Equation relating t/s parameters to sensitivity vs frequency
 User Name Stay logged in? Password
 Home Forums Rules Articles diyAudio Store Blogs Gallery Wiki Register Donations FAQ Calendar Search Today's Posts Mark Forums Read Search

 Multi-Way Conventional loudspeakers with crossovers

 Please consider donating to help us continue to serve you. Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving
 16th November 2008, 10:15 PM #1 thadman   diyAudio Member   Join Date: Dec 2005 Location: west lafayette Equation relating t/s parameters to sensitivity vs frequency What is the equation relating t/s parameters to sensitivity vs frequency? __________________ "It is a profound and necessary truth that the deep things in science are not found because they are useful; they are found because it was possible to find them."
 16th November 2008, 11:03 PM #2 BHTX   diyAudio Member     Join Date: Feb 2006 η0 - The reference or "power available" efficiency of the driver, in percent. The expression ρ/2πc can be replaced by the value 5.445×10^-4 m^2*s/kg for dry air at 25 °C. For 25 °C air with 50% relative humidity the expression evaluates to 5.365×10^-4. A version more easily calculated with typical published parameters is: The expression 4π^2/c^3 can be replaced by the value 9.523×10^–7 s³/m³ for dry air at 25 °C. For 25 °C air with 50% relative humidity the expression evaluates to 9.438×10^–7. From the efficiency, we may calculate sensitivity, which is the sound pressure level a speaker produces for a given input: A speaker with an efficiency of 100% (1.0) would output a watt of energy for every watt input. Considering the driver as a point source in an infinite baffle, at one meter this would be distributed over a hemisphere with area 2π m² for an intensity of (1/(2π))=0.159154 W/m², which gives an SPL of 112.02 dB. SPL at 1 meter for an input of 1 watt is then: dB(1 Watt) = 112.02+ 10*log(η0) SPL at 1 meter for an input of 2.83 Volts is then: dB(2.83V) = dB(1 Watt) + 10*log(8/Re) = 112.02+ 10*log(η0) + 10*log(8/Re)
 16th November 2008, 11:15 PM #3 BHTX   diyAudio Member     Join Date: Feb 2006 GAH!.. forum screwed it up. Anyway, it's all right here.
diyAudio Member

Join Date: Dec 2005
Location: west lafayette
Quote:
 Originally posted by BHTX GAH!.. forum screwed it up. Anyway, it's all right here.
Thanks.

Is there an equation that uses box volume as a variable to calculate sensitivity at the lower end of the systems bandwidth?
__________________
"It is a profound and necessary truth that the deep things in science are not found because they are useful; they are found because it was possible to find them."

 17th November 2008, 12:16 AM #5 Ron E   diyAudio Member     Join Date: Jun 2002 Location: USA, MN Perhaps explain what you want to achieve, since the question you want answered seems to be a moving target. It sounds like you want frequency response calculations - you may find them (and a ready made spreadsheet) at www.diysubwoofers.org __________________ Our species needs, and deserves, a citizenry with minds wide awake and a basic understanding of how the world works. --Carl Sagan Armaments, universal debt, and planned obsolescence--those are the three pillars of Western prosperity. —Aldous Huxley
diyAudio Member

Join Date: Dec 2005
Location: west lafayette
Quote:
 Originally posted by Ron E Perhaps explain what you want to achieve, since the question you want answered seems to be a moving target.
I'm trying to find an equation that defines the optimal driver parameters and box volume for a given bandwidth (ie highest sensitivity over that bandwidth).
__________________
"It is a profound and necessary truth that the deep things in science are not found because they are useful; they are found because it was possible to find them."

