Transmission Line Theory and Modeling

Veleric

Member
2016-02-26 6:26 pm
I have been reading MJK's great articles on Transmission Line theory. I'm starting to understand, but I'm coming up with lots of questions too. I'm sure most of the answers are in the articles, but there's so much to read maybe you guys can help me with some of these:

How can I get access to the models? Is it only through the Yahoo users group? I just signed up for it but not yet approved...

I've been reading and re-reading "Anatomy of a TL Loudspeaker". Some questions about that:

It's clear that stuffing is critical to achieve a reasonably smooth SPL. But is the objective to extensively damp all the standing wave modes except the 1/4 wave mode? That is, including the 3/4, 5/4, 7/4, 9/4 and above?

It seems that the higher frequency modes contribute less and less to the ripples in the far field SPL. Is there a limit to how far up they really need to be damped? That is, if you could damp just, say, the 3/4, 5/4 and 7/4 modes would that typically be enough?

How much freedom does the MJK model allow to vary the stuffing density along the length of the TL?

It seems that the examples typically set the tuning frequency of the TL at the Fd of the driver. Is that a pretty good rule of thumb for this design? I guess the model would let me play with that question but meanwhile is that where the sweet spot usually ends up?

Thanks,

Eric
 

Veleric

Member
2016-02-26 6:26 pm
Oh, here's another:

Has MJK written done a similar analysis of a base reflex enclosure? Reading into (maybe too much) some of his comments about similarities between TLs and BRs, I started wondering if all the tapering and stuffing was effectively just the hard way of making a BR enclosure. How far off is that?

Eric
 
I've about a ton of essays to mark, so will have to be brief. FWIW:

How can I get access to the models? Is it only through the Yahoo users group? I just signed up for it but not yet approved...

AFAIK, Martin has discontinued distributing his worksheets.

It's clear that stuffing is critical to achieve a reasonably smooth SPL. But is the objective to extensively damp all the standing wave modes except the 1/4 wave mode? That is, including the 3/4, 5/4, 7/4, 9/4 and above?

Basically it depends what you're trying to do. 'Transmission Line' has become something of a catch-all phrase, to the point where it can be (and often is) used to describe enclosures that are functionally almost the exact opposites of each other. In the narrowest sense, a Transmission Line speaker would be a line designed with the single object of providing the flattest possible impedance, no other considerations. It's rarely used so narrowly though and the vast majority of TL variations assume preservation of the fundamental resonance & damping out the unwanted harmonic modes. F3 & F5 are the two main ones -the higher harmonics are comparatively easily suppressed with very light damping, so if you've got enough in there to flatten F5, F7 et al will typically be killed in the process.


How much freedom does the MJK model allow to vary the stuffing density along the length of the TL?

Essentially complete, although something of a moot point since he's discontinued distribution. Note that in all software a number of assumptions are made about the damping coefficient / properties; all damping materials in practice behave in somewhat different ways (and you can get variability in the same nominal type of material too) so while it will usually get in in the right region, you will likely need to make some changes to optimise it fully.

It seems that the examples typically set the tuning frequency of the TL at the Fd of the driver. Is that a pretty good rule of thumb for this design? I guess the model would let me play with that question but meanwhile is that where the sweet spot usually ends up?

Again, depends on what you're trying to do. Traditionally that was the case, and Martin adopted it for his alignment tables also, I imagine to simplify things somewhat. In practice, it varies. A maximally flat impedance line will be tuned to F0/Qt (in Hz) for e.g. In general, given the damped nature of the line (assuming you don't go for a very high taper ratio), you're usually better off tuning above Fp, assuming a peaking alignment without damping.

Has MJK written done a similar analysis of a base reflex enclosure? Reading into (maybe too much) some of his comments about similarities between TLs and BRs, I started wondering if all the tapering and stuffing was effectively just the hard way of making a BR enclosure. How far off is that?

The underlying physics for bass reflex alignments is Helmholtz (cavity) resonance, which assumes a uniform internal air-particle density and no Eigenmodes (standing waves). The equations are closed-form and solved. In a quarter-wave line the dominant resonant behaviour is, unsurprisingly, quarter-wave, or pipe resonance if you prefer. That is not a synonym for Helmholtz. However, where you get into a grey zone is the fact that all speaker enclosures will have some internal Eigenmodes. It's just a matter of degree. So if you design, say, a tall, thin enclosure under Helmholtz assumptions, there will in fact be a number of Eigenmodes present, which are not predicted in the baseline assumptions because they aren't part of them. They may be minor, they may be significant, to the point where the box tuning is affected. So ideally, you need to consider these when designing the cabinet & how best to exploit or suppress them.
 
