the frequency domain from this yellow wave with fourier transform?"

If you can get the event to repeat, and can trigger the scope reliably on the rising voltage (shouldn't be a problem by the looks of it), then you can indeed use the scope's FFT function to get a spectrum. (but see the other responses about how this isn't the same as the emitted radiation)

"since this is a non-periodic wave, can I get the frequency spectrum"

yes, even non-periodic functions can be expressed as a sum of sines, cosines, and exponential rise/decay, which is the idea behind the fourier transform and its relatives. The exponentials are complex frequency.