SanjiWatsuki
500+ Head-Fier
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- Oct 21, 2011
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Hello, Head-Fi Sound Science forum. I've been doing a lot of research on amplifiers and damping factor and this question has very much bugged me. I'm wondering if you guys think my logic is solid.
Allow me to say first off that there is no room to doubt that low impedance headphones/earphones, such as balanced IEMs or highly efficient portable headphones, will be greatly affected by high source impedance. Their frequency response will be all messed up, their sound decay time might double in length making their bass muddy and "loose", their crossovers will fail, etc. What I'm concerned with, however, is the effect of a high impedance headphone out (~50 ohms, a number found often in low cost headphone amps and the headphone out of professional audio equipment) on the sound of higher impedance headphones, anything from 50 to 600.
To start, let's focus on the frequency response aspect. This part is relatively easy if there is a published impedance chart for the headphones. We can take the maximum impedance, add in the source impedance, and calculate the change in dB and do the sound for the lowest impedance. Using a combination of these two values we can determine a range that the sound changed based upon the source impedance mathematically. Here's an example:
Using Tyll's chart for the Grado SR60i, we'll measure the dB differences in this low 32ohm impedance headphone when fed a 50ohm source impedance amplifier. The lowest impedance appears to be 32 and the highest appears to be 42. We will assume a 1 volt source.
Voltage at 32 ohm: 32 / (32 + 50) = .39
Voltage at 42 ohm: 42 / (42 + 50) = .457
Frequency response deviation: 20 * log (.457/.39) = 1.38dB
So, at one volt, we experience only a 1.38dB variation in sound -- basically, barely audible for this highly efficient headphone that doesn't require an amp. Results will, of course, differ headphone to headphone. Furthermore, there can be some massive loss in voltage if the headphone is of a lower impedance than the amp, but that's very difficult to predict how much will be lost. The gist of what I'm saying is that, if you can calculate a small difference in the frequency response, this aspect of headphone impedance can be ignored.
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The next important aspect of output impedance is the electrical damping factor. Think of it as the amount of control the amplifier has on the driver. The lower the damping factor, the more the driver will vibrate after it isn't supposed to vibrate. The question is how much damping factor is needed and how much does it affect the sound quality?
I found this study on the effect of damping factor on speakers for this aspect. Granted, these are speakers and not headphones but the general principles apply. The main thing in my mind when I was reading this was that, because of the lower mass of headphone drivers, the less of an effect electrical damping will have on it. The driver has less mass moving and, therefore, will be less affected by damping factor. I feel Tyll's graphs for him testing the DT 48e at his normal testing impedance and then again with a 120 ohm source impedance (damping factor of .208) backs me up with this idea. The differences between the impulse decay time and the difference in time for it to make the sine waves changed in what appears to be an insignificant time. Furthermore, just the overall impulse response time for headphones just seems much lower than the decay time for speakers. Granted, these are different testing mechanisms and the numbers are not completely compatible, but I think it conveys the gist of the idea. Therefore, we can assume the differences in decay time for speakers is of some level of magnitude greater than it would be for headphones.
The study I linked came to the conclusion that any damping factor over 10 could safely be said to have no audible differences. Given that the decay differences is some degree of magnitude greater than it would be for speakers, it seems logical that a damping factor closer to the range of 1 to 3 would safely result in non-audible differences due to the amplifier's control over the driver. If we take the extreme and divide the decay time of the speaker by a Tyll impulse response time and multiply it by the damping factor of 10, the number would be significantly under 1, but that doesn't seem to be a logical step to take.
--
Heading onto the further implications of these conclusions, let's observe if the HD 650 could be capably powered by a $19 Behringer Micromon MA400 headphone amp. We will try to power it to 110 peak SPL ( Antilog ( ( 110 – 103) / 20 ) = 2.2 Vrms ). The Behringer spec sheet says it has . We calculate Vrms from dBu by antilog (dBu / 20) * .775 = V. Given that the dBu is +10, we can find the rated output to be 2.45Vrms -- more than enough to power the HD 650 to 110 peak SPL! Next, we'll calculate the frequency response changes.
From Tyll's charts for the HD 650, we know the lowest impedance to be around 300ohm and the highest to be around 520ohm.
Voltage at 300 ohm: 300 / (300 + 30) = .91
Voltage at 520 ohm: 520 / (520 + 30) = .945
Frequency response deviation: 20 * log (.945/.91) = 0.27dB
There is an inaudible frequency response change at 0.27dB.
Finally, the damping factor of the headphone is 10 -- effectively inaudible. Assuming the Behringer Micromon MA400 amp has distortion below audible levels, it is a $20 desktop amp which should be able to power the Sennheiser HD650.
