What is the conversion to change an efficiency spec that is in dB/2.83w to one that is in dB/1w so that one can compare apples to apples.
Since the power would be 2.83 times less it would seem that the efficiency rating would be reduced by a little over 3 dB. But what is the actual correction?
Since the power would be 2.83 times less it would seem that the efficiency rating would be reduced by a little over 3 dB. But what is the actual correction?
8 ohm speaker: 2.83 volts = 1 watt
4 ohms speaker: 2.83 volts = 2 watts. At equal efficiency, the 4 ohmer will have a plus 3 dB higher rating at 2.83 Volts than an 8 ohms speaker.
2 ohms speaker: 2.83 volts = 4 watts. The two ohm speaker at equal efficiency will have a plus 6 dB higher efficiency at 2.83 volts than it will at one watt.
4 ohms speaker: 2.83 volts = 2 watts. At equal efficiency, the 4 ohmer will have a plus 3 dB higher rating at 2.83 Volts than an 8 ohms speaker.
2 ohms speaker: 2.83 volts = 4 watts. The two ohm speaker at equal efficiency will have a plus 6 dB higher efficiency at 2.83 volts than it will at one watt.
moving_electron said:
Its not quite apples to apples.
It depends on the load handling capability of an amplifier.
Take an amplifier 50W on the point of clipping into 8 ohms.
With 16 ohms output will be typically ~ 28W into 16 ohms.
With 4 ohms amplifiers vary a lot, typically producing between
55W and 90W into 4 ohms, the latter value is more load tolerant.
Speakers of equal efficiency will give max outputs directly
related to the power output of the amplifier into that load.
But note that a 8 ohm speaker 3dB less efficient than a 16 ohm
speaker will have nearly the same maximum output with the
above amplifier.
For 4 ohm tolerant amplifiers the the same reasoning can be
used, a 4 ohm speaker 6dB less efficient than a 16 ohm
speaker will have nearly the same maximum output with the
above amplifier.
If you also note that bass extension is generally inversely
proportional to efficiency, less efficient more bass extension,
it becomes clear amplifier matching is critical to optimise
maximum performance.
2.83V is 1 Watt into 8 ohm. (dB/2.83V)
For impedance Z, you change the dB/2.83V
by 10 x log (Z/8) to derive the dB/W figure.
sreten.
dB~=10*log10(Re/8)
If you have a 4ohm speaker with a 3 ohm voice coil, rated at 93dB/2.83V, its 1W sensitivity would be
dB=10*log10(3/8) = -4.26dB or 88.74dB
-------------
The least ambiguous spec is the 2.83V spec. Manufacturers play around with the ambiguity of the 1W spec so I wouldn't trust it.
If you have a 4ohm speaker with a 3 ohm voice coil, rated at 93dB/2.83V, its 1W sensitivity would be
dB=10*log10(3/8) = -4.26dB or 88.74dB
-------------
The least ambiguous spec is the 2.83V spec. Manufacturers play around with the ambiguity of the 1W spec so I wouldn't trust it.
Ron:
You gave us the following equation for comparing SPL at 2.83 volts to SPL at 1 watt:
dB~=10*log10(Re/8)
The only thing is: you assume that an 4 ohm rated speaker with a 3 ohm voice coil should be rated at 3 ohms. But that an 8 ohm rated speaker should be rated with a DC resistance, (Re), of 8 ohms.
If you are going to use the DC resistance of the 4 ohm speaker, then you should use the DC resistance of the 8 ohm speaker.
As you know, a speaker rated at 8 ohms is very likely to have a DC resistance, (Re) of between 5.5 and 6.5 ohms. Call it 6 ohms as an estimate.
So your equation becomes:
dB~=10*log10(Re/6) = 10*log10(3/6) =-3.01 dB.
So the 4 ohm speaker rated at 93 dB @ 2.83volts will be 89.9999dB at 1 watt. Or 90 dB for short.
Am I correct on this?
You gave us the following equation for comparing SPL at 2.83 volts to SPL at 1 watt:
dB~=10*log10(Re/8)
The only thing is: you assume that an 4 ohm rated speaker with a 3 ohm voice coil should be rated at 3 ohms. But that an 8 ohm rated speaker should be rated with a DC resistance, (Re), of 8 ohms.
