ashwin said:
The components on the different sides interact. For example, the components on the mechanical side can be "pushed through" the gyrator. If so, you see the electrical impedance having components that originates from the mechanical side, as we discussed earlier. With Qes it's the other way around. Re can be pushed through the gyrator in the other direction, and a new *mechanical* resistance will appear, having the value Res=Bl^2/Re. If you form a resonator from Mms, Cms and Res you will end up with Qes. If you use Res+Rms you end up with Qts.
It may seem strange that the electrical resistance can give a mechanical resistance, but think of it this way: First, short the speaker terminals. This is equivalent to turning the volume down on the driving amplifier. Now, push the cone by hand. The coil will move in the magnetic field, and since the terminals are shorted there will be a current flowing through the coil, and power will be dissipated in it. This power must come from your hand, and the hand must see this as a mechanical resistance, since the power is lost (as heat). This electrically generated mechanical resistance will add to the losses (Rms) on the mechanical side and they will together with Mms and Cms form Qts.
Crystal clear, right?
For Azira and any who might be interested:
I have the Richard Small articles "Closed-Box Loudspeaker Systems: Part 1: Analysis" and "Part 2: Synthesis" on my hard drive. They are from the Journal of The Audio Engineering Society and from 1971.
If you want me to Email them to you, let me know. If your Email request bounces back, try again-my Email box seems to fill up a lot these days, (that's what happens when you try to run it at 90% capacity, lol).
I send them GIF, and each page is about 200 KB. They are not meant to be read on the computer like that, but they print out beautifully. If you want them, let me know what the capacity of your Email box is. It might take a couple of Emailings.
I have the Richard Small articles "Closed-Box Loudspeaker Systems: Part 1: Analysis" and "Part 2: Synthesis" on my hard drive. They are from the Journal of The Audio Engineering Society and from 1971.
If you want me to Email them to you, let me know. If your Email request bounces back, try again-my Email box seems to fill up a lot these days, (that's what happens when you try to run it at 90% capacity, lol).
I send them GIF, and each page is about 200 KB. They are not meant to be read on the computer like that, but they print out beautifully. If you want them, let me know what the capacity of your Email box is. It might take a couple of Emailings.
Hi all,
In post 17 I gave an electro-mechanical model of a speaker. I did that because it is rather straightforward. But maybe some explanation is handy for those not familiar with such modelling.
In a speaker there is a voice coil motor. This motor generates a force on the moving mass of the cone assembly. This is modelled by H1. The current through the voice coil generates a force proportional to the BL product and is acting on the mass. The mass will now be accelerated (a = F/m). When we integrate acceleration over time we get the speed of the cone assembly. The mechanical damping is nothing else than a force depending on speed (= friction). This force counteracts the driving force of the voice coil and is modelled by Ds. Also the speed of the voice coil generates a back EMK proportional to the BL product in the voice coil. This back EMK counteracts the driving voltage and is subtracted from the input voltage by E1. In fact the combination of H1 and E1 is analogous to the gyrator of Svante’s circuit.
When we integrate speed over time we end op with displacement. Also this displacement generates a force counteracting the driving force. This force comes from the spring action of the surround and the spider of the speaker and is modelled by Sprng_s.
You can model all the mechanical properties to analogous electrical properties as in Svante’s circuit. That is also what Thiele and Small did. But you can’t do that without knowing what the mechanical thing actually is.
You can write down the model of post 17 in closed form and translated to the S-domain you will end up with the formulas of T&S. I made my model because I have all results I am interested in available at the same time. It works in the frequency domain as well as in the time domain.
The work of T&S is hard reading. It assumes you are already familiar how to convert mechanical things into electrical equivalents. Anyway is worth reading, at least you get some idea.
BTW I am not a mechanical engineer nor a scientist but just an EE, like many of you.
Cheers
In post 17 I gave an electro-mechanical model of a speaker. I did that because it is rather straightforward. But maybe some explanation is handy for those not familiar with such modelling.
In a speaker there is a voice coil motor. This motor generates a force on the moving mass of the cone assembly. This is modelled by H1. The current through the voice coil generates a force proportional to the BL product and is acting on the mass. The mass will now be accelerated (a = F/m). When we integrate acceleration over time we get the speed of the cone assembly. The mechanical damping is nothing else than a force depending on speed (= friction). This force counteracts the driving force of the voice coil and is modelled by Ds. Also the speed of the voice coil generates a back EMK proportional to the BL product in the voice coil. This back EMK counteracts the driving voltage and is subtracted from the input voltage by E1. In fact the combination of H1 and E1 is analogous to the gyrator of Svante’s circuit.
When we integrate speed over time we end op with displacement. Also this displacement generates a force counteracting the driving force. This force comes from the spring action of the surround and the spider of the speaker and is modelled by Sprng_s.
You can model all the mechanical properties to analogous electrical properties as in Svante’s circuit. That is also what Thiele and Small did. But you can’t do that without knowing what the mechanical thing actually is.
You can write down the model of post 17 in closed form and translated to the S-domain you will end up with the formulas of T&S. I made my model because I have all results I am interested in available at the same time. It works in the frequency domain as well as in the time domain.
The work of T&S is hard reading. It assumes you are already familiar how to convert mechanical things into electrical equivalents. Anyway is worth reading, at least you get some idea.
BTW I am not a mechanical engineer nor a scientist but just an EE, like many of you.
Cheers
Yes, "our" models are perfectly equivalent, if anyone doubted that. I love the way with two controlled voltage/force sources to model the motor/generator of the speaker.
In both cases one has to know the mechanical and electrical parameters. The main obstacle with understanding "my" model is the gyrator, I guess. OTOH the equivalent of your two sources is the gyrator...
In both cases one has to know the mechanical and electrical parameters. The main obstacle with understanding "my" model is the gyrator, I guess. OTOH the equivalent of your two sources is the gyrator...
crystal clear!
Actually, yes Thanks. I was under the impression that Qes was for a purely electrical circuit, and Qms for a purely mechanical one. I didn't realise that they differed only in which _resistance_ they took into account, reactance being the same for both.
- Ashwin
Svante said:
Crystal clear, right?
Actually, yes
Thanks. I was under the impression that Qes was for a purely electrical circuit, and Qms for a purely mechanical one. I didn't realise that they differed only in which _resistance_ they took into account, reactance being the same for both. - Ashwin
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