Zaph|Audio - SB Acoustics 2-Way : Woofer Close-Mic to 4-pi

Woofer Measurement - From Close Mic to 4-Pi

The woofer highpass is the most difficult measurement, especially for those of us into DIY. The wavelengths are too long for standard measurements, especially indoors. A number of ways to get around this problem exist, but all have drawbacks in one way or another. We'll look at one way to approximate the highpass using a close-mic measurement and some modeling techniques. We'll also see that there is some support for the relative accuracy using a pure model. This alternate is the more common one using Thiele-Small (T-S) parameters. It is useful for designing the box prior to actually building it, of course. The measurement scheme described here is one way to confirm the design and/or provide low end data to use for design, if need be. This will show if the T/S parameters that were used are reasonable.

The Close-Mic Measurement Scheme

We want to actually measure the woofer highpass, but it's not possible to do reliably for most of us, even for a midrange that has significant output below the frequency limit dictated by reflections. It usually comes down to accepting an approximation. T/S parameters help, but they do not cover the baffle step, that part of diffraction relating to the 2-pi to 4-pi transition. This is where the method described here will help. We'll start with a standard close-mic measurement. This was first presented by D. B. Keele, Jr. in an AES paper entitled "Low-Frequency Loudspeaker Assessment by Nearfield Sound-Pressure Measurement". The paper and others of interest can be found at his web site.

It's also important to note that the measurements here were made using LAUD that is inherently calibrated. The sound card is a dedicated unit that has a built-in mic preamp that is nearly flat to its limits and does not require calibration for typical usage. More importantly, it's a programmable card that allows the software to convert any signal level used during measurement into a nominal 2.83V @1m. If you make measurements in a system that is not calibrated, the method described here will be more problematic.

The graph below shows the close-mic responses of the woofer and passive radiator (PR) measured independently with predicted response from Unibox that shows that the measured response is easily within the ballpark of what we expect. We can see the box tuning easily. They look ordinary, right? From all that we've seen it should be flat down to about 100Hz or a bit below. What we'd like is to be able to splice at or near the low limit of the quasi-anechoic response. The problem is that woofer response when taken close-mic is also a 2-pi response and also does not account for the baffle step, the transition from 2-pi to 4-pi. So what can, or should, we do?

There are several things we could do. The first possibility is to default and consider the modeled response from Unibox (or other box software) below the splice point to be accurate and splice it with the quasi-anechoic reponse, somewhere. The problem with this approach is that it is completely dependent of the T/S parameters and it does not inherently include the baffle step. That has to be added into the model.

A midwoofer in a 2-way box is still in the transition region, the baffle step, at typical splice frequencies, say 300-500Hz. In the in-box measurement below overlayed with the diffraction signature set, the response at the low limit of the measurement can be seen to be several db above the 2-pi region. The diffraction 2-pi level (high end) was set roughly at the midband and happens to closely overlay the 1m measurement. When the measurement is windowed properly, there seems to be a good correlation with the modeled diffraction signature. This is deceiving and not accurate, though my first inclination was to think that it was accurate and to use that. It does show that the measured response tends to track the prediction in shape, however. The problem is due to the woofer response in the 300-800Hz range when measured quasi-anechoic on the large baffle. As the manufacturer's measurement shows, there's an inherent dip in response in the region. Add diffracion loss and it will be steeper as the actual measurement shows. The SB Acoustics supplied curve shows rougly 200-400Hz with additional SPL rise down to about 150Hz. The driver has a small deviation from flat, but this is not uncommon.

SB Acousics Measurement

Since the close-mic response is 2-pi and we want to splice to the 4-pi quasi-anechoic response, you may think that shifting the close-mic response by 6db, the total step change, would suffice. Well, not quite. You can see the result below. It's not what we want. So what's wrong with this?

The problem is the baffle step. The baffle step for a woofer in a box of this size is just starting to go below the 2-pi level at 450Hz. That means that it's still got 6db to go to be fully in the 2-pi region. If the diffraction prediction is accepted, the 2-pi region is not fully reached until somewhere around 55Hz for this case. What we need is to correct the close-mic response for the baffle step. You can see the results of this correction in the next graph for both the Unibox prediction and the actual close-mic measurement. An indication that this will work for us is the SPL level at 100Hz. All models converge there. The box influence begins just below that point. The diffraction corrected close-mic in-box response is very close to the level it would be if we simply shifted the whole in-box measurement down 6db.

