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Topic: Calculating Loudness from Efficiency/Sensitivity (Read 37243 times) previous topic - next topic
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Calculating Loudness from Efficiency/Sensitivity

Reply #50 –
Ok, while IF's measurements are more optimistic than Audeze's, even if it more reflects reality, that doesn't take into consideration the various versions of LCD2 that exists. The newest LCD2 has 97.4 db/mw, but the 2012 LCD2 requires 0.75mw to reach 90db spl.

90 + 20 * LOG ( 1/0.209 ) = 103.6 db/Vrms @ 59ohms = 91.3 db/mw.
(Above data is exclusively from the 2012 version measurement of LCD2 listed in IF's page here: http://www.innerfidelity.com/images/Audeze...4circa2012.pdf)

2012 LCD2 based on IF (91.3 db/mw):
105db
23.4mw
110db
74.1mw
115db
234.4mw
120db
741.3mw

Latest LCD2 based on Audeze (93 db/mw):
105db
15.8mw
110db
50.1mw
115db
159.5mw
120db
501.2mw

Latest LCD2 based on IF (97.4 db/mw):
105db
5.75mw
110db
18.2mw
115db
57.5mw
120db
182mw

Pdq, sorry if it seems like I am ignoring your posts.  So Xnor, I am assuming that you agree with Pdq's calculation of 761mw max output @ 70 ohms? One thing I almost forgot to account for is that the impedance of 2012 LCD2 is lower... making it slightly easier for O2 to deliver more power to the headphone. That, combined with the calculated 761mw max output and the fact that 120db is already more than enough leeway, I think it's safe to call the O2 capable of powering the LCD2 under all realistic conditions.

Quote
Let's look at those specs, converting to voltage and current:

15R, 337 mW - V = 2.2, I = 0.15
33R, 613 mW - V = 5.0, I = 0.14
150R, 355 mW - V = 7.3, I = 0.048
600R, 88 mW - V = 7.3, I = 0.012

As you can see, the amplifier is limited to either 7.3 volts or 0.15 amps, depending on the load impedance.
The power would be a maximum of 7.3 * 0.15 = 1.1W at a load impedance of 7.3 / 0.15 = 49 ohms, and less at any other impedance.


Ok...hmm...
P=VI (Got if off the internets.  )
88= V x I
How did you get 5v to calculate 0.14 amps? Can't it be like... 0.14v and 5amps?

O2's max output:
Max Output (33 Ohms)   613 mW
Max Output (150 Ohms)   355 mW
Max Output (600 Ohms)   88 mW

15R, 337 mW - V = 2.2, I = 0.15
33R, 613 mW - V = 5.0, I = 0.14
150R, 355 mW - V = 7.3, I = 0.048
600R, 88 mW - V = 7.3, I = 0.012

(7.3^2)/600 = 88.8mw Correct
(7.3^2)/150 = 355mw Correct
(5^2)/33 = 757mw  ??? Doesn't match the 613mw ?

Calculating Loudness from Efficiency/Sensitivity

Reply #51 –
Yes, the correct value of V for P = 0.613 and R = 33 is 4.5 volts, not 5 (don't know how I slipped up on that one). The rest seem to be OK.

Calculating Loudness from Efficiency/Sensitivity

Reply #52 –
Code: [Select]
P = V * I
I = V / R

P = V * (V / R) = V^2 / R




I wouldn't worry about reaching 120 dB SPL. IIRC, even some Audeze guy said that 110 dB SPL is a good target, since that's about what you reach in a concert hall when it gets really loud.
Add 3 dB headroom to that if it makes you feel better.

The only thing to keep in mind with the O2 is that you need to get the gain right.
"I hear it when I see it."

Calculating Loudness from Efficiency/Sensitivity

Reply #53 –
EDIT:
Ninja'ed by the Xnor 

Calculating Loudness from Efficiency/Sensitivity

Reply #54 –

Right now I can only think of one more question.
Regarding the increase in distortion when one gets close to the max output voltage... doesn't this picture by NWavguy describe the effect (or lack thereof)?:
http://lh4.ggpht.com/-KUA--R4e84w/TknSJHme...55B3%25255D.jpg

What percentage of THD+N should we be striving for here?

Calculating Loudness from Efficiency/Sensitivity

Reply #56 –
Quote from: pdq on
If you refer to my earlier post and do a little bit of calculations, you will find that the projected output power at 70 ohms is 7.3^2 / 70 = 761 mW.

Question:
This is a projection, an estimation. The 70 is obviously given in the problem. The power is what we're trying to find out so obviously we don't know the answer. How do we know the voltage is 7.3? It can be anywhere from 5 to 7.3, no?

