# Mic calibrations & phase: how the pros do it



## Anechoic (Jan 16, 2009)

I just got back from the Internoise 2012 conference in NYC. The conference is geared toward noise control (my day job) but they had a session to discuss microphone calibration issues. As you might image, my interest was piqued.

There were papers given my representatives from calibration labs in Europe and South America, as well as mic manufactures such as Bruel & Kjaer and 01dB. Most pro measurement mics are calibrated using electrostatic actuators to determine the pressure response, and then a correction is applied to derive the free-field (or diffuse field) responses. However it seems that there is interest in determining the free field response directly using the substitution method, which requires a measurement setup similar to what I put together for my calibrated mic measurements. Several of the papers address issues related to improving the accuracy and precision of these calibrated measurements.

These labs care very much about the precision of their measurements and it shows. I haven't done a statistical analysis of my measurement setup but based on the comparison of my setup with results taken from NIST-traceable calibration labs, as well as the repeatability of my setup, I've always but the precision of my method at around +/- 1 to 1.5 dB between 100 Hz and ~8 kHz, with the tolerance increase by a dB or two above and below that range. The error bars these guys are dealing with are around +/- 0.3 dB up to 20 kHz, and around +/- 0.7 dB out to 40 kHz! The session had a lot of discussion about things they could do in increase precision by 0.05 dB or so.

So in general, those guys seem to do things like I do, with slight changes to increase the accuracy of the method (most of which I was aware of, one of which I was not).

For example:

1. For the free field measurements, the reference speaker driver is placed in (an approximation of) an infinite baffle, usually in a wall or the floor, to prevent diffraction off the edge of the baffle from causing problems. I use a loudspeaker in a box and I'm aware of the diffraction problem (and I correct for it). As much as I would love to have an infinite baffle, I just don't have the space for it right now.

2. Rather than putting the test mic on a mic stand, the mic is usually suspended either by it's cable (for vertical measurements, where the speaker is embedded in the floor) or by strings in horizontal measurements. Once again, I am aware that the mic stand can cause problems with the measurements (and again I correct for it) but I can't practically support the mic using another method.

3. One of the big questions that came up was whether or not to use time gating to window out reflections. The preference was to not use any time gating, but the reality was that even in the largest rooms shown in the presentations, comb filtering from the early reflections was still a problem, so folks reluctantly used a window.

4. One thing I was _not_ aware of: the microphone "center" at the diaphragm actually changes with frequency by a few mm, so that for a proper mic calibration, the microphone should be moved slightly closer or farther away depending on the frequency being measured. A couple of the setups shown in the session have the mic supports connected to a motorized mount that automatically moves the mic back and forth by the required distance as the frequency changes. So, yeah, that's a setup that's a little out of my price range right now, especially since it might only get be a couple tenths of dB in precision, but there is an IEC standard that can be used to calculate the mic-center distance, so I'll review it and keep it in my pocket for future consideration.

I was pleased to see that I was doing things "right" however. 

After the session, I spent time at the exhibition hall to hobnob with the venders. I spent a little time at the B&K both, and at the end of the exhibition, I had a 15-minute talk with a B&K rep about everyone's favorite topic: how to measure microphone phase.

As I've mentioned before, they generally don't care about the absolute phase of their mics, they tend to be more concerned about the phase difference between any two arbitrary mics, especially for their sound intensity measurement rigs. But they can and do measure absolute phase. The preferred method appears to be using the electrostatic actuator method since they can control the phase of the actuator. They also do substitution methods using a reference mic with a known phase curve. 

I asked the rep about whether condenser mics can be considered minimum phase devices. He said that at the low frequency end, where the response/rolloff is controlled by the back venting of the diaphragm, condenser mics are _not_ minimum phase. However, at the higher end, near the diaphragm resonance frequency, condenser mics can be considered minimum phase, which would imply that above the range affected by the diaphragm back vent (above around 100 Hz) it's probably okay to assume condenser mics are minimum phase.

However, getting back to the electrostatic actuator method for measuring phase, if the phase response is proportional to the actuator response, that means the phase response is proportional to the pressure response of the mic, not the free-field response. That would mean that the Hilbert transform needs to be performed on the pressure response, not the free-field response, so that still complicates things. However I do have the pressure responses of my reference mics, so I suppose I could try to back out the phase of one of those mics, and then measure phase of of other mics using the substitution method. Again, something to keep in my pocket until I have time to research it further.

