Headphone Amplifier Measurement Routine Development: THD+Noise

Preliminary Total Harmonic Distortion + Noise vs. Frequency
There's a long row to hoe here, so don't get too wrapped up with the measurements above. There are plenty of places for gremlins to hide in setting up these measurements for the first time. I've build one cable, but there are plenty more to go. Some of the measurements above have different cables with some adapters in the loop. Got to double check the system grounding. Bottom line: don't believe anything you see yet. That said, so far THD+Noise measurements have been pretty repeatable ... and I'm glad to see the system finally drawing lines about headphone amps.

Today's measurements were Total Harmonic Distortion + Noise vs. Frequency (THD+Noise vs. F). This is a measure of the linearity of the gain curve (or transfer function) of an amplifier. Imagine a big bass note going up and down at 40Hz with a little 10kHz high frequency note superimposed on it. As the bass note goes up and down, the high frequency note is sometimes being amplified on the positive part of the gain curve, and sometimes it's in the negative part of the gain curve. In a very linear amplifier, the high frequency note will amplified by exactly the same amount regardless. In single ended tube amplifiers, the gain is not linear, and the small high frequency signal will generally have less gain as the grid voltage goes positive.

Here's the simple version: if the gain isn't linear, the signal will get squished sometimes, usually near the top and/or bottom of the operating region. This squishing distorts the signal.

Here's the weird thing: when you put a pure sine wave of 1kHz, for example, in to an amp with some distortion, you'll get the 1kHz signal back out, but you'll might also get a little 2kHz, 3kHz, 4kHz etc. at the output as well. This is called harmonic distortion, and if you add up all the little distortion peaks you get the amount of Total Harmonic Distortion.

In the graphs above, the tester puts out a pure sine wave at 1Vrms. I adjust the volume of the amp so that it outputs a 1Vrms signal that gets sent back to the analyser. The measurement system then slowly sweeps the frequency of the audio signal from 10Hz to 22kHz in 100 steps. The signal out of the amp goes into the analyser where it first goes through a very deep notch filter that is stepped along with the frequency of the generator, which completely gets rid of the main driving tone. What's left is the various harmonics created by the non-linearities of the amplifier --- the harmonic distortion.

But! There's another thing there: the noise from the amplifier. So the meter in the analyser is reading both the total amount of harmonic distortion and the noise. That's why this measurement is called THD+Noise v Frequency.

Again, this is too early and there are too many places where gremlins can pop in to state the above graph is accurate, but let's just take it at face value for the moment and talk about a few of the graphs.

You can see the Burnson HA-160D has the highest amount of THD+Noise. This is most likely because this is the highest gain amplifier, and therefore has the most noise. The noise is a constant, so noise dominated measurements tend to be featureless and flat. You'll also notice a small dip around 120Hz. This likely occurs because the AC transformer is putting a little hum in the system. When the filter of the analyser gets swept past 120Hz, it gets rid of the 120Hz component of the signal. Since the dip is small, it's fair to say the contribution of the hum to the measurement is somewhat less than the broadband noise of the amplifier.

You can see that the Pico Slim has a large feature in the bass. This is a very small portable amplifier with a single ended supply and has some capacitive coupling. When low notes start getting filtered out by the capacitive coupling it distorts them, and results in a rise in harmonic distortion in the lows.

The TTVJ Slim is not as flat a line in general as the other amps. This means that there is some change in distortion with frequency. I'd bet a fine Belgian beer that this is evidence of Pete Millett's fancy fiddling. He tends to do some tricky stuff for really good reasons, even if it makes the numbers change a bit.

The HeadAmp Pico had the lowest THD+Noise of all the amps above 100Hz, but one channel is producing a rather noisy measurement. Here be them gremlins methinks. I've got to make some dedicated cables and retest --- getting the grounding absolutely nailed down is a huge deal in measurement systems.

The bottom trace is the measurement with the outputs of the Audio Precision tester just looped right back into the inputs of it's analyser. It is much lower in distortion than the amps measured, and tells me the system is not adding any artifacts to the other measurements.

Okie dokie, next is more cable making, and I'll probably try to make a THD+Noise vs. Power test. See you then!

13mh13's picture

nwavguy's Objective2 (O2) headphone amp was putatively designed from the get-go to measure optimally. So inclusion of that amp would be worth seeing.