If you are going to use the DC resistance of the 4 ohm speaker, then you should use the DC resistance of the 8 ohm speaker.
As you know, a speaker rated at 8 ohms is very likely to have a DC resistance, (Re) of between 5.5 and 6.5 ohms. Call it 6 ohms as an estimate.
So your equation becomes:
dB~=10*log10(Re/6) = 10*log10(3/6) =-3.01 dB.
So the 4 ohm speaker rated at 93 dB @ 2.83volts will be 89.9999dB at 1 watt. Or 90 dB for short.
Am I correct on this?
base 10 was assumed for the log and nominal impedance assumed.
Re values can be very misleading and the above doesn't
take into account different impedance characteristics.
But the above is correct, if you use Re values, the Re
of 8 ohms nominal is nominally 8/root2 = 5.6R.
Nominal Re for 4ohms is 2.8R.
The correct ratio's are Z/8 or Re/5.6.
sreten.
2.828 Volts is 1Watt into 8 ohms
2.828 volts into 3 ohms is 2.828^2/3 = 2.666Watts into 3 ohms
10*log10(2.666)= 4.26dB
I made no errors, Kelticwizard.
The question was how to convert 2.83V ratings to a 1W rating.
It does not matter if the 4ohm voice coil is actually 2 ohms or 3 ohms or 4 ohms. The conversion from volts to watts with an assumed resistive load is not difficult...............
sreten wrote:
sreten is wrong.
2.828 volts into 3 ohms is 2.828^2/3 = 2.666Watts into 3 ohms
10*log10(2.666)= 4.26dB
I made no errors, Kelticwizard.
The question was how to convert 2.83V ratings to a 1W rating.
It does not matter if the 4ohm voice coil is actually 2 ohms or 3 ohms or 4 ohms. The conversion from volts to watts with an assumed resistive load is not difficult...............
sreten wrote:
sreten is wrong.
Ron E said:
Okay, but what bothers me is that a speaker with a 3 ohm voice coil will not be playing at 3 ohms in practice. The lowest impedance it will be playing at will be 4 ohms.
So why are we using Re in that formula instead of nominal impedance? It is never going to play at 3 ohms.
It seems to me that by the same token, if we have a speaker with a 6 ohm voice coil that is rated 90 dB @ 2.83 volts/1M, then at 1 watt we have:
dB~=10*log10(Re/8)
dB= 10 log (6/8) = -1.25
A speaker with an Re of 6.0 is certain be rated at 8 ohms.
The eight ohm speaker is 88.25 db @ 1W/1M
but 90 dB at 2.83V/1M
Is that true? That just about every speaker rated 8 ohms is really less efficient than what the 2.83V specs would indicate?
Ron E said:
I'm afraid Ron E it is you who has got it all wrong.
I never assumed resistive loads, I assumed nominal loudspeaker loads.
Speakers are tested with a constant voltage for dB/2.83V.
A 4 ohm speaker with with the same voltage sensitivity as
an 8 ohm speaker is basically 3 dB less efficient, not 4.26.
If you want to compare relative efficiencies of speakers
then Z/8 or Re/5.6 can be used makes no difference.
The fact that 2.83V into an 8R resistor is 1 Watt is a nicety.
If you insist using this then the relative efficiency according
to your method of an 8ohm speaker is 10log 6/8, i.e. -1.26,
and the relative efficiency of 4 and 8 ohm speakers with the
same voltage sensitivity is still - 3dB.
People do not seem to understand the meaning of nominal speaker impedance :
The average impedance of the speaker must be higher or = nominal.
The lowest impedance must not be less than nominal/root2.
One of the two will decide the nominal impedance,
unless the manufacturers cheat in their specifications,
which is not exactly unknown.
It should be obvious that dB/2.83V is easy to measure.
Real efficiency is must harder as it depends on the
impedance curve and is an essentially useless figure.
However using Z nominal of the speaker will give you an idea.
Using Re of a driver will give an unrealistically low figure.
sreten.
Sreten, I agree with you. Bottom line here is that sensitivity is *not* an efficiency measure and that it is easy (for the manufacturer) to increase the sensitivity by decreasing Re. This will *not* change the efficiency though.
The sensitivity measure should always be paired with an impedance measure if efficiency is to be considered.
