Impedance vs. Loudness (for motherboards)

[Spuriae]

One of the most common questions on the subforum is whether a motherboard is capable of powering <X impedance> or <insert headphone here>.

 

Almost every time, someone will suggest that high impedance headphones are harder to drive and low impedance headphones are easy to drive.

 

Normally someone else will chime in, suggesting that sensitivity is also important. But is the original rule of thumb – that low impedance headphones are easier to drive – actually true in practice for motherboards?

 

General Trends

 

To test the rule of thumb that higher impedance headphones are hard to drive, I plotted headphones on a Loudness vs. Impedance graph to see if a correlation between the two existed. For the purposes of this experiment, I calculated loudness using a model of a typical high-end consumer motherboard, an ALC1220 with 75Ω output impedance. Motherboards usually have a ~75Ω output impedance.^{[1][2][3][4][5]} Although different chips will produce different loudness results, the same trends should remain true for any Realtek codec, since their only relevant effect on loudness in this scenario is maximum voltage swing.

 

I chose AudioScienceReview's headphone measurements as a starting point for this research, since it reports its own sensitivity and impedance measurements (I did not want to go looking up specs for every single headphone listed). I also figured that its dataset would be applicable to the sorts of headphones that a modern headphone buyer would be considering (unlike, say, Innerfidelity, which is high quality but has a more esoteric headphone selection).

 

There is no significant correlation between impedance and loudness for a headphone driven from a typical motherboard, at least with this dataset. If anything there is a very weak trend suggesting that higher impedance headphones are easier to drive.

 

Perhaps the sample size on AudioScienceReview is too small. Here is the same exercise repeated with Reference Audio Analyzer's tested open and semi-open headphones (closed headphones were omitted because their measurements included active headphones), with 191 measurements in total.

Expanding to a larger dataset doesn't suggest that high impedance headphones are harder to drive.

 

Overall, then, I would say that the general rule of thumb that high impedance headphones are harder to drive is false; at least from a motherboard, there is either no correlation between impedance and loudness, or a very weak positive correlation between impedance and loudness.

 

What about Planars?

 

Some might argue that the rule of thumb has an exception: planars. I would argue that it isn't a very good rule of thumb if it isn't applicable half the time. Still, though, does a general rule that high impedance dynamic headphones are harder to drive hold true?

 

With the dynamic headphones tested on ASR, not really. Though the direction of the trendline has reversed, the correlation between impedance and loudness is still too weak to suggest any general rule; the R² is about the same as it was before. And even if the correlation were strong, the expected difference between a 32Ω and 300Ω headphone would be only 2dB.

 

The same was repeated with the conventional dynamic AKG, Audio Technica, Beyerdynamic, and Sennheiser headphones on RAA. I sanitized this dataset manually somewhat (removing variations and the K1000; consider this a possible source of bias). Once again the correlation is weak.

 

A Better Rule of Thumb

 

Just use efficiency and ignore impedance.

 

There is a strong correlation between headphone efficiency and loudness, even without correcting for impedance (impedance numbers are displayed for each headphone plotted). Headphones with particularly high or low impedances deviate from the trendline somewhat, but not by much. It's certainly much better than relying on impedance, which has little to no correlation with loudness on its own.

 

This is expected; impedance has at most a linear effect on loudness, while efficiency is a measurement in decibels: an exponential effect. Mathematically, sensitivity/efficiency should almost always have a larger effect on loudness than impedance.

 

Overall, the rule that high impedance headphones are harder to drive is not generally true in practice. Instead sensitivity/efficiency should be treated as the main indicator of how difficult a headphone is to drive, even in the absence of impedance information.

 

Appendix: Beyerdynamic

The Beyerdynamic DT series is unique for having multiple impedance variations on supposedly otherwise identical headphones. "Which Beyer model should I get?" is one of the more common variations of the "can my motherboard handle X impedance?" question.

 

In both datasets (ASR and RAA) the DT990 Pro 250Ω is an outlier for low efficiency. I wonder if this common headphone in particular is responsible for some of the perception that Beyerdynamic's high impedance headphones are hard to power. Despite being rated at the same efficiency as all the other DT990 variants, it is more power hungry and more voltage(!) hungry than even its 600Ω Beyerdynamic brethren.

 

 

Because efficiency measurements are not reliably comparable between different measurement rigs, I have color-coded the comparable ones.

 

RAA has tested three variants of the DT770 Pro (in yellow). Innerfidelity has tested three variants of the DT880 (in blue). RAA has also tested the DT990 600Ω and DT990 Pro 250Ω (in red). Although these are not exactly the same model of headphone, in practice a prospective DT990 buyer would almost always consider these the standard variants for each of those impedances. Beyerdynamic officially rates all of the headphones here at 96 dB/mW.