15R, 337 mW - V = 2.2, I = 0.15
33R, 613 mW - V = 5.0, I = 0.14
150R, 355 mW - V = 7.3, I = 0.048
600R, 88 mW - V = 7.3, I = 0.012

Calculating Loudness from Efficiency/Sensitivity

Reply #57 –
Quote from: Dark_wizzie on
Quote from: pdq on
If you refer to my earlier post and do a little bit of calculations, you will find that the projected output power at 70 ohms is 7.3^2 / 70 = 761 mW.

Question:
This is a projection, an estimation. The 70 is obviously given in the problem. The power is what we're trying to find out so obviously we don't know the answer. How do we know the voltage is 7.3?


From the post pdq linked above:

Quote from: pdq on
As you can see, the amplifier is limited to either 7.3 volts or 0.15 amps, depending on the load impedance.


Since 7.3v across 70 ohms is less than .15 amps, the maximum voltage is 7.3v.

You are making this fantastically more complicated than it needs to be though.  The output limit on that amp is so high you will never hit it in a useful scenario,  so you can just plug in 7.3v into sensitivity and be done with it for loudness calculations.

Calculating Loudness from Efficiency/Sensitivity

Reply #58 –
Quote from: saratoga on
Quote from: Dark_wizzie on
Quote from: pdq on
If you refer to my earlier post and do a little bit of calculations, you will find that the projected output power at 70 ohms is 7.3^2 / 70 = 761 mW.

Question:
This is a projection, an estimation. The 70 is obviously given in the problem. The power is what we're trying to find out so obviously we don't know the answer. How do we know the voltage is 7.3?


From the post pdq linked above:

Quote from: pdq on
As you can see, the amplifier is limited to either 7.3 volts or 0.15 amps, depending on the load impedance.


Since 7.3v across 70 ohms is less than .15 amps, the maximum voltage is 7.3v.

You are making this fantastically more complicated than it needs to be though.  The output limit on that amp is so high you will never hit it in a useful scenario,  so you can just plug in 7.3v into sensitivity and be done with it for loudness calculations.

I want to know why 70 ohms is less than 0.15 and therefore max is 7.3v. I'm trying to understand everything related so somebody won't catch me off guard with some terms I'm not familiar with.

Also, I'd like to thank every one of you for teaching me all you have so far... It's been awesome.


Fruits of your labor?

http://linustechtips.com/main/topic/221772...uirement-vs-o2/

Calculating Loudness from Efficiency/Sensitivity

Reply #60 –
Why are headphones measured at 1khz to figure out sensitivity? Isn't it wholly possible that a headphone requires more power at another frequency so that 1khz reading is misleading?

Inner Fidelity's readings don't specify how the number is calculated (for volts or mw required to hit 90db spl). Is that 1khz or...
Here's an example if you want to check: http://www.innerfidelity.com/images/Audeze...423021Fazer.pdf

Calculating Loudness from Efficiency/Sensitivity

Reply #61 –
Quote from: Dark_wizzie on
Why are headphones measured at 1khz to figure out sensitivity? Isn't it wholly possible that a headphone requires more power at another frequency so that 1khz reading is misleading?


Not just possible, but absolutely certain.  Impedance cannot be constant for a pair of headphones.

If you really want, you can measure the complex impedance and then numerically integrate it to compute the exact power transfer, which will result in a difference maybe as large as single click on a volume knob

Calculating Loudness from Efficiency/Sensitivity

Reply #62 –
Quote from: saratoga on
Quote from: Dark_wizzie on
Why are headphones measured at 1khz to figure out sensitivity? Isn't it wholly possible that a headphone requires more power at another frequency so that 1khz reading is misleading?


Not just possible, but absolutely certain.  Impedance cannot be constant for a pair of headphones.

If you really want, you can measure the complex impedance and then numerically integrate it to compute the exact power transfer, which will result in a difference maybe as large as single click on a volume knob

Planar magnetic headphones have almost identical impedance throughout different frequencies though.

Calculating Loudness from Efficiency/Sensitivity

Reply #63 –
1 kHz is in the middle of audio bandwidth and is used as starting point for all sorts of audio measurements and experiments (see equal-loudness for example).

It's actually a pretty good choice for headphones too, although some manufacturers also use 500 Hz. Below that, headphones might have sucked out mids, rolled-off or boosted bass. Above that, the frequency response can be really erratic with headphones. You might hit a nasty peak or dip that could easily change sensitivity by +/- 10 dB.

