5dBA 120mm Fan.
Posted: Sat Feb 19, 2011 7:36 am
5dBA 120mm Fan. Sounds incredible but may actually be true.
Reader beware: This post may be received like the never ending conflict between baseball fans who seem to hate or love statistics! I am a little tone deaf, and cannot really distinguish the subtleties of fan noises when they are loud enough to hear, so in some sense I do not understand this game. But I can appreciate a beautiful fan that is super quiet, and I want to have a tool to use to help me keep multiple sound sources quite. I tried to do this post so it is understandable for those with some science background, but if you role your eyes at this type of thing just read the next paragraph and then skip down to the last few paragraphs!
I think this post may be more readable if you go to a window display, full height of your screen, half width of screen, rather that a full screen window.
Actual noise of a low RPM fan as if it was all by itself in the universe cannot be measured accurately by SPCR with a single measurement because of the ~11dBA background level and meter and electronics sensitivity. However it is possible to use standard data reduction techniques to estimate the noise level of the fans as if there was no other noise source around. This is partly a fun exercise, but I did it so I can use better estimates of noise resulting from multiple fans when they are operated at RPMs that are "noiseless" for any one by themselves.
As an example, consider the SPCR data for Noctua NH-D14 Cooler fans, 120mm and 140mm, data at http://www.silentpcreview.com/article1020-page5.html . See TABLE ONE. Both fans were tested at lots of different voltages (more than normal), and are quiet at low RPM. There is also data for both fans combined so the analysis method can be checked out by comparing the calculated pair noise with measured pair values.
For this analysis, there actually is a little problem with using the SPCR data. From physics point of view, the noise likely a function of the fan rotational speed, and only indirectly a function of the voltage on the fan. When you raise the voltage, the noise does not go up because you changed the voltage; it goes up because the fan is rotating faster. Unfortunately for this analysis, SPCR controlled variable in their measurements was the voltage on the fan, not the fan RPM. I am not saying they did it wrong, their method is an appropriate, practical approach: obviously voltage is what we can control easily in our own PCs. This issue can be overcome though. Fortunately these fans are not PWM fans so the RPM is actually a direct function of voltage: double the voltage and you double the fan RPM. See Graph One. The best line fit to the data is actually a second order polynomial and not a straight line through the origin, but the directly proportional model is close enough for the purposes of this discussion. SO, I will look at sound levels as a function of voltage, not RPM.
Now look at the data for the 120mm fan, Graph Two. It is clear that the sound level has a linear relationship with fan voltage above the measurement floor (greater than 6V, 700 RPM). Sound engineers can probably explain the physics here, but not me! I only need the practical result that we can fit the data to a simple model: the measured noise (Nm) is a linear function of voltage unless the voltage is reduced so much that we have to consider the background noise (Nb). So, if the trend continues, the noise of the fan alone will be a straight line at the low voltages.
Hopefully the background level Nb is constant so this model can work. The noise levels as defined are in dBA. So we need to fit the data to the classical model of how to add noises together. You have to use the definition of decibels: convert the dBA to the square of their power level, add these together, and then re-convert to dBA:
Nm(f) = 10 X Log10 ( 10^(Nf(f)/10) + 10^ ( Nb/10) )
Using least squares fitting, the data fits a background level of 8.4 dBA. (Sorry for the bad formating of the graph titles, they seem to change when I go from Excel to pictures, and they should say "CALCULATED AND ACTUAL NOISE"
This seems lower than anticipated from the comment in most of the SPCR noise measurements that the noise floor is 11dBA, but I suspect that they really mean that the noise floor is definitely less than 11dBA and fluctuates between fan noise analysis sessions and probably even during a session. But consider this: the estimated fan noise is equal to the background noise at about 5.5V. Add two noise sources of equal value you get 3dBA increase, in this case to 11.4dBA. Since this is the actual reported value of background plus fan, this low value makes sense despite the note on background by SPCR.
The calculated dBA for the fan alone after subtracting out the 8.4 dBA calculated background noise is shown in Graph Three. The fan at low RPM, according to this model, is REALLY quiet, effectively it goes down to 7dBA! As a quick check, the straight line noise curve for the fan alone can be added to the fitted background noise level. As you can see the dashed red line follows SPCR total noise measurement quite well.