Tyll Hertsens's picture
Remember, this is an exercise in developing a test routine, and not really appropriate - yet - for comparison purposes. That said, I have chatted with NwAvGuy about getting an O2 in for this project. Mainly so that I can measure it and then send the measurements off to him to compare with his measurements. That should be the best check of all as we have comparable equipment and the measurements should jive.
br777's picture

The longer I am in this hobby, the more I am appreciating audio professionals such as yourself who take the time to measure gear. People like you and NwAvGuy are more of a service to the headphone community than 100 of the purely subjectively based reviewers who are often doing more harm than good. I hope to see you two collabarating together, or at least continuing to learn from each other and maintaining interest in each other's work more and more in the future.

You two would make a great checks and balances team. There is nothing like two respected reviewers sharing objective consensus.

Keep up the good stuff as always!!

johnjen's picture

And he's off to the races…

Now we'll Finally get to see some actual numbers on amps and such!

Yea it will take some fussing with the knobs and seeking out and then eliminating the gotcha's and hidden sources of contamination. Especially when you're reaching down into the triple and quadruple digits behind the decimal point.

But we are gunna get some directly comparable numbers and dynamic responses to testing parameters and then correlate them to what we hear!


Go Tyll Go…

JJ :thumb :D

bfwiat's picture

Looking forward to more in this article as time goes on.
Out of interest, was the Burson measured through the H gain jack or the L gain jack . . .and indeed are there any measurable differences? (many people (myself included) think the Burson sounds better on the L gain jack (even with high impedance cans)) . . . also, any valve amps planned in the future in this test procedure? I understand they will inevitably test worse/different to SS amps, but it would be good to compare Valve to Valve amps at the least (ie power vs impedance vs distortion) . . . and perhaps start the age old discussion of good sound vs Observable good measurements and the correlation (or lack thereof) between them.

Looking forward to more . . .


svyr's picture

i think it's also a good chance for testing manufacturer honesty.
For amps/dac outputs they quote AVG thd+n (or smoothed lol?), or THD+N at 1khz at X output level (not disclosed anywhere), or the opamp theoretical THD+N

mikeaj's picture

I agree. Often they don't list the load impedance either, which probably means they just tested into the analyzer (or line in of whatever), assuming they did any testing in the first place. The test of practical interest is high output levels into low impedances.

For that matter, Tyll, I know you're just in the process of setting things up, so I'm going to guess that the top teaser graph is with the amps unloaded?

Good luck, and take your time, to get things right. I'm looking forward to results!

svyr's picture

ops yep, forgot to mention the load impedances. (and they rarely state output impedances on amps too :D )

The only amp I can remember listing detailed specs on this is the M3 and B22 (they at least list the loads and power out level).

Funk LPA-02 had graphs of THD+N vs power at a specified impedance as well. http://www.funk-tonstudiotechnik.de/LPA-2%20englisch.pdf

Tyll Hertsens's picture
Load impedance in this case was 300 Ohms. Once real testing begins the amps will be measured with multiple loads: 15; 30; 150; and 600 probably
dalethorn's picture

From the many comments and mini-reviews of amps, particularly the recent portable headphone amps I read about, there is much to be explained about why they sound so different. This work here has the potential to clear some of that up. I sure hope it works out.

arnaud's picture

Hi Tyll,

Very interesting, is it really % on the scale or actual units? e.g. the Burson has 1% distortion all across or 0.01%? I wonder where the audible part kicks in? Also, any way to subtract the noise by measuring the output without any input signal?

mikeaj's picture

I doubt it's 1% THD+N. 1% would be pretty terrible unless it was intentionally designed in. 0.01% is more like it. Some of the quieter amps with low THD should be under 0.001% (-100 dB) with 1V output, particularly when unloaded. This isn't too incredible, considering that some IEMs have sensitivity like 130 dB SPL / 1V. If the noise floor itself was around 0.001% referenced to 1V, then you'd be able to hear it easily with such IEMs.

When these amps are loaded with headphones-level impedances, particularly lower impedances, you'll see the much higher THD+N figures. For example, see this white paper from Benchmark Media:


I'm pretty sure the AP can do a pure THD test though, if you wanted. Arguably that's also interesting to see, in addition to THD+N.