So at 1 kHz we have a pretty stable frequency response, but it's a bit like nominal impedance: a ballpark figure (especially the numbers provided by manufacturers).


IF uses 1 kHz as well, afaik. It matches HD800, HD650 ... because Sennheiser properly specifies sensitivity at 1 kHz with 1 Vrms. It also matches if you plug in the impedance @ 1 kHz.
What about the new Fazer? It's easier to drive than the other versions.
"I hear it when I see it."

Calculating Loudness from Efficiency/Sensitivity

Reply #64 –
Quote from: xnor on
1 kHz is in the middle of audio bandwidth and is used as starting point for all sorts of audio measurements and experiments (see equal-loudness for example).

It's actually a pretty good choice for headphones too, although some manufacturers also use 500 Hz. Below that, headphones might have sucked out mids, rolled-off or boosted bass. Above that, the frequency response can be really erratic with headphones. You might hit a nasty peak or dip that could easily change sensitivity by +/- 10 dB.

So at 1 kHz we have a pretty stable frequency response, but it's a bit like nominal impedance: a ballpark figure (especially the numbers provided by manufacturers).


IF uses 1 kHz as well, afaik. It matches HD800, HD650 ... because Sennheiser properly specifies sensitivity at 1 kHz with 1 Vrms. It also matches if you plug in the impedance @ 1 kHz.
What about the new Fazer? It's easier to drive than the other versions.

The fazer revision simply raises the line to 70 instead of 59. It's still a flat line. I went around various measurements for HD800, HD600, AKG q701, DT 770 600ohm, Grado ps1000, Shure 1540, Ad700x, M50x. 1khz is consistently one of the lowest impedance points for the headphone. Sometimes the impedance drops that low or lower at 10hz but nobody can tell the quality of a 10hz note anyways. Any other deviation from my "rule" is too small to matter. At 100hz most dynamic headphones have the highest impedance.

Calculating Loudness from Efficiency/Sensitivity

Reply #65 –
Quote from: Dark_wizzie on
Isn't it wholly possible that a headphone requires more power at another frequency so that 1khz reading is misleading?


Yes, if the impedance is lower at other frequencies. So nothing to worry about with planar magnetics. Dynamic headphones usually have near the lowest impedance at 1 kHz too.

Some ANC headphones have a weird impedance curve in active mode due to their built-in circuitry, where impedance significantly drops with increasing frequency, but those usually draw most power from the batteries anyway ...
"I hear it when I see it."

Calculating Loudness from Efficiency/Sensitivity

Reply #66 –
The top is the old LCD2, the bottom is the new LCD2 with Fazor.


BTW what does the phase line mean?

Calculating Loudness from Efficiency/Sensitivity

Reply #67 –
Quote from: Dark_wizzie on
BTW what does the phase line mean?


Its the time delay between voltage and current expressed in fractions of wavelength.  You can think of it as how resistive a circuit is, with 0 degrees being pure resistive, and 90 degrees being pure reactive.  Otherwise its not too important for your purposes.

Calculating Loudness from Efficiency/Sensitivity

Reply #68 –
Quote
15R, 337 mW - V = 2.2, I = 0.15
33R, 613 mW - V = 4.5, I = 0.14
150R, 355 mW - V = 7.3, I = 0.048
600R, 88 mW - V = 7.3, I = 0.012

Above as calculated, is the limit of O2. Here we see that the O2 isn't totally perfect, the amount of voltage it delivers can be under 7.3v. Of course, one can argue that's not a big deal unless we're talking HE-6. Other than that, not really any headphone will have impedances that low and be terribly inefficient. LCD 2 for example is from 59-70 ohm impedance.

Quote
P = I x V.
I= V/Z.
P=V/Z*V
P = V^2/Z.
Z is constant for a given pair of headphones. Therefore, really you are saying that you need a given voltage. Usually this is what people care about, and why sensitivity is often quoted in db/V.

Saratoga here mentioned that Z is a constant. The Z is R aka impedance. So I = voltage/impedance.

P = V^2/Z
Ok, let's assume V^2 = 5 for the sake of argument.
P = 5/Z
If impedance is 100:
P = 1/20
If Impedance is 600:
P = 1/120

Questions:
1. 1/20 what? 1/20 watts? So 50 mw?
2. What I just did with P = 1/20 @ 100ohm vs P = 1/120 @ 120 ohm is basically show that power required drops as impedance increases, right?
3. P = V^2/R. That voltage is what, the amount of voltage a headphone needs or the amount of voltage an amp can (and will) deliver? It's the former, right?