Now look at the dBA for the 140mm NF-P14 fan as function of voltage, Graph Four. The dBA/Voltage seems linear 6-11V, very nice straight line. The highest RPM data point seems too far off a straight line compared to the other points, so I ignored it for the rest of the analysis. Do the least squares fit and you get Graph Five, noise floor value of 10.8 dBA. This is more like the expected value per SPCR comments. Again, at low RPM, the calculated fan noise is REALLY low around the same 7dBA, but at a higher RPM than the smaller fan. And again the model seems to hold up as indicated by the dashed red line that fits the SPCR data quite well.
Now what to do with the calculated noise levels? Predict what the noise level of the two together would be, and check the calculated values against SPCR measured values. The noise measurement should be the noise of the two fans plus a background noise, but what is the background noise? We can calculate the expected combined noise for a range of background levels, see Graph Six. Not bad fit, eh? The calculated dBA are typically within o.5dBA of the SPCR values for 8dBA background level, except at the highest voltages. So it seems the drop in noise compared to the linear model at large voltages may be due to something happening with the fans…that is, the model fails at large voltage/noise levels. Also, the assumption that RPMs are directly proportional to voltage may be hurting the model since at larger voltages the actual RPM is lower than a linear estimate.. But then this fall off is not at noise levels we have any real interest in.
Minor point I need to raise…the article is not totally clear if the two fan noise level is measured at 6 or 6.5V (see the asterisk in Table One). However the data is more consistent with 6V, not 6.5V, so I used 6.5V.
So in summary, one can use the fan’s noise level as function of fan voltage measurements to subtract out the background noise and get the noise of the fan itself. Now one can add noise levels together to get estimate of noise level of multiple fans. There will be problems for scenarios different that this set of SPCR data..the fans did not move from their position during the measurements. But in your PC, they will be put at different distances from the listener, and have different sound paths to the listener. So this noise estimation process can only be used as a guide.
OK, but where did my title come from? SPCR’s reference Nexus fan of course! It calculates to less than 5dBA for RPMs less than 625cps!
According to this model, I can put up to 4 fans in my pc build (P/S, heat sink, one or two case fans through a low air resistance filter, positive pressure, overclocked 2600K) with expectations of max noise of 11dBA from the fans if operated at <650rpm, less if I have a good case than does not let the noise go directly to the user. I am going for computing power, not gaming, so I will not have a video card, just use on board graphics.
Reader beware: This post may be received like the never ending conflict between baseball fans who seem to hate or love statistics! I am a little tone deaf, and cannot really distinguish the subtleties of fan noises when they are loud enough to hear, so in some sense I do not understand this game. But I can appreciate a beautiful fan that is super quiet, and I want to have a tool to use to help me keep multiple sound sources quite. I tried to do this post so it is understandable for those with some science background, but if you role your eyes at this type of thing just read the next paragraph and then skip down to the last few paragraphs!
I think this post may be more readable if you go to a window display, full height of your screen, half width of screen, rather that a full screen window.
Actual noise of a low RPM fan as if it was all by itself in the universe cannot be measured accurately by SPCR with a single measurement because of the ~11dBA background level and meter and electronics sensitivity. However it is possible to use standard data reduction techniques to estimate the noise level of the fans as if there was no other noise source around. This is partly a fun exercise, but I did it so I can use better estimates of noise resulting from multiple fans when they are operated at RPMs that are "noiseless" for any one by themselves.
As an example, consider the SPCR data for Noctua NH-D14 Cooler fans, 120mm and 140mm, data at http://www.silentpcreview.com/article1020-page5.html . See TABLE ONE. Both fans were tested at lots of different voltages (more than normal), and are quiet at low RPM. There is also data for both fans combined so the analysis method can be checked out by comparing the calculated pair noise with measured pair values.
For this analysis, there actually is a little problem with using the SPCR data. From physics point of view, the noise likely a function of the fan rotational speed, and only indirectly a function of the voltage on the fan. When you raise the voltage, the noise does not go up because you changed the voltage; it goes up because the fan is rotating faster. Unfortunately for this analysis, SPCR controlled variable in their measurements was the voltage on the fan, not the fan RPM. I am not saying they did it wrong, their method is an appropriate, practical approach: obviously voltage is what we can control easily in our own PCs. This issue can be overcome though. Fortunately these fans are not PWM fans so the RPM is actually a direct function of voltage: double the voltage and you double the fan RPM. See Graph One. The best line fit to the data is actually a second order polynomial and not a straight line through the origin, but the directly proportional model is close enough for the purposes of this discussion. SO, I will look at sound levels as a function of voltage, not RPM.
