Diaphragm Compliance-Box Volume Ratio

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I read some where that TS test exercise is all about arriving at the optimal volume for a give speaker. Irrespective of the speaker size and its resonance, this optimal volume is said to have a definite ratio to the speaker compliance. This compliance is said to be 1.56 times (before porting) and 1.44 times after porting.

Can somebody confirm whether this is true?
Since this string has not elicited much response, I thought I should elaborate on it.

Diaphragm Compliance-Box Volume Ratio is mentioned in James F. Novak's artile in the "Wireless World." I am sure Novak knew of Thiele-Small equations. Novak states that an optimal bass reflex box is that which, when the port is closed, rises the speaker free-air resonance 1.56 times and 1.44 times when ported.

I am specifically interested in this ratio aspect because if TS parameters is all about this, it would be easy to arrive at an optimal box volume by trying out the speaker in a test box whose volume can be made variable. Im my part of the world 1% MFRs, not to speak of close tolerance, MIL specification components and dedicated DMMs (fluke and family) are dream stuff. I am looking for a mason's commonsense approach.


It should be noted that there is not a single optimal ratio when it comes to box designs. When mentioning optimal parameters, one must specify which performance characteristic is being optimized. For instance, if best transient response is desired, it is said that an SBB4 alignment is best for ported boxes. If optimal bass extension is a design priority, then an EBS alignment is suggested.

Software can help you see the effects of changing box/driver parameters. Try the following software.

WinISD Pro
Subwoofer Simulator

Cheers :)
Radio between Diaphragm Compliance and Box Volume

Many thanks for your reply. But I dont think I understand you correctly. If there is no one ratio, then, perhaps, there are several feasible ratios depending on what kind of end response one is trying to get?

I tried the sites you mentioned in your reply. Some of them I had visited earlier. I am afraid I did not get what I wanted -- mostly because I still do not understand what I am looking for. Finally, what is this SSB and SSB4? I will appreciate if you could throw a line or two on this.

Thanks again.
If there is no one ratio, then, perhaps, there are several feasible ratios depending on what kind of end response one is trying to get?


You have to know what you want before you can design a subwoofer (or anything really). Are you looking for maximum bass extension, for what kind of software will the subwoofer be used -- movies and/or music, what is your budget and so on... These are a few of the basic questions you should ask yourself when designing a subwoofer.

SBB4 is short for Super Fourth-Order Boom Box, it is one possible alignment that is said to have good transient response. The penalty is higher cutoff frequency relative to, say, an EBS alignment. An Extended Bass Shelf alignment allows for deeper bass, but you have to accept the rather larger enclosure that it requires.

Look for Vance Dickason's book, Loudspeaker Design Cookbook -- highly recommended introductory book. It explains subwoofers, crossovers etc. in more detail :)
Compliance and Box Volume


Thanks. I was just wondering whether there are ways of circumventing Thiele-Small measurements. It appears there are none.

I have come across some of the freeware you have mentioned, but they require TS input.


BTW, I began my acoustic journey with a book by Abraham P. Cohen, an audio engineer back in the 50s or 60s in one of those venerable speaker companies in the US. Cohen refers to electrical analogues to speaker, but there is no way he must have come across TS while writing the book. Like most books of the time, the one by Cohen also provides a nomogram to design bass reflex boxes (a simple cut in the box, no tube). His nomogram consists of exponential curves. I wonder how they arrive at these curves? surely, there must be some formula?

Any idea?
The electrical analogue of a speaker is actually the ground for TS prameters. You translate the mechanical parts of the speaker into electrical and add them to the existing electrical parts.

Then you have a schematic that you can use regular electronical calculation methods on.

The boxes are also translated into the schematic so they can be counted for. So is the bas reflex port.

This is the reason why it is quite simple to calculate a closed or a vented box.



Just curiosity. If diaphragm compliance and volume ratios is dependent on various alignments, on what basis did our Novak suggest this ratio of 1.56 and 1.44 in his Journal of Audio Electronics article? To repeat, Novak's procedure consisists of measuring the free air resonance of the driver and its resonance in a standard box (about 0.5 cft for an 8" woofer) and then arriving at an optimal volume with the aid of a nomogram. Novak claims that his method guarantees good transient response, extended bass, freedom from hangover etc.


I haven't ready any of Novak's work, sorry. Basically, box ratios are based on Qts, Vas and Fs.

Again, those ratios are just a set of countless possible ratios. Really, there's no need to be overly critical of ratios, your design goals, driver details and listening room dictate the size and position of the box [in your listening room]. You'd only look up tables to start you off in the design process or if you don't have a way of using simulation software.

If you'd like to keep group-delay down and transient response acceptable, try to come up with a transfer function that doesn't suddenly "bend." A gradual bend from the passband to the transition band of the transfer function gives good results.

Your room's acoustics will seriously dwarf any slight difference your candidate box may have with the optimal box.
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