If so, this is only useful when comparing speakers with same overhung to gap ratio.
Dc resistance is Rdc in my books.
Dc resistance is Rdc in my books.
But higher than Re, and closer to 4.1 than 3.3. It’s whatever the AC resistance is, at the frequency of interest, in the absence of energy storage (or nulled out). Fb will vary, depending on cabinet design. Of course, the lower you tune the box the closer to Re it will be. There are limits to how low you want to tune a box, because you want to make use of the local excursion minimum associated with it. And AC resistance does tend to go up as it heats or as the motor becomes nonlinear. Either reduces the newtons per watt, so using a higher value is more realistic. Hornresp shows all the impedance minima going all the way down to Re, but that’s not what really happens. Each one gets a little less deep because that AC resistance is rising. Unless they properly model it with the “long coil“ option - in that case it will be higher than Re.
This is usually referred to as Impedance, as impedance accounts for reactance of the circuit of which inductance and frequency are components, while they are not for resistance. You are right in your first reply that eddy currents (mechanical resistance, Qms/Rms) and even inductance will affect the Re, but designing an enclosure around the impedance at certain frequencies would only be useful if you are only playing test tones. And even then that is assuming your BL is a constant, which it changes with excursion and even current. Inductance also changes with current, so that leaves small signal parameters in the dust.
I think we are putting too much focus on small signal parameters to determine a driver's total performance, it is mainly used for basic classification of a driver and how it will be best used. The most reliable parameters to model from that I have personally found is the Klippel LSI3 "large signal + warm", because your parameters actually change quite drastically at higher drive and excursion levels compared to small signal.
Believe it or not, there is actually a mechanical component to BL. It's mechanical resistance, or Rms. Rms, which is the main factor in Qms, is also one of the most misunderstood parameters as it is the mechanical resistance from the reactive components such as inductance and eddy currents. Most people think it is just the resistance of the suspension, but it is not. If you build two identical drivers; one with an aluminum voice coil former and no shorting rings, and the other with a non conductive former and a shorting ring, they will both have different BL numbers. Mms is also a variable for Rms, so you will get different BL numbers by pulling parameters on a driver and then putting weight on the cone and pulling parameters again.
https://sbacoustics.com/wp-content/uploads/2021/01/Measuring-Thiele-Small-parameters.pdf
For most purposes the BL isn't very important. And if you look at the formula, you will notice the VC impedance has a big influence, 4 Ohm drivers have half of the BL of 8 Ohm ones. Keep that in mind if you compare the BL of a driver, if it's high impedance, don't be too impressed, calculate it back to 8 Ohm to actually compare them.
BL is pretty important, as it dictates what size and Q a driver can be as well as what alignments it can be used in.
You can do that with a lot of other parameters too so you can design speakers without ever knowing the BL.
Of course BL is important, but without knowing Re, it doesn't means much. BL can be very high but if the Re is also very high, we still can have a weak motor (high Qes, Qts). And with the same BL but lower Re, we can have a stronger motor (lower Qes, Qts).
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It definitely seems that's the case. Thiele, in his 1961 journal paper, used the symbol Re and defined it to be the voice coil resistance. Equivalently, in his 1970 journal paper, Small defined Re to be the DC resistance of the driver voice coil.
Without Re the BL value is useless. You can guesstimate what the driver can or cannot but you are better off looking at fs, Qts and Vas/Cms or EBP.
In this niche, pretty much every driver you use is going to be somewhere between 4 and 8 ohms. If your 18" subwoofer has a BL of 2, and your 2" full range has a BL of 60, you don't need to know the Re of each to know that they are not going to work.
In practice, designers never look at BL without looking at Re, but even the hypothetical of looking at just BL by itself isn't useless. I still disagree with the following statement:
In practice, designers never look at BL without looking at Re, but even the hypothetical of looking at just BL by itself isn't useless. I still disagree with the following statement:
On a subwoofer with BL of 2 you'll know that they are not going to work just by looking at them! No need to go past the picture. Or look at the Qts. Gee, no technical data is useful if there's no reference to it, either in units or defining value.
Officer: "How fast were you going?"
hurri: "200"
Officer: "two hundred?!"
hurri: "yeah, mouse strides per 15 minutes"
Don't you get it? If you don't know the impedance, you can't take the BL to tell if it's possible to use it. A BL of 20 isn't something you'd put in a horn but once you've learned it's a 2 Ohm VC, you suddenly have a monster on your table! So yes, the BL alone says absolutely nothing!