Quote from: xnor on
Audio amplifiers are usually voltage sources. So they control the output voltage, and try to let the load draw as much current as it needs (Ohm's law).
The impedance peak of headphones you can see in the bass range is the resonant frequency. Here, the driver has the highest efficiency. Given that the frequency response of both the headphone and signal is flat, this is the point where the amplifier has the easiest job, because it needs to provide the least amount of power.


O2 delivers 7.3v stable, throughout most impedances and loads. Not only does the amount of voltage the O2 pushes out not change, the amount of voltage a headphone needs at various impedances also don't change? I'm having a hard time grasping why the latter is true just because the former is true.

Or uh...
P = V * I
300 = 7.3 * I  What you mean by controlling output voltage... The O2 will just set the V as 7.3 (or its max voltage output)... We still need a fixed amount of power... So I increases or decreases depending on amount of powered required?

Calculating Loudness from Efficiency/Sensitivity

Reply #69 –
Ignore the post above this one, HA caps how long I have until I can edit a post...

Quote
15R, 337 mW - V = 2.2, I = 0.15
33R, 613 mW - V = 4.5, I = 0.14
150R, 355 mW - V = 7.3, I = 0.048
600R, 88 mW - V = 7.3, I = 0.012

Above as calculated, is the limit of O2. Here we see that the O2 isn't totally perfect, the amount of voltage it delivers can be under 7.3v. Of course, one can argue that's not a big deal unless we're talking HE-6. Other than that, not really any headphone will have impedances that low and be terribly inefficient. LCD 2 for example is from 59-70 ohm impedance.
Quote
P = I x V.
I= V/Z.
P=V/Z*V
P = V^2/Z.
Z is constant for a given pair of headphones. Therefore, really you are saying that you need a given voltage. Usually this is what people care about, and why sensitivity is often quoted in db/V.

Quote from: xnor on
Audio amplifiers are usually voltage sources. So they control the output voltage, and try to let the load draw as much current as it needs (Ohm's law).
The impedance peak of headphones you can see in the bass range is the resonant frequency. Here, the driver has the highest efficiency. Given that the frequency response of both the headphone and signal is flat, this is the point where the amplifier has the easiest job, because it needs to provide the least amount of power.

O2 is a voltage source. It is able to provide close to 7.3v max no matter the situation (typically). A "perfect voltage source" can deliver its max voltage across any and all impedances.
O2 can deliver max of 7.3v but it doesn't always deliver 7.3v. It depends on how many volts the headphone needs.

Quote from: xnor on
1 kHz is in the middle of audio bandwidth and is used as starting point for all sorts of audio measurements and experiments (see equal-loudness for example).

It's actually a pretty good choice for headphones too, although some manufacturers also use 500 Hz. Below that, headphones might have sucked out mids, rolled-off or boosted bass. Above that, the frequency response can be really erratic with headphones. You might hit a nasty peak or dip that could easily change sensitivity by +/- 10 dB.

So at 1 kHz we have a pretty stable frequency response, but it's a bit like nominal impedance: a ballpark figure (especially the numbers provided by manufacturers).

IF uses 1 kHz as well, afaik. It matches HD800, HD650 ... because Sennheiser properly specifies sensitivity at 1 kHz with 1 Vrms. It also matches if you plug in the impedance @ 1 kHz.

Calculating Loudness from Efficiency/Sensitivity

Reply #70 –
Quote from: Dark_wizzie on
Quote
15R, 337 mW - V = 2.2, I = 0.15
33R, 613 mW - V = 4.5, I = 0.14
150R, 355 mW - V = 7.3, I = 0.048
600R, 88 mW - V = 7.3, I = 0.012

Above as calculated, is the limit of O2. Here we see that the O2 isn't totally perfect, the amount of voltage it delivers can be under 7.3v.


I think someone explained above that this was a safety limit to prevent you from damaging things with it.

Quote from: Dark_wizzie on
1. 1/20 what? 1/20 watts? So 50 mw?


Yes, power will be in watts.

Quote from: Dark_wizzie on
2. What I just did with P = 1/20 @ 100ohm vs P = 1/120 @ 120 ohm is basically show that power required drops as impedance increases, right?


Correct.  Remember, when I told you that its easier to work with voltage and impedance (which are constant) than with power (which is a function of impedance)?  This is part of the reason. 

Quote from: Dark_wizzie on
3. P = V^2/R. That voltage is what, the amount of voltage a headphone needs or the amount of voltage an amp can (and will) deliver? It's the former, right?


Its not necessarily one or the other.  It depends on what you are measuring.