The sensitivity measure us useful when designing the balance between woofer/tweeter, and I guess why that is the more popular way of expressing "loudness per input".
The true efficiency is of more academic interest. Important, but not always easy. For example, the efficiency of a closed box speaker can be 10-20 dB higher at system resonance. Sensitivity is not.
I have seen this definition a lot recently. When I was little I was tought that the actual impedance should never be lower than 80% of nominal. Who changed this? Somebody who wanted higher sensitivity figures?
The sensitivity measure should always be paired with an impedance measure if efficiency is to be considered.
The sensitivity measure us useful when designing the balance between woofer/tweeter, and I guess why that is the more popular way of expressing "loudness per input".
The true efficiency is of more academic interest. Important, but not always easy. For example, the efficiency of a closed box speaker can be 10-20 dB higher at system resonance. Sensitivity is not.
sreten said:
The average impedance of the speaker must be higher or = nominal.
The lowest impedance must not be less than nominal/root2.
I have seen this definition a lot recently. When I was little I was tought that the actual impedance should never be lower than 80% of nominal. Who changed this? Somebody who wanted higher sensitivity figures?
Re: Bogus numbers?
Here a spec for a 12" car subwoofer, the first I found with a search :
PBO Advanced Fiber cone with rubber surround/gasket
"tornado-style" design minimizes resonance and maximizes rigidity
dual 4-ohm voice coils
frequency response 20-600 Hz
recommended power range 25-600 watts RMS (300 watts per coil)
peak power handling 1,200 watts
sensitivity 93 dB
top-mount depth 5-15/16"
sealed box volume: 1.0 cubic feet (from 0.8 to 1.5 acceptable)
ported box volume: 1.5 cubic feet (from 1.0 to 2.0 acceptable)
Recommended Box Type: 1, 2, 3
2-year warranty
The sensitivity is quoted as 93dB.
If this is dB/2.83V it is very likely to have been measured
with the voice coils in parallel, whilst a more honest way
of doing it would be to wire the coils series for 8 ohms.
So a reasonable assessment of sensitivity is 87dB/W.
Which is the sort of real sensitivity you need for a
decent alignment of a 12" in the box sizes suggested.
sreten.
eplpwr said:
Here a spec for a 12" car subwoofer, the first I found with a search :
PBO Advanced Fiber cone with rubber surround/gasket
"tornado-style" design minimizes resonance and maximizes rigidity
dual 4-ohm voice coils
frequency response 20-600 Hz
recommended power range 25-600 watts RMS (300 watts per coil)
peak power handling 1,200 watts
sensitivity 93 dB
top-mount depth 5-15/16"
sealed box volume: 1.0 cubic feet (from 0.8 to 1.5 acceptable)
ported box volume: 1.5 cubic feet (from 1.0 to 2.0 acceptable)
Recommended Box Type: 1, 2, 3
2-year warranty
The sensitivity is quoted as 93dB.
If this is dB/2.83V it is very likely to have been measured
with the voice coils in parallel, whilst a more honest way
of doing it would be to wire the coils series for 8 ohms.
So a reasonable assessment of sensitivity is 87dB/W.
Which is the sort of real sensitivity you need for a
decent alignment of a 12" in the box sizes suggested.
sreten.
Sreten, Svante,
Both Leo Beranek and J.E Benson desribe the quantity "power available efficiency", from which the common sensitivity equation is derived:
dBref_1W=112.2+10*log10(9.6e-10*Fs^3*Vas/Qes)
where Vas is in liters.
The quantity in brackets is also equal to k*BL^2*Sd^2/(Mms^2*Re), where k is equal to some constant of proportionality. I think it is 5.4 something to a power of 10.
This relation is very frequently used as the quoted sensitivity of the driver - at 1W/1m. The other commonly quoted number - in fact the most common one - is the 2.83V number.
dBref_2.83V = dBref_1W + 10 * log10(8/Re) is the reference sensitivity at 2.83Volts, not because of some happy coincidence that 2.83volts is one watt at 8 ohms, but precisely because 2.83V volts is one watt at 8 ohms.
Both Leo Beranek and J.E Benson desribe the quantity "power available efficiency", from which the common sensitivity equation is derived:
dBref_1W=112.2+10*log10(9.6e-10*Fs^3*Vas/Qes)
where Vas is in liters.