I get the big picture; I am the actual real world speaker designer in a sea of hobbyists here. But this whole campaign you have started that BL isolated as a variable being useless is just strange. Especially claiming to design speakers without ever needing to know their BL - that is just ignorant.
It is wise to advise consumers and hobbyists not to look at BL without looking at Re, but it's ignorant to go on and say that BL by itself is useless.
I don't claim by any means you'd be bad at it but I've seen in forums a lot more excellent speaker developers than professional ones anywhere. That's a fact, not an insult and - again - not meant to say anything about you either personally or generally. But that is no foundation on why you are (allegedly) automatically right about something.
I think it is ignorant to still claim BL alone is important to judge a driver just because you're a speaker designer. Especially since a lot of readers will start comparing the BL without realizing that it's obligatory to use the Re and to calculate it to the same impedance to be able to actually compare it. To plant the idea BL alone is so important is such a massive disservice to the forum, I can't let it stand uncorrected.
I know for deciding what driver to build ie a horn, it's useful and I would look onto the BL too. There are much more important things to look at, like if the cone is stiff and strong enough to withstand the high pressure. Or the cooling features. But by no means is the BL the most important value, let alone without any context.
This is the only scenario where the logic makes sense - consumers comparing different drivers by just the BL on a parameter sheet without knowing any better. Outside of this, it is not a even real world scenario. That's just not even a thing, especially in the design realm.
You are saying that it is a useless parameter by itself, and I am just saying that it is actually still important even as an isolated parameter. I'm not saying you can characterize a speaker's total and exact performance envelope over it, but just that it is not useless (verbatim) as you said. And you also said that you can design speakers without even knowing the BL. That is why I am speaking as a designer - that statement is totally false. I'm not sure what even made you initially chime in with that notion to begin with.
In simplified form or even basic common sense.
The perceived behavior of a tight suspension and loose suspension
is often opposite of first assumptions.
Tight suspension is already difficult to move.
So the box ends up large to have no further restriction.
It doesnt move easily, and a small box makes it even harder
Loose suspension already moves very easily
so a smaller box doesn't restrict the movement as much.
It already moves easily.
Of course depending on the strength of the magnet itself.
The variations will be different.
In all simplicity it is the basic behavior.
And the models will show the same outcome.
Qts is the main clue, it is total quality the formula constants includes
the mechanical Q rather stiff or tight. and Electrical Q
rather weak or strong. So regardless if the suspension was say very tight
and also has a weak magnet. The Qts would convey that and be very high.
If they tossed more magnet at it. Qts would then change or be lower.
Same answer to Original Post, rather suspension is tight or loose.
or magnet weak or strong. If the driver needs to work in a small box
Qts at a glance is a big hint without even modeling first.
Low Qts drivers will need a smaller box.
Can you post an example showing the above?
I cannot see how the electrical input impedance magnitude could ever exactly equal Re, except at 0 Hz.
The Power Compression tool can be used to demonstrate this.
The grey trace in the chart below is for a voice coil temperature of 20 deg C. The black trace is for a voice coil temperature of 270 deg C.
Cheating there a little bit - that’s an actual horn with the effects of radiation resistance. In a simple sealed box, reflex box, or T-line with a way undersized mouth you don’t get much of that. Maybe hundredths of ohms. So the dips come all the way down to the only number it knows - re. Well, Re+Rrad. It isn’t any 8 tenths of an ohm for an SW115 poorly coupled to the air (implying a half space reference efficiency around 20%, and it’s known to be about 1.5%) so even Zmin simulates as re or damn close. Le produces a general rise, but is reactive not real, and gets cancelled at/near resonances. There needs to be other parameters besides the T/S model to simulate the actual increase in the VC’s AC resistance as frequency goes up. The old version I’m running doesn’t have the ”long coil“ option - does that “internally” mess with Re? It’s still a small signal sim, right? I’ve just adjusted Re for power compression - the temperature coefficients of copper and aluminum are well known. The trick there is estimating how hot the coils really get, given manufacturer compression data (and they don’t always say how bad it is). If a coil can actually get to 275C without smoking copper will double. If you don’t get 6 dB of compression at full power it’s obviously not that hot.