Spark calibration of microphones

I actually seem to have the best luck just putting the sparker right next to the microphone (1.3") and using a very weak spark with no capacitance. I'm just touching some alligator clips together to trigger, and I suspect the arc drawn between them when the coilpack is loaded by a capacitor is one factor in the spark trains. I did think of using a powerful magnet to quench the arc, but haven't tried it yet.

The result does bear a significant resemblance to the datasheet curve.

The signal level for the close weak spark measurements is about the same as the far strong spark measurements, and the latter tend to have more of the LF problem. It seems to be correlated mainly with spark strength.

I know it is not noise because I can see it in the impulse response as a level shift after the impulse. After the impulse the signal is at a voltage offset and it slowly settles back into the background hum. The shift always follows the impulse in polarity. I can affect it by swapping coilpack polarity, but this does not change the polarity of the shift.

Another indication it's not noise is that it has a clean phase curve. Noise would not.
 

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You would also need to think about near and far field reflections and your window functions etc. I agree thats an odd result. I have several schemes I have been planning to test with two calibrated B&K 1/4" mikes to see what i learn. I have some stuff in the way right now but hopefully soon.
 

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I think I have some of those EM172 mikes. Once the Quad thing I'm doing is out of the way I'll set up to check them. I have seen in the past that the primo's do roll off above 10 KHz. I suspect that's very intentional since they do have others with extended HF.

My normal setup uses a Pioneer ribbon that's good to 60 KHz or so that I validate with the B&K's. It seems measuring above 60 KHz or so can be really problematic since the wavelengths are so short and I have seen that. The Panasonic ribbon is too large for those wavelengths and you get "fresnel" zones where the response changes a lot with a small change in distance. I'm really interested in spark gaps to extend the limitation in acoustic HF response testing.
 
Has anyone succeeded in generating the spectrum from equations 31 and 33 from the reference in post #19? I believe equation 33 is wrong, and cannot produce the spectrums shown in the plots. The cosine term does not have the same roots as the bessel function it replaces.

Substituting the cosine term with this works:

(sin(2*pi*t*time)/(2*pi*t*time)^2-cos(2*pi*t*time)/(2*pi*t*time))^2

I'm not a math genius, I got the idea here:

j1(x)=0 - Wolfram|Alpha
 
I suspect using flyback to generate the spark may be the wrong idea. The inductive source wants to keep the spark on after firing. This is known to be the case for spark plugs, lasting about 1.25mS in the glow discharge phase which is about the length of the level shift I am seeing. So I have been thinking that my LF response issues may be due to the spark staying on longer than it should due to stored energy in the coil.

If this is the case then what we want is a flyback circuit that charges a capacitor slowly through a diode. Slowly is important so that the generator doesn't have enough current to keep the spark alive. Perhaps a Marx generator with a resistor before the final capacitor.

Or perhaps use a R//C in series with the spark gap.

I think there must be a lower frequency limit to the doublet response where the thermal energy of the spark creates a pressure change. After all only 1-2% of the energy comes out as sound. A glow discharge period is just drawing the discharge out and releasing more heat.

Or maybe I'm still thinking about this wrong. We have a shockwave doublet which is great at HF but bad at LF. Then we have a thermal impulse which actually gives us something to work with in the low frequencies. If we can generate both with consistency, then this can actually lower the frequency limit for the measurement.
 
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It's fun that this thread has turned to the direction of spark gap calibration. I've done it, in an odd sort of way. I was recording a violent thunderstorm with a pair of mismatched mics - and AT-2020 and an MXL. I used the impulse of the thunderclap to match the MXL to the AT-2020 since I already knew the AT response. Seemed to work OK, and they were much closer in FR than I had thought.

For years I've wanted to use a spark gap to measure room acoustics but it's not an easy task. I've built many spark generators for theater use, Jacob's ladders, static electricity generators and such. We even used an 80 kV generator that was for painting or powder coating. Nice long sparks that look cool, but don't make much noise. You need a fat spark with very high current to make a big noise. It can be a short arc, but does need plenty of current for good SPL. Lightening strikes do that. :)

Just a data point for you. High current makes it loud, and seems to add LF energy.
 
That seems to agree with my observations, but why does no one else seem to comment on the LF part? I think it could possibly be derived from first principles.

I thought there was already a thread on spark calibration. I thought this was it, which is why I posted here. But maybe this should be moved to its own thread? I could make a new thread and include references in the first post.