Putting Them Together

Now that we've got some predictions and measurements with corrections applied for the diffraction signature, we can splice them, but where and why? Before we try to splice, let's examine a bit more. We can splice the 2-pi quasi-anechoic response with a close-mic response when mounted on a large baffle (no box), shown below. This demonstrates that it's a reasonable approach. We would probably splice anywere from 200-300Hz. Were we to shift the close-mic level to get a smooth splice at 500HZ the result would be about 1.5db too low. The reason that the close-mic response looks so much better above 200Hz is due to the mic proximity. When placed only 1/4" from the cone, the variations one would see from the full diaphragm surface radiation is masked. It is essentially smoothed and flattened.

Another reality check is to subtract 6db from the quasi-IEC 2-pi measurement and overlay it with the in-box close-mic measurement. The latter has a bit better extenstion due to the measurement conditions, so it's a bit more representative of the driver response. This is an artifact of the measurement technique and the limitations of measuring in-room. He result is the system response before any baffle step is introduced. It's essentially what you would have if you mounted the box with the baffel front flush to a large wall. We could splice there anywhere from 200-300Hz as well. The trend is good so far.

Let's look again at several of the graphs to see what we might do. We've got the in-box quasi-anechoic response, the close-mic measurement and the diffraction corrected version to work with now. It's clear that there's still a small discrepency if we try make a direct splice of the files. Examining the response of the close-mic responses indicates that an accurate splice point is likely going to be no lower than 300Hz, especially if the driver has some small variations down low. A good guess here would be to extend the quasi-anechoic in-box response flat down to the desired splice point It would be easier if we could get down to 300Hz in-room, but this is usually not the case for DIY. Still, it's a reasonable compromise given what we know about the splice for the large baffle case.

We could use the common procedure of shifting the unprocessed close-mic response to align it with the quasi-anechoic response. That method works just fine for drivers that are flat down to the splice point. However, this method would show the woofer low end to be about 2db higher than actual for this driver.

This may be the reason why many DIY designers add in baffle step correction (BSC) of only 3-4db. The low end may in reality be higher than modeled. The assumption is that there will be some boost due to room response. This is probably true for woofers in a 3-way, but for a 2-way there is need for more correction when stand-mounted. 3-4db correction used when the model is low could result in a final design low end rise that is flat anechoically. Also, a rise of 2db or so at the low end of a 2-way is a common design trick that gives the impression of more bass in a 2-way and was used in this design due to the more limited low end extension.

Were we to simply shift the processed close-mic response to align it with quasi-anechoic response we would lose about 1.5db at the low end in the spliced response. Neither one of these results is accurate.

There are several ways that we could extend and splice. An easy way is to lowpass the close-mic response to set the match point, at least for this driver example. Care must be taken to prevent rolling off the area below the splice point. The example shown here involved using the free version of Praxis. It has a filter function that was set to lowpass with a Butterworth 5th order at 340Hz. This brought the splice point down to the SPL at the low end of the quasi-anechoic response, shown in the next two graphs followed by a third graph that shows the result of splicing at 300Hz.

How Do They Compare?

We've got two different full-range models, one from a large baffle spliced with a close-mic measurement and corrected for baffle diffraction and another from an in-box measurement that inherently includes baffle diffraction and spliced an in-box close-mic response also corrected for baffle diffraction. The real test is to see how closely they compare to the full-range response predicted by the design software. That assumes, of course, that the design software is accurate for the data entered, the T/S parameters. A ground plane measurement would also be useful, but that's not available.

The overlay of the results below shows that all three methods are in reasonably close agreement. The difference between the large baffle and in-box measurements is likely due to two reasons. First, the large baffle measurement allows use of a longer impulse response, thus more data for more detail. Second, the in-box measurement is subject to actual diffraction that is impacted by the driver directionality, an assumption entered into the diffraction simulator related to diameter of the driver only. The lower region will be more accurate than the upper region for this reason. Finally, the software T/S method varies from in the region of the splice due to direct extension from the lowest frequency in the actual measurement. It does not include the slight increase up to the splice point used for the other two models, it goes down directly from the low point in the measured response. This is where the variability of the low end due to measurement limitations can inject additional error.

Which Result is More Accurate?

The short answer is, we don't know. It requires a true anechoic measurement to know that. The large baffle measurement does not have fully accurate diffraction results, but does look good otherwise. The in-box measurement has diffraction inherent in the quasi-anechoic part and should have a very close approximation of corrected diffraction results. The full model from the design software that uses the T/S paramters to create the low end should, we hope, also be very close. All three are in relative agreement, but my bet is on the in-box measurements, even though the close-mic portion is processed for diffraction. The baffle step area of the diffraction is probably the most reliable part of it.

David L. Ralph © 2009