 22nd November 2008, 04:45 PM #7 Ron E   diyAudio Member     Join Date: Jun 2002 Location: USA, MN Ah, you are rediscovering Hoffman's Iron Law, then? Efficiency = k*Vb*Fc^3 (or use efficiency equation above) Without going through a whole derivation and achieving a true relation, you could substitute some curve fit relations for vented box such as: Vb=20*Vas*Qts^3.3 Fc=.42*Fs*Qts^-0.96 to back out some parameters. Sealed box can be done analytically with Qtc/Qts=Fc/Fs=sqrt(Vas/Vb+1) I think you will find you are always bouncing off of constraints you need to place on Fs, Vas, Qes, Qts, etc to make a realizable driver. You often end up with a Fs of 3 and a Vas of 10000 and a Qts of 0.13 or some other such nonsense. __________________ Our species needs, and deserves, a citizenry with minds wide awake and a basic understanding of how the world works. --Carl Sagan Armaments, universal debt, and planned obsolescence--those are the three pillars of Western prosperity. —Aldous Huxley
 22nd November 2008, 08:44 PM #8 Rybaudio   diyAudio Member   Join Date: Mar 2003 Location: State College, PA thadman, If by the equation for "sensitivity vs frequency," you mean the equation that gives you the sound pressure at 1m from the speaker with a constant voltage input as a function of frequency, then yes, there is such an equation. If the following assumptions are made, the equation below describes just this: - radiation into half-space - sealed enclosure on the rear - low frequencies (so the radiation is omnidirectional, the radiation impedance looks like a mass, the cone acts as one lumped mass, and the air in the box acts as one lumped spring) - small signal (speaker is linear) Parameters: Mm: effective moving mass (including air out front) Rm: lumped mechanical resistance of moving parts Cm: lumped compliance of the suspension Bl: force factor Le: voice coil inductance Re: voice coil resistance Sd: piston area Vb: rear enclosure volume constants: rho: density of air (~1.2 kg/m^3) gamma: heat capacity ratio (~1.4) Po: rest pressure of air (~10^5 N/m^2) variables: s: complex frequency (s = i*w = i*2*pi*f where w is angular frequency and f is frequency) Then the sound pressure at 1 meter, with 1V of input is: p = rho*Bl*Sd*s^2 / [2*pi * (Le*s + Re) * (Mm*s^2 + Bl^2*s/(Le*s + Re) + 1/Cm + Sd^2*gamma*Po/Vb] Note this is a complex transfer function. The magnitude is obtained by taking the magnitude of this expression. Also, if you want to display it in dB you need to take the ratio of the magnitude to reference pressure (2*10^-5 N/m^2) and then take 20*log10 of that. This is the equation that describes the LF behavior of the speaker in a sealed box. If you search around the net you'll find the relationship between T/S parameters and the parameters above- they are the same thing, just described a bit differently. The reference efficiency, Hoffman's iron law, etc all come from this. This is the equation from which you might be able to obtain "an equation that defines the optimal driver parameters and box volume for a given bandwidth (ie highest sensitivity over that bandwidth)" I can't tell precisely what you mean by the last statement, but whatever it is, you might be able to get it from this. There is a corresponding equation for vented enclosures. I can figure that out and put it on here if you want it.

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Site     Site Announcements     Forum Problems Amplifiers     Solid State     Pass Labs     Tubes / Valves     Chip Amps     Class D     Power Supplies     Headphone Systems Source & Line     Analogue Source     Analog Line Level     Digital Source     Digital Line Level     PC Based Loudspeakers     Multi-Way     Full Range     Subwoofers     Planars & Exotics Live Sound     PA Systems     Instruments and Amps Design & Build     Parts     Equipment & Tools     Construction Tips     Software Tools General Interest     Car Audio     diyAudio.com Articles     Music     Everything Else Member Areas     Introductions     The Lounge     Clubs & Events     In Memoriam The Moving Image Commercial Sector     Swap Meet     Group Buys     The diyAudio Store     Vendor Forums         Vendor's Bazaar         Sonic Craft         Apex Jr         Audio Sector         Acoustic Fun         Chipamp         DIY HiFi Supply         Elekit         Elektor         Mains Cables R Us         Parts Connexion         Planet 10 hifi         Quanghao Audio Design         Siliconray Online Electronics Store         Tubelab     Manufacturers         AKSA         Audio Poutine         Musicaltech         Aussie Amplifiers         CSS         exaDevices         Feastrex         GedLee         Head 'n' HiFi - Walter         Heatsink USA         miniDSP         SITO Audio         Twin Audio         Twisted Pear         Wild Burro Audio

 Similar Threads Thread Thread Starter Forum Replies Last Post Kaoss Multi-Way 4 13th August 2008 05:17 AM veracohr Analogue Source 2 29th February 2008 05:24 PM bvan Full Range 12 5th November 2007 08:57 PM rhythmdiy Multi-Way 5 5th November 2007 12:33 PM ERICSPEEd Multi-Way 0 30th May 2005 04:48 AM

 New To Site? Need Help?

All times are GMT. The time now is 12:57 AM.