The quantity in brackets is also equal to k*BL^2*Sd^2/(Mms^2*Re), where k is equal to some constant of proportionality. I think it is 5.4 something to a power of 10.
This relation is very frequently used as the quoted sensitivity of the driver - at 1W/1m. The other commonly quoted number - in fact the most common one - is the 2.83V number.
dBref_2.83V = dBref_1W + 10 * log10(8/Re) is the reference sensitivity at 2.83Volts, not because of some happy coincidence that 2.83volts is one watt at 8 ohms, but precisely because 2.83V volts is one watt at 8 ohms.
Eplpwr:
If you really want to know about SPL@1 Watt, you should know that it can be calculated from other Thiele-Small parameters like Qe and Vas.
There is a formula for it, but I don't have it. No matter. Bullock and White have written a freeware program, BoxModel, in which you input your Vas, Qe, Fs, etc and on the bottom appears other information, such as your Qts and SPL@1 Watt/1M. Very useful.
http://www.hal-pc.org/~bwhitejr/
Of course, you are still dependent on the manufacturer giving you correct information for Vas and Fs, etc. But you would surprised at how many SPL specs do not even agree with the manufacturer's own specs for Qe, Vas and Fs!
The illustration below is a screen shot of the program for a high Qts speaker. The top box, white letters on dark blue, is where you enter the Thiele-Small parameters. The light green box below is where the remaining parameters are calculated, including sensitivity, (Sns) at 1 Watt/1M.
The parameters listed are for the driver. They are unaffected by whatever enclosure type-closed box, ported, or passive radiator-that you use it in.
PS: When inputting data in the dark blue part the program, be sure to use the right arrow key before entering your value. That hung me up for awhile.
PPS: Don't use the Transmission Line part of the program. Even Bullock later wrote that it is inaccurate. The rest of the program is just fine, though. For dealing with T-lines, use the free MathCAD software at Martin King's site, www.quarter-wave.com
If you really want to know about SPL@1 Watt, you should know that it can be calculated from other Thiele-Small parameters like Qe and Vas.
There is a formula for it, but I don't have it. No matter. Bullock and White have written a freeware program, BoxModel, in which you input your Vas, Qe, Fs, etc and on the bottom appears other information, such as your Qts and SPL@1 Watt/1M. Very useful.
http://www.hal-pc.org/~bwhitejr/
Of course, you are still dependent on the manufacturer giving you correct information for Vas and Fs, etc. But you would surprised at how many SPL specs do not even agree with the manufacturer's own specs for Qe, Vas and Fs!
The illustration below is a screen shot of the program for a high Qts speaker. The top box, white letters on dark blue, is where you enter the Thiele-Small parameters. The light green box below is where the remaining parameters are calculated, including sensitivity, (Sns) at 1 Watt/1M.
The parameters listed are for the driver. They are unaffected by whatever enclosure type-closed box, ported, or passive radiator-that you use it in.
PS: When inputting data in the dark blue part the program, be sure to use the right arrow key before entering your value. That hung me up for awhile.
PPS: Don't use the Transmission Line part of the program. Even Bullock later wrote that it is inaccurate. The rest of the program is just fine, though. For dealing with T-lines, use the free MathCAD software at Martin King's site, www.quarter-wave.com
Attachments
One good thing about Ron's bringing up the subject of a speaker's Re, (DC resistance), is that efficiencies can vary even among similarly rated speakers rated at the same SPL.
For instance:
Speaker A is rated at 4 ohms and 90 dB@2.83v/M. It's DC resistance, (Re), is 3.3 ohms.
Speaker B is rated at 4 ohms and 90 dB@2.83v/M. It's DC resistance, (Re) is 2.5 ohms.
Both speakers are rated 4 ohms. Both the same SPL @ 2.83 volts. Yet Speaker B, (2.5 ohms), will actually give 1.2 dB less SPL when driven by one watt than Speaker A, (3.3 ohms), will.
And I have seen speakers rated at 4 ohms that have Re's of 2.5 ohms, and speakers rated at 4 ohms that have Re's of 3.3 ohms.
For instance:
Speaker A is rated at 4 ohms and 90 dB@2.83v/M. It's DC resistance, (Re), is 3.3 ohms.
Speaker B is rated at 4 ohms and 90 dB@2.83v/M. It's DC resistance, (Re) is 2.5 ohms.
