LM-1 Testing Driver Distances

Distance Assessment via Interferometry

Sounds fancy, doesn't it? The first step for me in crossover design is to measure the acoustic distance between the drivers in the cabinet. What? You don't do this? You never heard of this? This information is key to any good crossover.

Prior Art

In 2011 Jeff Bagby documented a procedure from which this work may be derived, though not knowingly. He might even be it's inventor. I encourage you to read up on it here and at least give him the credit he's due for helping the DIY community. As I learn more about the provenance of this procedure I'll gladly update this document to give credit where due.

I learned this technique by reading some tips online and experimenting myself, and a result all of the writing, measurements, pictures and errors here are my own and written without the benefit of his paper.

The Procedure

First, build a test baffle. The actual size or even if it's really a cabinet or not is up to you.  The important part is that the drivers have the same distance from each other and from the listening location. So, if you are building a box with a flat baffle like we are, you could use a single sheet of plywood for your testing assuming it was thick enough to inset  properly or you could use the actual cabinet, like I did.

As you can see I attempted to inset the odd shaped peerless woofer and it's ugly. Maybe not so much if I had painted it. Anyway, point is, the drivers are placed in the cabinet at the correct location and inset depth. 

The goal is to get the correct acoustic distance between the two drivers so when we design the crossover the simulation has the correct phase information to calculate the correct frequency response.

The Test Setup

You'll need a measurement microphone, 3' (approximately 1meter) from the listening axis. From the beginning to the end of these steps you must not move either the speaker or the microphone at all. Any movement will throw off the results. The listening axis is usually the tweeter, but some makers prefer it to be the woofer, the pro's and con's are beyond our work here. If you see a speaker with the tweeter below the woofer you'll know how they had to go about measuring though.

Believe it or not, a calibrated microphone is not needed for these tests.  Any microphone that is relatively accurate and covers the range of the tweeter (more or less) will do.

You may use a 10 to 20uF capacitor on the tweeter if you so desire to protect it from bass. 10uF is large enough that it won't affect the areas we care about much. 20uF is even better. :)   The more expensive the tweeter the more delicate they tend to be so study the tweeter's requirements carefully.

Here is a schematic with a 10uF capacitor protecting the tweeter, S1. Of course, during testing you'll need to decide which driver to leave connected or not.

This test signal does not need to be very loud.  A test signal that is 70 dB or more at 3' is fine. That should be well above the noise floor of your measuring room.

If you are analyzing an existing loudspeaker  you must ensure you  have removed any existing crossover components from the circuit.  

The Tools

 The tools we'll be using for this excursion are the following:

• OmniMic - Published by Dayton Audio, authored by Bill Waslo. Inexpensive speaker measurement system for beginners to intermediary users. Everything from FR, phase, distortion, waterfalls. Comes with calibrated microphone.
• XSim - Free Crossover design and simulation tool from Bill Waslo

You do not need any of them to build the LM-1 as we'll be giving you the complete results and schematics. However if you wish to do what is shown you'll need some version of these tools.

Data files suitable for XSim have been posted to Google drive here. 

The Measurements

Of course, for all of my testing I'm using OmniMic  but any test tool that can export an FRD file to XSim is fine. In no particular order, measure:

• The woofer alone
• The tweeter alone (or with a cap to protect it) 
• The woofer and tweeter (if you use a cap to protect the tweeter use it again here)

Save each of these measurements to a separate FRD file. In case you end up re-using the files in crossover design, make sure you click the "Show phase" checkbox.

Inference

Inference is the technique of discovery when you cannot measure or know a particular data point directly. For instance, if you touch a door knob and it's very hot, you can infer there is a fire on the other side of the door. What we're doing is much safer than that!

We will infer the distance based on how the delays of the acoustic centers affects the combined frequency response. The fixed difference in time and distance between the drivers we are measuring will cause varying amounts of phase changes across the frequency spectrum. These phase changes cause a unique set of destructive and constructive interference. These changes occur at no other distance but this particular one. This is in effect a finger print of the distance.

With the three FRD files collected,  create a schematic in XSim to represent the woofer and tweeter together. Do NOT include the tweeter capacitor or any other crossover component in your schematic for interferometry.

Import the FRD file with the combined tweeter and woofer responses in the Frequency Response window on the right. Here you see the actuual measured Frequency Response plot of the combined output in red, as well as the simulation's output in blue for the LM-1.

See how poorly the simulation's FR chart matches the actual measured response around 5 kHz? That's what we want to improve. It's mismatched because XSim doesn't have the correct distance to predict the correct destructive interference at 5kHz, or many other places either.

Usually woofers are at least 1" behind the tweeter, so "Tune" S2, and set the "mod delay" to 1.0" as a starting point.  Increase the delay slowly until the two frequency charts match from 5kHz upwards. Like this:

For the LM-1 prototypes this happens at about 1.32".

I've decided to surface mount the woofers, so I will need to re-measure when the new baffles show up but this exercise shows you exactly how to calculate the distances you would need to proceed to actual crossover design.

In the next posts we'll cover different theories of measuring speaker drivers, as well as show examples.

Do Not Panic!

At this point you may be thinking to yourself "Those are horrible looking graphs! This speaker is going to suck!" Not true.  Look at this example.  I used the same speaker drivers, but measured in a real book case.  See how the crossover improves the results?

By the end of this arc we'll be pretty close to that, not anywhere near the graphs we used for speaker measurements, so take some deep breaths and go massage your brain, it's worked hard!