 

Although there appears to be a trend, the differences between impedance SKUs within a single headphone model are small; likely on roughly the same order as unit-to-unit variations.

[GoldenSound]

Seriously high-quality stuff!
Thanks for doing this.

There's a few other factors that are worth considering such as the fact that dynamic driver headphones do not have a flat impedance curve and many can see an impedance spike vastly higher than what their specs say, as specs for both impedance and sensitivity are typically calculated using a 1khz signal.

HD800 impedance curve for example goes upto about 650ohms at 100hz:

Whereas planars have a flat impedance curve.

This effect could potentially skew things a bit but as it's different for each headphone it's a bit hard to present the data in as nice a fashion as you've done. 

[Spuriae]

7 hours ago, GoldenOne said:

There's a few other factors that are worth considering such as the fact that dynamic driver headphones do not have a flat impedance curve and many can see an impedance spike vastly higher than what their specs say, as specs for both impedance and sensitivity are typically calculated using a 1khz signal.

Since frequency response deviations due to output impedance are usually seen as undesirable, I felt that the boost it can create within a narrow frequency band shouldn't be considered when calculating loudness. Instead I feel that it should be another reason to not use low impedance dynamic headphones with a motherboard, but that discussion is beyond the scope of this topic.

 

For ease of calculation in the original post, I used the "default" values used by each of the measurement sources (RAA reports average sensitivity and impedance across the audible band; ASR and IF report 1kHz sensitivity so I used the 1kHz impedance values for those measurements). In other words, the RAA dataset partially accounts for variable impedance/sensitivity, while the ASR dataset does not. There isn't a significant difference in overall loudness trends between the two.

 

The effect of the output impedance amplitude boost on overall loudness isn't significant. For instance, here is the impedance curve of the Focal Clear Mg (the most extreme impedance curve for a dynamic that I know of):

 

Here is its calculated frequency response deviation when driven by a 75Ω source:

 

A 5dB bass boost centered on 50Hz is created by the 75Ω ouput impedance. The difference in (linear average) loudness ends up being 1.2dB for this worst-case headphone. For more typical headphones the difference in average loudness is lower (not pictured); for instance the KSC75 is around 0.5dB and the HD800 is about 0.25dB. Loudness perception isn't linear in practice, but I don't have a good way of calculating the actual value.

9 hours ago, GoldenOne said:

Whereas planars have a flat impedance curve.

Aside from the Meze Liric (20Ω to 85Ω).

[H713]

@Nimrodor, since there are no datasheets available for the ALC1220, would you mind posting the calculations/model you used for this? It would be useful for those who are less-than-familiar with the standard chips used for onboard audio.

[Spuriae]

1 hour ago, H713 said:

@Nimrodor, since there are no datasheets available for the ALC1220, would you mind posting the calculations/model you used for this? It would be useful for those who are less-than-familiar with the standard chips used for onboard audio.

I don't have any official materials, unfortunately.

 

This is based on

• The ALC1220 is known to be rated for 2.1Vrms output
• This seems to be borne out in third party measurements
• Since motherboards generally use 75Ω series resistors, current limits are unlikely to have an effect

Here has a list of output levels for some different codecs. The 1200, 1220, and 4080 Vrms numbers rely on igorslab; the rest are taken from Realtek datasheets.

 

The process for calculating loudness goes:

1. Find impedance and sensitivity/efficiency (or convert another unit to sensitivity)
2. Using impedance, use the voltage divider formula to calculate the voltage delivered to the headphone
3. If using dB/mW efficiency, convert the voltage to power delivered to the headphone
4. Using sensitivity/efficiency and voltage/power, calculate the headphone's loudness

For instance, with the Ether CX from the ASR dataset:

1. ASR lists 23Ω at 1kHz, which can be used as is. But it reports sensitivity as 182mV required to reach 94dB. Convert this to efficiency using dB/mW = 94 - 10*log10((182^2)/23/1000) = 92.4dB/mW
2. Voltage delivered to headphone = 2.1Vrms*23Ω/(23Ω+75Ω) = 0.493Vrms
3. mW power delivered to the headphone = V^2/R = 10.56mW
4. Loudness = 92.4dB/mW + 10*log10(10.56mW) = 102.65 dB SPL

For the purposes of loudness with a large series resistor, only the output voltage level of the codec matters. The 75Ω output impedance isn't a feature of the chips themselves; many of the chips' headphone outputs are rated for full voltage output into 32Ω. But since the reference circuits usually include 75Ω resistors on all I/O, that's what the motherboard manufacturers end up doing.