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Veleric

Member
2016-02-26 6:26 pm
A maximally flat impedance line will be tuned to F0/Qt (in Hz) for e.g. In general, given the damped nature of the line (assuming you don't go for a very high taper ratio), you're usually better off tuning above Fp, assuming a peaking alignment without damping.

Sorry for my ignorance, but by F0 do you mean the Thiele/Small Fs? And by Qt do you mean the Thiele Small Qts?

And Fp is what?

Thanks,
Eric
 
Sorry for my ignorance, but by F0 do you mean the Thiele/Small Fs?

Yes. F0 was the original term, & still sporadically used, although Fs has become popular as an alternative.

And by Qt do you mean the Thiele Small Qts?

Yes. It's just an abbreviation.

And Fp is what?

Pipe fundamental resonance or pipe tuning if you prefer, in the same way that Fb denotes the box tuning frequency of a reflex cabinet.
 

Veleric

Member
2016-02-26 6:26 pm
I've about a ton of essays to mark, so will have to be brief.

A maximally flat impedance line will be tuned to F0/Qt (in Hz) for e.g. In general, given the damped nature of the line (assuming you don't go for a very high taper ratio), you're usually better off tuning above Fp, assuming a peaking alignment without damping.

Scott,
I hope you didn't mark the essays too hard. I always hated essays...

Anyway, thanks for your responses. Regarding F0/Qt tuning (or Fs/Qts, or even Fd/Qts if you prefer, all the same right?): You're saying it makes sense to tune the tube (i.e set Fp) to a frequency above Fs?

That is, to make the tube shorter, so that Fp is nearer to Fs/Qts (roughly 2 to 3 x Fs), rather than make the tube so Fp ~Fs, is that right?

Your response confused me a bit, when you said "tuning above Fp". I'm thinking you meant "tuning Fp to be above Fs".

That seems to be what Augspurger is showing with Figures 5 and 6 in his "Transmission Lines Updated, Part 1" article.

Do I have that right?

Eric
 
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Veleric

Member
2016-02-26 6:26 pm
Basically it depends what you're trying to do. 'Transmission Line' has become something of a catch-all phrase, to the point where it can be (and often is) used to describe enclosures that are functionally almost the exact opposites of each other. In the narrowest sense, a Transmission Line speaker would be a line designed with the single object of providing the flattest possible impedance, no other considerations. It's rarely used so narrowly though and the vast majority of TL variations assume preservation of the fundamental resonance & damping out the unwanted harmonic modes. F3 & F5 are the two main ones -the higher harmonics are comparatively easily suppressed with very light damping, so if you've got enough in there to flatten F5, F7 et al will typically be killed in the process.

Scott,
Thanks again for your response. I'm replying in parts because I have so many questions....

I do understand that "it all depends on what you are trying to do". So, let me describe (as best I can) what it is that I am actually trying to do!

Presently, my objective is to build a pair of one way "crossover-less" speakers using moderately priced full range drivers.

Being an engineer and craftsman, I want to understand and use the available tools and principles to make a respectable set of speakers that I can be proud of, and learn something along the way.

From what I've read, it means getting access to one or models, playing with them until I find something interesting, and then building it.

Also, from what I've read, I'm thinking that my objective is to design an enclosure (possibly based on the TL/Quarer wave concept) in which the design broadens the low frequency response of the full range driver through constructive interference of the tube and driver outputs without introducing nasty artifacts anywhere in the spectrum.

So my questions should be viewed from that perspective....hope that helps.

Eric
 

Veleric

Member
2016-02-26 6:26 pm
.... requires a 1.0 Qts' for a Fp = Fs alignment.
GM

GM, thanks for clarifying that.
Now, showing my ignorance even more, can you explain what is meant by the concept of "alignment"?

Does alignment refer to the kind of enclosure you are using? Or does it refer to the relationship of the driver specs to the cabinet specs? Or does it mean something else?

Eric
 
You're welcome!

The relationship of the cabinet size, type, tuning to the driver specs, i.e. ideally one finds a driver with the right specs [aligned] to meet the size, performance needs of the intended app. This is the way manufacturers originally did it and the most successful still do, i.e. if it doesn't exist, they either modify an existing one or make it from scratch; whereas DIYers tend to buy a driver for whatever reason then try to 'shoehorn' fit it to meet the needs of the app and instead too often run headlong into what the inventor Tom Danley refers to as 'the wall of science'. :(

GM