Measuring Phase Response of Drivers

[Iain McNeill]

I'm trying to measure the phase response of my drivers and the results I'm getting aren't what I expected. Has anyone successfully measured the phase response of their speakers?

I'm using an MLS test signal with a microphone at 1m on axis with the driver in a sealed cabinet measured out in the garden. With the electrical MLS signal used as a reference, the measured phase response also includes the delay due to the 1m travel time.

What I've done is subtract out a correction phase response corresponding to a pure time delay and iteratively tweaked the time delay to get the gentlest phase curve for the driver response (excess phase?) I've attached the response I got.

Does this look right? I guess I'm having problems with the low frequency acoustic output leading the electrical signal in. If I invert the signal from the microphone things look better but then my impulse response is upside down (peaks negative)

[Shaun]

You can apply a Hilbert-Bode transform (HBT) to your amplitude FR data to get the minimum phase response. Should give same result as your subtraction of distance data.

Getting the low frequency response right depends on a few factors:

1) Level of electrical noise in your measuring equipment (gets worse as you approach DC)
2) Sampling rate (you get better resolution at lower sampling rates)
3) Reflection off adjacent objects (do nearfield measurement of LF drivers, then splice them to you far field data of the whole system).

[Iain McNeill]

Of course, the Hilbert Transform, thanks for helping with the Alzheimers

Plotting HT on the same chart I get the attached so I guess I got some work to do. I'll try your suggestion of splicing near field measurements at different sample rates together using the free field as a paste template.

Great suggestions, thanks again!

[Iain McNeill]

As a sanity check I simulated a butterworth 2nd order high pass at 50Hz together with a 2nd order low pass at 2000Hz and compared to what I measured. It actually compared quite favorably. I tweaked the delay time compensation a bit more and got the attached curve which is pretty convincing in my mind.

So why didn't the Hilbert Transform agree? Hmmm.

[Shaun]

Iain

I believe that the effectiveness/accuracy of the HBT is dendent on the "rightness" of the data at the extremes of the FR plot, now that I think of it. So, achieving minimum phase response with HBT requires a bit of extra work. In the referenced document, the FR plot needs to be manipulated to get HBT to work correctly ("tailing off" at the extremes).

Acoustic Centre Evaluation using HBT

[HiFiNutNut]

So if our interest is to get accurate phase for at least 20Hz to 20kHz from HBT, what are the extremes of the frequencies should we use for measurement of amplitude response, which is realistic with normal mics and soundcards, for example, from 5Hz to 40kHz?

[dlr]

Originally posted by HiFiNutNut
So if our interest is to get accurate phase for at least 20Hz to 20kHz from HBT, what are the extremes of the frequencies should we use for measurement of amplitude response, which is realistic with normal mics and soundcards, for example, from 5Hz to 40kHz?

If you're using an MLS system with a good card that doesn't roll off prematurely and have calibration data for the mic to correct for its response, the result will have accurate phase data to the limit of your measurement system and the calibration data. This will be the driver minimum-phase plus the excess-phase due to the time-of-flight from the driver's acoustic center to the mic center (very close to the tip usually).

What you need to do to get correct minimum-phase response is to create a model that is close at the extremes, then adjust until the phase matches. The highpass is pretty easy. For a tweeter you easily get a good measurement of the highpass. The extension of the slope (tailing) is usually a simple matter, most often 12db. For a woofer, mid-woofer or midrange, you can use the box model from T/S parameters or estimate the Fb and tweak the highpass to get the match. The lowpass for most drivers requires some trial-and-error to estimate it. Programs such as SoundEasy make this a pretty easy task. You can also use the FRC from the FRD consortium.

Tweeters usually need a lowpass around 20K or 30K depending on the typical extension of that driver. I usually take the manufacturers response as being typical and start from there. If your measurement system stops at 20K, you can extend to flat above, then roll off and check the HBT and change slope/Fc until you get match. Done right the phase always matches after a few attempts.

