Sensitivity and efficiency?

[sachi]

hello,
could any of you please give me the exact mathematical relationship between the sensitivity and efficiency of a speaker.
also how different are the two. besides which is more important and how does the impedance of the speaker affect each of them.

also what do u mean by impedance of a speaker to be 8ohms and i see another rating Nominal impedance=say5.04 ohm.
thanks

 

[Mr Evil]

Unless I'm mistaken, there is no exact mathematical relationship betwen the two, although generally high sensitivity speakers are also more efficient.

Sensitivity is defined as the SPL measured on-axis at a distance of 1m with an input voltage of 2.83V, which corresponds to 1W into an 8ohm resistive load. Since speakers aren't 8ohm resistive (they have resistive and reactive components giving a total impedance that varies with frequency and is not very close to 8ohms most of the time), the actual input power will differ by an undefined amount.

Efficiency is the proportion of electrical power converted to acoustic power.

Since sensitivity has only a nominal relationship to power, you couldn't possibly convert between them. Furthermore, sensitivity only measures sound at one spot; a speaker that focuses all acoustic power onto that spot would have higher sensitivity without being more efficent. This also makes it impossible to correlate the two.

 

[Snickers-is]

I can not give you the exact matematical relationship to absolute efficiency, but it can generally be measured in two terms:

% and dB@1W/1m.

The first one is simply how much accoustic effect in watt do we get out when pushing 1 watt in.

The second one is the number of dB output at 1 meter distance (anechoic chamber) with exactly 1 Watt input.

Sensitivity is based on measuring with 2,83 volts input. At 8 ohms this will be the same as 1 watt. At all other impedances it will differ from the efficiency.

Therefore the sensitivity will give an indication on how loud the speaker will play at a given input voltage for a given frequency. That is also the situation with most amplifiers so this is the method to determine frequency response.

The efficiency will tell us how heavy load the speaker will be for an amplifier. It must be combined with the electrical phase to get the full truth about the speaker load.

 

[sachi]

thanks.
i know amp and speakers are rated for some freq range.
now because of the reactive elements does the speaker show a peak output for some particular freq in the rated freq range or is the output the same throughout.
what do you mean by the fs rating of a speaker. is this the lowest freq the speaker can reproduce or is it something else. i must say this is sounding dumb. but i really want to know.

i read somewhere that for example For an 8Ω speaker, the sensitivity and efficiency figures are the same, but a 4Ω speaker with a sensitivity of 90dB would have an efficiency of only 87dB.
so how is impedance making a difference.
iread someplace that the efficiency is derived for some watt input while the sensitivity is derived for a volt input and hence the dependece on impedance. is this true.
Snickers-is

The efficiency will tell us how heavy load the speaker will be for an amplifier. It must be combined with the electrical phase to get the full truth about the speaker load.

if i am right the lesser the impedance the heavier the load. how does phase figure in all this.

 

[Snickers-is]

Since the amplifier delivers a voltage controlled signal and the voltage sensitivity is more or less flat the impedance is close to ignorable VS frequency response. But that is also depending on the power amplifier.

Low impedance is usually heavy load. That is because:

A driver with sensitivity 90dB@2,83volt/1m may for example have 8ohms at 1khz, and 4 ohms at 50 hz. Then you will need twice the power at 50 hz, but since the amplifier provides voltage the driver will just use twice the current.

The reactive components makes the current drawn out of phase with the output voltage of the amplifier. This forces the amplifier to deliver high current when the output voltage is low (in the part of the signal period where the momentane voltage is close to 0), and the voltage drop over the transistors are high. This makes the amplifier to produce a lot of heat, and puts pressure to the power supply.

 

[BillFitzmaurice]

There is a precise formula, which I don't remember offhand, but 1 acoustical watt is about 120dB as I recall. There are some horns that can get to about 50% efficiency, which translates to about 117dB/watt. 25% efficiency would then be 114dB, 12.5% is 111dB and so forth. These figures might be off a dB or so but are pretty close.

 

[JMB]

I think that you are looking for this relationship:

sPl (1Watt/m) = 112 + 10*LOG (eta/100)

eta(%)=((2.7*10^-8*Fs^3*Vas)/Qes)*100

This can also be related to Ro/(2*PI()*c)*(Bl*Sd^2)/Re*Mms^2.