All-in-all, a very worthwhile trip for the metrology session alone.


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## Barleywater (Dec 11, 2011)

Microphone referencing by substitution employing inverse transfer function of real impulse responses from time domain:


A Behringer ECM8000 microphone referenced to Earthworksaudio OM-1 microphone:


Spectra are FFT 65k, Blackman-Harris windowing. Sampling rate is 44.1kHz. Results show difference of ECM8000 spectrum from OM-1 spectrum. Three results are shown using three different test fixtures: Aura 2” full-range driver (violet trace), Peerless 2” full-range driver (red trace), and Vifa NE25VTA-04 tweeter (green trace). 2” Drivers are mounted to 12” lengths of 2” diameter PVC pipe stuffed with Dacron. Microphones are placed on axis at less than 0.25” from driver surface.

For each test fixture frequency response difference is demonstrated with following procedure:

First the impulse responses of test fixture with OM-1 and ECM8000 are acquired using Log swept sine technique. Sweep is about 10Hz-22050Hz of 24sec long.

Then, for system incorporating OM-1, inverse transfer function is found such that convolution with impulse response returns identity function as Dirac pulse; spectrum is flat, and phase is flat. This demonstrates nulling of the reference response.

Inverse transfer function for OM-1 system is convolved with impulse response of test fixture with ECM8000 substituted. Resultant impulse response is difference of two systems, both in frequency and phase.

Results are referenced to 0db at 1kHz and displayed:












Detail 70Hz-2kHz:











0db shows results of reference impulse responses nulled with inverse transfer functions. Below is detail zoomed to about +/1 0.00001db:












The above method is used to reference OM-1 #2257 to its matched partner OM-1 #2224 using the Aura driver test fixture, producing the following result:









And using Vifa tweeter with sampling rate 96kHz and sweep length 12sec:










These results are in great agreement with the charts that came with the pair of OM-1 microphones.

(cont. in next post)


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## Barleywater (Dec 11, 2011)

*Part II:*

Since difference results are in the form of impulse response, its inverse may be derived and applied to any measurement made with microphone by convolution, producing a real corrected result emulating the result that would be obtained using the reference microphone:

Peerless fixture is set up with OM-1 microphone approximately 9” away on axis and impulse response acquired as above for reference measure. Measurement is repeated substituting the ECM8000 microphone. The two responses are displayed referenced to 0db at 1kHz:











Peaking typical of ECM8000 above 2kHz is clearly seen in above figure.

Detail:










The inverse transfer function is calculated for the difference impulse response of the OM-1 and ECM8000 as determined using the Vifa tweeter fixture in Part I. This is applied by convolution to the above IR of ECM8000 measurement of the Peerless fixture from 9”:









In figures above and below green trace is ECM8000 emulating the OM-1 response.










In the previous two figures it is seen that the fine grain structure of the ECM8000 response is mostly retained after the correction. Differences of the two microphones results are likely due to differing body sizes, end caps, capsule construction, and that no jig was used in locating microphones. The super near placement of the microphones to the test fixture during the referencing precludes free field behavior being captured. When using identically constructed microphones this is not a problem. The case of differing constructions is likely solved by performing referencing using conditions as in standard practice of substitution method.

Discussion:


The above where accomplished in living room with wood pellet stove blowers running.

This nulling method had profound implications for referencing transducers by substitution method.

Applied to closed coupler techniques undoubtedly enables exploration of low frequency.

P.S.

Herbert, 

I live just up the road and Turners Falls. I would enjoy an opportunity meet.

Regards,

Andrew


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## Anechoic (Jan 16, 2009)

Barleywater said:


> The above where accomplished in living room with wood pellet stove blowers running.
> 
> This nulling method had profound implications for referencing transducers by substitution method.


That's pretty much my procedure, the major difference is that I do everything in the frequency domain (which is basically the same mathematically except for phase errors) and I incorporate the reference response 

What is the gate duration you're using? 

Yeah, we should meet at some point, whenever my schedule stops being to crazy.


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## Barleywater (Dec 11, 2011)

Yes, collected this data in March. For demonstration no gates, fades, or smoothing are used.

Crazy's the word.

Andrew


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