I've come to like SoundEasy for creating models for minimum-phase when needed. If optimizing in CALSOD, I now just use direct measurements taken from the design point.

Dave

[Iain McNeill]

Thanks Dave,

If I can try and paraphrase you here just to see if I'm comprehending properly....

I would get a much better agreement with the Hilbert transform if I clean up the upper and lower roll off "tails" of the measured data as they hit the noise floor. Seems like you're suggesting that I "fade" my measured upper & lower roll off's to modelled roll offs - this would effectively buy more signal to noise right?

My woofer is rather underdamped in it's sealed cabinet and so deviates from the butterworth model. I hadn't considered this as a source of error. However, I did try doing a HT of the magnitude response of the modelled bandpass from post 4 and got excellent agreement between HT phase and modelled phase........after I multiplied the HT phase component by -2

All this still seems to confirm that my measurements are correct although perhaps not precise. As I'm trying to get my XO tuned in for the burning amp event I think I'm going to proceed with this data for now. The HT review may have to wait til later.

[dlr]

Originally posted by Iain McNeill
Thanks Dave,

If I can try and paraphrase you here just to see if I'm comprehending properly....

I would get a much better agreement with the Hilbert transform if I clean up the upper and lower roll off "tails" of the measured data as they hit the noise floor. Seems like you're suggesting that I "fade" my measured upper & lower roll off's to modelled roll offs - this would effectively buy more signal to noise right?

The tails serve two purposes. One, as you point out, they replace the "noisy" area, so-to-speak, since the data you'll get in the measurement will get lost in the noise floor at some point. But more importantly, they provide extended data in a reasonable manner to allow the software to provide a more accurate HBT. If the data is truncated, the software may extend the data on its own, sometimes flat from the last data point that may easily introduce additional error. Drivers are known to have a fairly narrow range for the lowpass rolloff, so making an assumption for the purpose of achieving a more accurate phase response in the measured region is both practical and realistic.

My woofer is rather underdamped in it's sealed cabinet and so deviates from the butterworth model. I hadn't considered this as a source of error. However, I did try doing a HT of the magnitude response of the modelled bandpass from post 4 and got excellent agreement between HT phase and modelled phase........after I multiplied the HT phase component by -2

I'm not sure what you mean by that last sentence. I assume that this means that you altered the slope of the SPL highpass response in the model. It may take several attempts to match the phase closely.

Woofers and midwoofers often have steeper lowpass slopes due to various reasons, diaphragm material, profile, damping, etc, at least for the initial response. They sometimes turn down more sharply after some initial rolloff, so each driver has to be considered individually. The highpass for a driver in a closed box may vary, but it will asymptote to 2nd order in any case.

All this still seems to confirm that my measurements are correct although perhaps not precise. As I'm trying to get my XO tuned in for the burning amp event I think I'm going to proceed with this data for now. The HT review may have to wait til later. [/B]

Correct but not precise? What does the driver with crossover response look like?

Dave

[Iain McNeill]

However, I did try doing a HT of the magnitude response of the modelled bandpass from post 4 and got excellent agreement between HT phase and modelled phase........after I multiplied the HT phase component by -2

Perhaps I should 'fess up to being a MATLAB user. The function I am using 'hilbert()' has no modifiers and is designed to take a magnitude only time domain signal and provide the corresponding analytic (complex) time based signal. I used this function on the frequency domain magnitude response I had to compute a frequency domain phase response.

I assumed that time/frequency domain equivalence would be upheld. I'm not so sure now and so this may not be a valid use case - this is what I need to research.

All I was saying was that I noticed that the HT phase component I got (unwrap(angle(hilbert(mag_response)))) was mirror image and smaller. When in trouble, I do everything by 6dB. This time I got lucky - +6dB and 180degrees made it match - perfectly. Always suspicious in my book.


Correct but not precise? I mean the method is OK but the data is compromised. Am I ±3dB? no idea. I can tell you what it sounds like!!!

I wondered if you'd ask about the "post-XO" response. Here it is together with how it sums:

There's no driver correction on thins.