Hope this helps,

Jay

 

[GhettoSQ]

Here's an article I found helpful:
http://www.stereophile.com/loudspeakerreviews/272/index5.html

The gist of it being that efficiency is measured at a particular frequency, whereas because sensitivity is measured by voltage, which is constant with transistor amplifiers, it (sensitivity) remains the same over the frequency range. In practical terms, apples and oranges, but nowadays sensitivity is considered a more useful benchmark. Everyone, feel free to correct me if I'm wrong

Can I chime in regarding load? Think of your amplifier as a car engine and the speaker as the chassis and everything else. A 140hp four-banger will not drive a semi (high impedance), but a 600hp V12 would be too much for a Civic (low impedance)...although the analogy only works if the V12 burns up in the Civic But then imagine that you have a good engine/chassis match, and you live in the mountains and frequently drive up and down steep hills, making the engine work harder going uphill, consuming more gas (wattage), but when you go downhill, it gets hotter (current).

OK, it sounded good in my head...someone smack me now.

 

[Sherman]

thanks.
...does the speaker show a peak output for some particular freq in the rated freq range or is the output the same throughout.
what do you mean by the fs rating of a speaker...

...if i am right the lesser the impedance the heavier the load...

All "raw" speakers (drivers) show peaks and valleys. Response is not flat throughout the stated frequency range. Better drivers generally have flatter responses but they are still not totally flat. When designing a speaker the designer tries to use the box, crossovers, stuffing, etc. to make the response as flat as possible (within reason).

Fs is the resonant frequency of the speaker. Generally a speaker can produce frequencies lower than its Fs, sometimes a lot lower sometimes not. That depends on the driver. However if you look at a frequency response chart for a particular driver you will notice a "hump" or increase iin output at Fs.

Think of the speaker as a bucket with a hole in the bottom and an amplifier as a faucet or hose. Impedance is the size of the hole in the bottom. A 4 ohm impedance is a much bigger hole than an 8 ohm impedance. Therefore your faucet may have trouble keeping up with the water leaking out the hole. (Your amp will work harder into a lower impedance.)

Don't worry about asking questions, everyone has to start somewhere and we've all been there at some point! In fact I'm only a little more advanced than rank beginner level myself. You can find a lot of information on the web by Googling for "speaker impedance and power" and similar terms.

Hope some of this helps!

 

[AndrewT]

Hi Bill & all
using the formula in post 7 gives a maximum output from a 100% efficient speaker of 112db and 50% will give 109db.
Do you think these are right?
They are close to a figure I saw quoted many years ago of about 108db(but I may be wrong) as the maximum that 1 watt can produce.
Note here we are quoting real watts that is 2*sqrt2=2.83v into 8ohms or 2v into 4 ohms etc.
regards Andrew T.

 

[454Casull]

Hi Bill & all
using the formula in post 7 gives a maximum output from a 100% efficient speaker of 112db and 50% will give 109db.
Do you think these are right?
They are close to a figure I saw quoted many years ago of about 108db(but I may be wrong) as the maximum that 1 watt can produce.
Note here we are quoting real watts that is 2*sqrt2=2.83v into 8ohms or 2v into 4 ohms etc.
regards Andrew T.

Approximately, yes. Those numbers assume omnidirectional radiation.


Can somebody explain what load and phase and all that jazz have to do with efficiency? I thought sensitivity was simply a logarithmic conversion of efficiency.

 

[Snickers-is]

Load (or impedance) is the connection between sensitivity and effeciency since sensitivity is determined only by voltage, and effeciency is determined by the real input power.

Phase is a component of the load, but in connection to sensitivity and effeciency it means nothing.

 

[sachi]

thank u all.
by the way the link was very useful Ghetto.

 

[454Casull]

Load (or impedance) is the connection between sensitivity and effeciency since sensitivity is determined only by voltage, and effeciency is determined by the real input power.

Phase is a component of the load, but in connection to sensitivity and effeciency it means nothing.

Refresh my memory as to why it's per 2.83V instead of 1W, again?

 

[BillFitzmaurice]

The semantic difference between efficiency and sensitivity is a matter of the method of measurement. Efficiency is the ratio of electrical power in to acoustical power out and is thus expressed as a percentage figure that compares electrical watts and acoustical watts. Sensitivity is expressed as a dB figure referenced to either a voltage or wattage input. While the two are directly related, sound pressure levels are almost always expressed in decibels, rarely in acoustic watts, so it's the measurement system that's expressed in dB's that's most commonly quoted.

