A different way to measure a subwoofer's frequency response

[Brian Steele]

(This is a condensed version of a small thread I started over at the DIYAudio Subwoofers forum).

The method for measuring a car's "transfer function" is pretty well known - basically do a close-miked measurement of a sealed subwoofer, measure again at the driver's seat (usual listening position), and then subtract the two measurements to get the transfer function. I was curious if this procedure could be used to measure a subwoofer's frequency response, as not all of us have large backyards and close-miked measurements only work properly for sealed or 4th order BP subwoofers (and even then if the driver is a large one, the measurement can be off a bit).

So I did a few trial runs, and the results look promising.

Basically the process was as follows:

1. Set up the subwoofer that would be used to derive the transfer function at the location that will be used for testing the other subwoofers. This "test" subwoofer should be a sealed or 4th order BP alignment - basically a design that can be accurately measured using the close-miked approach.

2. Perform a close-miked measurement of the subwoofer's FR (in this case a 4th order BP subwoofer, so all of its output was through the vent), call this measurement A.

3. Perform a measurement of the subwoofer's FR with the mic a suitable distance away from the subwoofer. Call this measurement B.

4. Derive the transfer function by subtracting A from B. Call this measurement C.

5. Replace the subwoofer that was used to derive the transfer function with the subwoofer that you want to measure and repeat step 3. Call this measurement D.

6. Derive the subwoofer's actual "anechoic" FR by subtracting C from D.

As I said, the results look promising, and think I know what introduced the errors (background noise), Also, I had to use Excel to do the calculations as I wasn't getting the results I expected using the features in REW to subtract one response from another. And this only works for magnitude, not phase. It also looks a bit complicated, but theoretically once you've calculated the transfer function for a particular mic and subwoofer location, then it should remain the same unless you change the environment, so it should be possible to re-use the transfer function for future measurements of other subwoofers.

I've attached the derived FR for my POC6 build, using the transfer function approach method, a measurement that I performed a few days ago. In this case the measurements were done in my living room, with the mike about 1.5M from the POC6. Yes, my LIVING ROOM, with all of its +/- 10dB resonances in the bass region! And POC6 is a MLTL type of alignment, so what you're seeing here is the combined output of the woofer and vent, which lines up quite nicely with the Hornresp sim. There was some background noise from the TV and SWMBO working away in the kitchen, which I suspect may have contaminated the measurement a little above 140 Hz. Background noise is the biggest problem here. Also, while I used a 4th order BP as the reference sub to derive the TF, I think I'll get better results with a sealed cabinet that has a smooth FR and an F3 as low as possible - this should help to reduce the impact of noise on the derivation of the TF. Looks like I'll have to get that 12" driver and sealed cabinet out of storage... .

I think the approach does show some promise. Bear in mind that theoretically I only have to get the TF right once, and just apply it to any measurements made afterwards with the mic and the DUT in the locations used to derive the TF. This means that I can keep using the same location in my living room, once I make sure that all the windows are shut like they were for the test and the furniture is in the same locations

[wogg]

This is an interesting method, thanks Brian! What do you think about the test sub getting too close to the noise floor if it doesn't have enough bandwidth to cover your whole measurement range? i.e. a small sealed sub that isn't doing much below 40, where the 20Hz measurement may get really close to your noise floor and make your transfer function invalid, or a bandpass that too far away from tuning frequency?

Is the typical method of measuring the woofer close mic then adding port / PR with diameter SPL adjustments not accurate enough?

[Brian Steele]

This is an interesting method, thanks Brian! What do you think about the test sub getting too close to the noise floor if it doesn't have enough bandwidth to cover your whole measurement range? i.e. a small sealed sub that isn't doing much below 40, where the 20Hz measurement may get really close to your noise floor and make your transfer function invalid, or a bandpass that too far away from tuning frequency?

Yup, the noise floor can be an issue - the further away from "flat" that the test subwoofer's response is, the greater the "noise" in the derived response is going to be. My reference subwoofer for example is about 20dB down by 20 Hz, and you can see that the derived response of the subwoofer that I measured by this approach starts to deviate a bit around there. There's also some noise introduced above 140 Hz - the test subwoofer is about 10dB down at that frequency, but I suspect that background noise from the TV and the kitchen had an impact there too . . I suppose that the accuracy might be improved by EQ'ing the reference as flat as possible, but I really haven't tested that yet.

Still, to give you an example of what measurements I had to work with to get that derived response, have a look at the attached image. The red graph is the response of the reference subwoofer, and the purple graph is the unsmoothed derived response of the subwoofer I measured using this approach. But see those lines in green and yellow? That's the response of the reference subwoofer and the subwoofer under test at the measurement point. From those awful response curves I was able to pull something useful using the TF approach. When I have some time, I'm going to redo the process to see if I can find a spot in the living room that adds less "noise" to the response. And like I said, once the TF is generated, I will be able to use if for subsequent measurements - theoretically I just need make sure that the DUT and mike are in the same locations that were used to derive the TF.

Is the typical method of measuring the woofer close mic then adding port / PR with diameter SPL adjustments not accurate enough?

That approach requires measuring the output from the port or PR and playing with its amplitude. Thing is, what you're measuring is not just the port or PR, but the output of the woofer too where the mic is located, particularly if the vent is located close to the woofer. While its impact on the measurement might be minor at the vent resonance frequency, away from that frequency it could have some impact.

[DanP]

This is really cool Brian, and something I've aleays wondered about. Have you tested how sensitive this method is to movement of the source? I'm wondering if you derived the room function with a sealed subwoofer, would it still be accurate enough measuring a sub with a rear port. What about baffle size?

Dan

[Brian Steele]

Have you tested how sensitive this method is to movement of the source?

No, but I think this will largely be dependent on the environment. My indoor test was close to a worst case scenario btw - I wanted to check to see how far I could push the idea. For better results, it would be best to do the test outdoors like in the garage driveway up against one wall of your house (which will significantly reduce any "room resonances", because there will be no "room"), and the only thing you'll have to worry about is wind noise and the impact at very low frequencies due to nearby buildings, etc. Unfortunately I can't perform outdoor tests at the moment to confirm this - I live at the end of a road that's called "Windy Trace" for particularly obvious reasons, and any serious outdoor measurements are limited to one or two months a year when the wind isn't howling away.

I'm wondering if you derived the room function with a sealed subwoofer, would it still be accurate enough measuring a sub with a rear port.

Ports to the rear of a subwoofer? Who does that? . Seriously I don't see why it should not work, though I suspect that again the environment will significantly impact the accuracy of the results. Indoor, just turning the subwoofer around might give different results because of room resonances - you basically have two sources (woofer and port) at locations subject to two different transfer functions. Outdoors, not so much.

What about baffle size?

See above .