Quote from: Dark_wizzie on
Not only does the amount of voltage the O2 pushes out not change, the amount of voltage a headphone needs at various impedances also don't change?[/b]


The impedance of a pair of headphones does not change (unless you are thinking about playing pure tones at different frequencies or something weird like that).

Quote from: Dark_wizzie on
300 = 7.3 * I  What you mean by controlling output voltage... The O2 will just set the V as 7.3 (or its max voltage output)... We still need a fixed amount of power... So I increases or decreases depending on amount of powered required?


For a given voltage and impedance, you will push a certain current through a load, which will enable you to calculate a certain power transfer.

Calculating Loudness from Efficiency/Sensitivity

Reply #71 –
Quote from: saratoga on
The impedance of a pair of headphones does not change (unless you are thinking about playing pure tones at different frequencies or something weird like that).

http://www.innerfidelity.com/images/SennheiserHD800.pdf
But here it very clearly shows the impedance changing. Goes over 600ohms are 100hz.


==
This is the question posed to me:
Quote
I also have a question, do certain frequencies take more / less power to produce?  If the driver has to flex more to make a low note than a high note, surely it would take more current to move it more?


P = (V x V)/R
With a planar we know R is the same no matter what frequency is being played. But how do we know whether the sensitivity is the same? Sensitivity reading is taken at 1khz. Who is to say it'll be anything like that at 100hz or 12,000khz?

Then isn't is possible for a dynamic headphone... to have a resonant frequency of 100hz, where its impedance is at its peak making it easier to drive, but have it counteracted by a lower efficiency?

I suggested taking more samples to find sensitivity at various frequencies but somebody said that's basically like taking the FR of a headphone? So it's related to FR? Then are the quieter parts of the FR lower sensitivity?

Calculating Loudness from Efficiency/Sensitivity

Reply #72 –
Or does it not matter? If I look at it at a different way: A FR graph isn't flat. Some frequencies are louder than others. If the quietest part of a FR is driven at 110dB, the not-so-quiet parts of the FR will be insanely loud and blow up our ears. So we just need to pick a spot that's somewhat average in its FR to get a reading on how loud a headphone is on average.

And, the quieter parts of the FR are the parts that are less sensitive, because it is given the same amount of voltage but is quieter? When we are thinking about an amp's ability to power a headphone, having the quietest parts of the FR be able to be run at 110dB is dumb, we just need to look at 1khz. 1khz is a good frequency to pick as it's often not screwed around that much through different sound signatures (unlike say, 12khz, which can be all over the place from one headphone vs another). 1khz is a good average to figure out how loud the headphone is.

So then: Sensitivity reading is literally just how loud a headphone is at 1khz given 1Vrms. And, a frequency response is just sensitivity, but for every single frequency. If we take a sample to find the sensitivity of a headphone for every single frequency from 20hz-20khz, and we plot it on a graph, and then connect the dots, that is a FR response graph.


Please tell me I'm right, that would explain everything and make everything internally consistent in my world...

I've been sitting here for the past 2-3 hours thinking about this. 

Calculating Loudness from Efficiency/Sensitivity

Reply #73 –
Yes.
"I hear it when I see it."

Calculating Loudness from Efficiency/Sensitivity

Reply #74 –
Quote from: xnor on
Yes.

I see. 

One more question...
When a headphone is insufficiently powered by an amp, it is to my understanding that it will either not be loud enough, or cause distortions such as clipping. Somebody just complained to me that onboard is not sufficient for his Sennheiser Game Zero headset (unique in its 150 ohm impedance rating). But more interestingly to me, he said that bass is missing in dubstep and rap when he listens to music. When he is gaming he doesn't notice a problem. I find this odd. His claim was that onboard amp cannot drive his headphone properly. I believe saying a headphone is not driven properly means it is not being powered properly (in other words, I think those two phrases are interchangable). I don't see how insufficient power would cut off the bass. Plus, modern rap music are heavily compressed, super loud tracks. His taste in music should make his life much easier for him. (Unless his preference for extra loud sound counteracts that. However, I'm actually referring to a 35 year old tech Youtube here, I doubt he listens past 105db peaks bro.)

Another member claimed that lack of power makes the music sound "flat". I'm assuming he didn't mean "neutral". 

If an onboard amp has too high of an output impedance, I can see FR being altered. But the 150 ohm impedance of this headset would make it uniquely immune to this effect, not the other way around. Bass should be extra less affected, if anything at all.

Am I wrong here?
(I wanted to find sensitivity or efficiency ratings of the headset but they simply don't exist on the internet.)