Is this a logical conclusion? Just wanted to make sure I wasn't going crazy.
Allow me to say first off that there is no room to doubt that low impedance headphones/earphones, such as balanced IEMs or highly efficient portable headphones, will be greatly affected by high source impedance. Their frequency response will be all messed up, their sound decay time might double in length making their bass muddy and "loose", their crossovers will fail, etc. What I'm concerned with, however, is the effect of a high impedance headphone out (~50 ohms, a number found often in low cost headphone amps and the headphone out of professional audio equipment) on the sound of higher impedance headphones, anything from 50 to 600.
To start, let's focus on the frequency response aspect. This part is relatively easy if there is a published impedance chart for the headphones. We can take the maximum impedance, add in the source impedance, and calculate the change in dB and do the sound for the lowest impedance. Using a combination of these two values we can determine a range that the sound changed based upon the source impedance mathematically. Here's an example:
Using Tyll's chart for the Grado SR60i, we'll measure the dB differences in this low 32ohm impedance headphone when fed a 50ohm source impedance amplifier. The lowest impedance appears to be 32 and the highest appears to be 42. We will assume a 1 volt source.
Voltage at 32 ohm: 32 / (32 + 50) = .39
Voltage at 42 ohm: 42 / (42 + 50) = .457
Frequency response deviation: 20 * log (.457/.39) = 1.38dB
So, at one volt, we experience only a 1.38dB variation in sound -- basically, barely audible for this highly efficient headphone that doesn't require an amp. Results will, of course, differ headphone to headphone. Furthermore, there can be some massive loss in voltage if the headphone is of a lower impedance than the amp, but that's very difficult to predict how much will be lost. The gist of what I'm saying is that, if you can calculate a small difference in the frequency response, this aspect of headphone impedance can be ignored.
--
The next important aspect of output impedance is the electrical damping factor. Think of it as the amount of control the amplifier has on the driver. The lower the damping factor, the more the driver will vibrate after it isn't supposed to vibrate. The question is how much damping factor is needed and how much does it affect the sound quality?
I found this study on the effect of damping factor on speakers for this aspect. Granted, these are speakers and not headphones but the general principles apply. The main thing in my mind when I was reading this was that, because of the lower mass of headphone drivers, the less of an effect electrical damping will have on it. The driver has less mass moving and, therefore, will be less affected by damping factor. I feel Tyll's graphs for him testing the DT 48e at his normal testing impedance and then again with a 120 ohm source impedance (damping factor of .208) backs me up with this idea. The differences between the impulse decay time and the difference in time for it to make the sine waves changed in what appears to be an insignificant time. Furthermore, just the overall impulse response time for headphones just seems much lower than the decay time for speakers. Granted, these are different testing mechanisms and the numbers are not completely compatible, but I think it conveys the gist of the idea. Therefore, we can assume the differences in decay time for speakers is of some level of magnitude greater than it would be for headphones.
The study I linked came to the conclusion that any damping factor over 10 could safely be said to have no audible differences. Given that the decay differences is some degree of magnitude greater than it would be for speakers, it seems logical that a damping factor closer to the range of 1 to 3 would safely result in non-audible differences due to the amplifier's control over the driver. If we take the extreme and divide the decay time of the speaker by a Tyll impulse response time and multiply it by the damping factor of 10, the number would be significantly under 1, but that doesn't seem to be a logical step to take.
--
Heading onto the further implications of these conclusions, let's observe if the HD 650 could be capably powered by a $19 Behringer Micromon MA400 headphone amp. We will try to power it to 110 peak SPL ( Antilog ( ( 110 – 103) / 20 ) = 2.2 Vrms ). The Behringer spec sheet says it has . We calculate Vrms from dBu by antilog (dBu / 20) * .775 = V. Given that the dBu is +10, we can find the rated output to be 2.45Vrms -- more than enough to power the HD 650 to 110 peak SPL! Next, we'll calculate the frequency response changes.
From Tyll's charts for the HD 650, we know the lowest impedance to be around 300ohm and the highest to be around 520ohm.
Voltage at 300 ohm: 300 / (300 + 30) = .91
Voltage at 520 ohm: 520 / (520 + 30) = .945
Frequency response deviation: 20 * log (.945/.91) = 0.27dB
There is an inaudible frequency response change at 0.27dB.
Finally, the damping factor of the headphone is 10 -- effectively inaudible. Assuming the Behringer Micromon MA400 amp has distortion below audible levels, it is a $20 desktop amp which should be able to power the Sennheiser HD650.
Is this a logical conclusion? Just wanted to make sure I wasn't going crazy.