Both speakers are rated 4 ohms. Both the same SPL @ 2.83 volts. Yet Speaker B, (2.5 ohms), will actually give 1.2 dB less SPL when driven by one watt than Speaker A, (3.3 ohms), will.
And I have seen speakers rated at 4 ohms that have Re's of 2.5 ohms, and speakers rated at 4 ohms that have Re's of 3.3 ohms.
Ron E said:
Hi Ron E,
The above equation, for all practical purposes is not applicable.
The equation is only true at the one frequency a single drivers impedance
is resistive and equal to Re, at all other frequencies its meaningless.
All it is telling you at that frequency is the blantantly obvious,
that if Re = 8R, then dB/W and dB/2.83V are one and the same,
and that they are not the same if Re does not equal 8R.
It is not, in any shape or form, the definition of reference
efficiency, only a reference efficiency for a single driver at
the frequency the above is true, and a not particular useful
reference either, because its simply the difference between
dB/W and dB/2.83V for any given resistive load.
But is is not how a complex loudspeakers quoted dB/W is defined,
or more to the point estimated from its dB/2.83V sensitivity.
All you have to do to make it generally applicable is replace Re
with Z, where Z is the nominal impedance of the speaker / driver.
(And by implication the 8 represents 8 ohms nominal, not 8R)
sretenkelticwizard said:
simply put again,
the relative efficiency at the frequency the drivers
impedance is resistive and equal to Re is not the
only issue.
Otherwise drivers would be rated by Re not ohms.
Drivers can have different Re's and the same nominal
impedance due to differences in the main resonance peak
and the inductances of the drivers.
Its not worth getting bogged down in details because nearly
always nominal impedances are rounded to the nearest ohm
for drivers - sometimes to the nearest convenient sounding
impedance - sometimes they are simply innacurate.
For complex loudspeakers phase angles come much more into
the picture to arrive at a reasonable estimation of the average
resistive load an amplifier sees.
sreten.
moving_electron said:
This, sreten, was the actual question, the fact that the original poster misused terminology and misunderstood that one was a voltage rating and one was a power rating is beside the point.
Just so we are all on the same page, efficiency is a number specified in percent, and sensitivity is a number specified in dB for a given input.
Problem, we need a rating that will allow someone to have some idea of how sensitive the driver is. We can measure the driver and use that, but you will find that almost all sensitivity specs are calculated with the formulas I have given.
An sensitivity spec, is just that, a spec. It is one number and doesn't have anything to do with the actual efficency of the driver at any frequency, because we all know the efficiency of the driver changes with frequency.
It doesn't matter that efficiency or impedance varies with frequency because SENSITIVITY is a spec based on Re, to which my equations apply precisely.
Look back to the references I cited and you will understand that.
Ron E said:
OK, let's get back to the way this equation was derived. The complete equation for efficiency that is used is:
eta=rho0/(2pi*c) * (Bl)^2/Re * Sd^2/Mms^2 , so the constant k that you mention is rho0/(2pi*c) which is about 5.4e-4 [kg s /m^4]
The conditions for this equation is that the speaker is operating in half space, in its mass controlled range with no effect of the lossy voice coil inductance. Given this, the impedance of the driver is near the DC resistance.
If the efficiency was 100% the acoustic output power would be 1 W. If this power was spread across a half-sphere with the radius 1 m, the intensity would be 1/(2pi)*1=0.159 W/m^2. This intensity corresponds to the intensity level 10*log(0.159/1e-12)=112.01 dB. These are the 112.2 dB in your equation. Now, if the efficiency is lower, the output level will drop as the level of the efficiency= 10*log(eta).
Bingo, there is the Beranek equation.
The above is a calculation of the efficiency of a simplified model of the electrodynamic loudspeaker. The sensitivity figure is a measure which tells you what SPL you get from 2.83 volts, preferably from real measurements. Since the power that enters an 8 ohm loudspeaker at 2.83 volts is not 1W for all frequencies, the dB@1W value will be different from the dB@2.83V value. The difference depends on the impedance, and varies with frequency.
Since it is the amplifier voltage (not power) that is proportional to the input signal, the dB@2.83V value is the only one of the two that makes sense.
Then again, I don't know if this is much to argue about really.
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