Now look at the data for the 120mm fan, Graph Two. It is clear that the sound level has a linear relationship with fan voltage above the measurement floor (greater than 6V, 700 RPM). Sound engineers can probably explain the physics here, but not me! I only need the practical result that we can fit the data to a simple model: the measured noise (Nm) is a linear function of voltage unless the voltage is reduced so much that we have to consider the background noise (Nb). So, if the trend continues, the noise of the fan alone will be a straight line at the low voltages.
Hopefully the background level Nb is constant so this model can work. The noise levels as defined are in dBA. So we need to fit the data to the classical model of how to add noises together. You have to use the definition of decibels: convert the dBA to the square of their power level, add these together, and then re-convert to dBA:
Nm(f) = 10 X Log10 ( 10^(Nf(f)/10) + 10^ ( Nb/10) )
Using least squares fitting, the data fits a background level of 8.4 dBA. (Sorry for the bad formating of the graph titles, they seem to change when I go from Excel to pictures, and they should say "CALCULATED AND ACTUAL NOISE"
This seems lower than anticipated from the comment in most of the SPCR noise measurements that the noise floor is 11dBA, but I suspect that they really mean that the noise floor is definitely less than 11dBA and fluctuates between fan noise analysis sessions and probably even during a session. But consider this: the estimated fan noise is equal to the background noise at about 5.5V. Add two noise sources of equal value you get 3dBA increase, in this case to 11.4dBA. Since this is the actual reported value of background plus fan, this low value makes sense despite the note on background by SPCR.
The calculated dBA for the fan alone after subtracting out the 8.4 dBA calculated background noise is shown in Graph Three. The fan at low RPM, according to this model, is REALLY quiet, effectively it goes down to 7dBA! As a quick check, the straight line noise curve for the fan alone can be added to the fitted background noise level. As you can see the dashed red line follows SPCR total noise measurement quite well.
Now look at the dBA for the 140mm NF-P14 fan as function of voltage, Graph Four. The dBA/Voltage seems linear 6-11V, very nice straight line. The highest RPM data point seems too far off a straight line compared to the other points, so I ignored it for the rest of the analysis. Do the least squares fit and you get Graph Five, noise floor value of 10.8 dBA. This is more like the expected value per SPCR comments. Again, at low RPM, the calculated fan noise is REALLY low around the same 7dBA, but at a higher RPM than the smaller fan. And again the model seems to hold up as indicated by the dashed red line that fits the SPCR data quite well.
Now what to do with the calculated noise levels? Predict what the noise level of the two together would be, and check the calculated values against SPCR measured values. The noise measurement should be the noise of the two fans plus a background noise, but what is the background noise? We can calculate the expected combined noise for a range of background levels, see Graph Six. Not bad fit, eh? The calculated dBA are typically within o.5dBA of the SPCR values for 8dBA background level, except at the highest voltages. So it seems the drop in noise compared to the linear model at large voltages may be due to something happening with the fans…that is, the model fails at large voltage/noise levels. Also, the assumption that RPMs are directly proportional to voltage may be hurting the model since at larger voltages the actual RPM is lower than a linear estimate.. But then this fall off is not at noise levels we have any real interest in.
Minor point I need to raise…the article is not totally clear if the two fan noise level is measured at 6 or 6.5V (see the asterisk in Table One). However the data is more consistent with 6V, not 6.5V, so I used 6.5V.
So in summary, one can use the fan’s noise level as function of fan voltage measurements to subtract out the background noise and get the noise of the fan itself. Now one can add noise levels together to get estimate of noise level of multiple fans. There will be problems for scenarios different that this set of SPCR data..the fans did not move from their position during the measurements. But in your PC, they will be put at different distances from the listener, and have different sound paths to the listener. So this noise estimation process can only be used as a guide.
OK, but where did my title come from? SPCR’s reference Nexus fan of course! It calculates to less than 5dBA for RPMs less than 625cps!
According to this model, I can put up to 4 fans in my pc build (P/S, heat sink, one or two case fans through a low air resistance filter, positive pressure, overclocked 2600K) with expectations of max noise of 11dBA from the fans if operated at <650rpm, less if I have a good case than does not let the noise go directly to the user. I am going for computing power, not gaming, so I will not have a video card, just use on board graphics.