BTW, I had the idea of putting a reflector behind the spark to see if the primary wave and the reflection both have the LF rise.
 
I am starting this thread to collect information on calibrating microphones using a spark discharge as a source and to move posts out of another thread. The spark creates a doublet, which is like a high-passed impulse. Therefore the recording of a spark doublet run through a lowpass filter can be used to calibrate a microphone at frequencies above 2KHz or so, if the spark is carefully generated.

However past the doublet BW (10-100KHz depending on how well you generate the spark) you get a comb filtered HF response and there are mathematical derivations for making a correction curve. Earthworks figured out how to generate a spark with 100KHz bandwidth which is of course their secret.

This is probably the first thread to read:

Calibrating microphones and speakers


Scott Wurcer made a short PDF on his calibration jig and results:
http://wavebourn.com/images/audio/Proins/spark.pdf


References:

Many of these include further references that may be useful.


A Study of acoustic radiation from an electrical spark discharge in air (1974)
By Robert Edward Klinkowstein (Equation 33 appears to be wrong, the cosine term does not have the same roots as the bessel function it replaces)
http://dspace.mit.edu/bitstream/handle/1721.1/13778/24459264-MIT.pdf?sequence=2


How Earthworks Measures Microphones
https://earthworksaudio.com/wp-content/uploads/2012/07/how-earthworks-measures-mics.pdf


EXPERIMENTAL STUDY OF A SPARK DISCHARGE AS AN ACOUSTIC
SOURCE
http://www.sea-acustica.es/WEB_ICA_07/fchrs/papers/nla-02-004.pdf


Characteristics of a spark discharge as an adjustable
acoustic source for scale model measurements
Christophe Ayrault, Philippe Béquin, Sophie Baudin
https://hal.archives-ouvertes.fr/hal-00810828/document


Boston Audio Society November 2009 Meeting — Microphone Testing Clinic
http://www.bostonaudiosociety.org/pdf/BAS_2009_Microphone_Clinic_Report.pdf



Paywalled:
R. J. Wyber, ”The Design of a Spark Discharge Acoustic Impulse Generator”, IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-23 (2), 57-162 (1975)

Acoustic Impulse Generation by High Energy Spark Dischargers
http://www.aes.org/e-lib/browse.cfm?elib=3048



Not directly related:

Room Acoustic Scale Model Measurements using a "Spark Train"
https://acoustics-engineering.com/files/SPARK TRAIN MEASUREMENTS.pdf


Characteristics of Acoustic Response from Simulated Impulsive Lightning Current Discharge
https://www.researchgate.net/public...mulated_Impulsive_Lightning_Current_Discharge


An optoacoustic point source for acoustic scale model measurements
https://www.researchgate.net/public..._source_for_acoustic_scale_model_measurements
 
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One quick note, I did my experiment before I found any references to the N wave analysis (there is an older one also available free BTW) so I just guestimated. If you look at the plot you can sort of see the first null of the Bessel function so making the theory and data line up there should be pretty close up to 20kHz or so, no idea about going beyond that. The mic I had came with a calibration done in a B&K isolation chamber and it was certainly <1dB off up to 20kHz.
 
Well, I thought I would get to keep first post so I could keep the references updated. :/

Anyways, here is why it seems there is an impulse characteristic hidden in the doublet. Here is a simulator plot next to a picture from one of the references. Orange is a perfect doublet, yellow is an impulse, and red is both together.
 

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One comment, I usually ignore the low end because most omnis are fairly ideal pistons down to their low limit. I've played a little with medical pressure transducers, one in particular from GE that is dead flat to DC and goes up to 3500Hz or so. It also is calibrated (gauge or absolute). It works as a low frequency microphone but at very low sensitivity.

There is a utility called "digitize" that can grab plots from an article and send them to other software. You could take that plot and send it to an FFT program for instance. It allows you to click on the grid to scale the data.
 
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The sound from a spark is a thermal event so the combined nonlinearity of air compression and air thermal conduction will have an impact. (I got a long lecture from Dr. Hill of Plasmatronics on this. I understood very little.) I suspect it would help explain some of what you see. You also need to be pretty careful that you are not also picking up the EMI from the spark.

Popping balloons is another good way to make an impulse. I can imagine the Rube Goldberg apparatus needed to pop on trigger.