Using dB/2.83v sensitivity figures rather than dB/watt is a better way to get apples to apples comparison's of how one speaker will compare to another using the same amp, as amps are constant voltage sources and are limited in their absolute voltage output capabilities, while their current/power ratings change with the impedance load of the speaker being used.

 

[Snickers-is]

Refresh my memory as to why it's per 2.83V instead of 1W, again?

If you have 8 ohms load you simply will get 1W output, but that is not the interesting part of it.

When you play music the amplifier adjusts output voltage, and as a consequence of that it delivers the required power.
That means that if ylu messure the sensitivity VS frequency at 1W constant, and adjusts the sensitivity of a construction after that the voltage for example in the impedance minimum of the woofer will be very low. At the resonance frequency it will be maybe 10 times higher.

So if the speaker delivers 93 dB at 2,83 Volts input at most frequencies with just small peaks and dips (wich is quite normal) it will not perform anything like ok with constant 1W, but the natural consequence is also that it simply requires more power at the impedance minimum than at the resonance frequency with 2,83 volts input over the whole range.

 

[bear]

Hi Bill & all
using the formula in post 7 gives a maximum output from a 100% efficient speaker of 112db and 50% will give 109db.
Do you think these are right?
They are close to a figure I saw quoted many years ago of about 108db(but I may be wrong) as the maximum that 1 watt can produce.
Note here we are quoting real watts that is 2*sqrt2=2.83v into 8ohms or 2v into 4 ohms etc.
regards Andrew T.

Depends on the distance here... and I think this assumes 180 degree dispersion... at about 3 ft this is right for the 100% case.

Speakers are nothing near 100% efficient, more like 1%...

Oh, and that isn't maximum output, that's with 100% efficiency, which means all of the input power is converted to sound, making for 1 acoustic watt output.

If you have 8 ohms load you simply will get 1W output, but that is not the interesting part of it.

When you play music the amplifier adjusts output voltage, and as a consequence of that it delivers the required power.
That means that if ylu messure the sensitivity VS frequency at 1W constant, and adjusts the sensitivity of a construction after that the voltage for example in the impedance minimum of the woofer will be very low. At the resonance frequency it will be maybe 10 times higher.

So if the speaker delivers 93 dB at 2,83 Volts input at most frequencies with just small peaks and dips (wich is quite normal) it will not perform anything like ok with constant 1W, but the natural consequence is also that it simply requires more power at the impedance minimum than at the resonance frequency with 2,83 volts input over the whole range.

Ummm... this seems a bit confused and convoluted...

The amplifier does indeed change output with a varying input voltage. But for the sort of measurements were considering, there is usually a steady state input, not a varying one.

The 2.83 V signal coming from the amplifier to the load can be plugged into ohms law and found to be equal to 1 watt at 8 ohms.
Clearly, at other impedances, 2.83V is not one watt anymore!

But as said earlier, it is convenient to compare relative outputs of speakers - which may and do have different impedances - for the purpose of determining relative sensitivity (read: how loud they will play when hooked together on the same amp) usually when used in the same speaker system.

Sensiitivity is merely the measure of the output SPL vs. the input signal and is spec'd with an input level and an output SPL.

Efficiency is the measure of the conversion of electrical input signal to output as a percentage. It is measured as power in watts. It has no direct relationship to any input signal level or output level (SPL).

It can be seen by inspection that given the physics involved in the typical speaker that higher efficiency dynamic drivers tend to also have higher sensitivity as well.

You can see that efficiency isn't so easy to determine or straightforward if you consider the case of the ESL. What's the true efficiency of an ESL?

Now as far as the second quote, the typical amplifier does not change its voltage with respect to a varying load impedance. The current delivered changes, thus the power - not the voltage.

The exception to this rule is where the amp can not change power linearly with respect to load impedance, as in the case of a zero feedback tube amp (or with a so-called "current amplifier") where the maximum power is only available at one given impedance - due to the matching of the tube's plate impedance through the transformer to the load. Here the maximum power is available at one single impedance, say 8 ohms, and there is less power above and below that impedance (for example at 4 and at 16 ohms)

In this last case the frequency response of the speaker will be different than with the "typical amplifier" case. Which is part of the reason that tubes can and do sound different than the usual solid state amp...

_-_-bear