Tyll Hertsens's picture
It's 0.01%. NwAvGuy says .005% distortion is inaudible, but music masks the distortion somewhat so 0.01% distortion is the acceptable number. Remember however, that the Burnson was measured in high gain mode and the graph shows noise domination, so it's really just the amount of noise at that particular output. It really doesn't mean too much in this case. Again just wringing out the system here, and many other tests need to be done to have enough data to characterize the amp.

There are techniques to separate the noise from the distortion, not sure if I'll be doing them or not. We'll see. I will be measureing noise spectra however. Short the inputs and just do a spectral measurement.

sgrossklass's picture

IMO, THD+N is like adding apples and oranges. Remember that trained CW operators can decode at like -6 dB SNR? (And that's with a 3 kHz noise bandwidth at most.) That's because the human ear is frequency-selective, much like a spectrum analyzer. THD+N, by contrast, always refers to the entire audio bandwidth, so the THD part gets swamped by noise too early.

THD+N kinda does make sense once you are dealing with anharmonic distortion or simply a rising noise floor, as you might find in DACs or Class-D amps. For oldfashioned non-switching concepts like your average headphone amp, it's counterproductive at best.

Also try measuring THD at >20 kHz bandwidth (like 80 kHz) if you can, so as to get valid readings all the way up to 20 kHz. (With noise-dominated measurements, it's hard to tell whether you're doing that now.)
It's not like I'd be terribly happy with THD per se (when it comes to electronics, adding harmonics still is oranges and grapes at the very least *), but these swept tests do tell a thing or two about amplifier performance, and showing curves for the individual harmonics would result in a big mess unless resorting to 3-D graphs.

*) I conducted a little experiment in which I generated a 440 Hz tone and its individual harmonics and played them back over my trusty HD580s. I could trace the 7th and 8th down to -70dB (.03%) at sufficiently high playback levels, while 2nd was audible but not particularly bothersome at -40 dB (1%) and definitely gone at -60 dB (0.1%).

For an estimate of worst-case permissible distortion performance, you need to know about maximum expected playback volume and minimum hearing threshold. .005% (-86 dB) seems like a reasonable value. But as stated, that's a worst-case estimate. In practice, you may be able to get away with much higher values if the distortion is masked by the transducer or the auditory system. Noone is ever going to complain about an amp with -60 dB of 2nd harmonic throughout (assuming there is very little of higher order going on).

MayaTlab's picture

Thank you Tyll ! Very interesting work.

svyr's picture

heh, would you be also measuring IMD?

Tyll Hertsens's picture
Willakan's picture

Measurements! Yay! It is great to see we'll soon have another person who's got a decent measurement rig and is not afraid to use it peering at popular amplifiers.

My only gripe would be that I had to visit the comments section to find out the load impedance being used. This should be next to the graph, in giant purple letters, IMHO.

Looking forward to the tests with more challenging loads, anyhow. Should be very...illuminating.

Tyll Hertsens's picture
You're absolutely right, and when w get the the final product it'll be there ... not sure about the purple letters, though.

Basically, I set up the test and started slapping amplifiers on it, and once I had a pretty graph I said, "Hey! Bet the folks on teh interweb would like to see this." So, I posted it.

I'll be testing amps with 15, 30, 150 and 300 Ohm loads.

svyr's picture

haha, any chance of 8 ohm tests (probably outside most amp specs, but yea, some IEMs like that do exist)

Willakan's picture

I would say 8-ohm load tests would ideally be amplifier specific: there are some amplifiers which are clearly not designed to drive IEMs, so going lower than 15 ohms would perhaps be a little unfair. They are probably only worthwhile with amps specifically designed/advertised for IEMs.

mikeaj's picture

Are the load impedances you'll use for testing up for debate now? I know it takes time running many of the tests, particularly if you're hooking up different test loads, but I feel like you should consider doing something between 30 ohms and 150 ohms if possible.

Maybe something more like 60 to 80 ohms? It's the lower-impedance, lower-sensitivity headphones that will create more problems for most amplifiers anyway. If an amp does fine into 150 ohms, it should be fine into 300 ohms or 600 ohms or something higher, so those results are maybe not as interesting.

Many particularly power-hungry HiFiMAN and Audeze planar magnetics headphones are more like 50 ohms and may not be characterized well by the 30 ohms or 150 ohms tests. The newer Sennheiser HD 5xx models are in that range, AKG Kx4x and Kx7x as well as the popular K701/702 and Q701, many Ultrasone models, and so are some relevant IEMs.

MrSaikes's picture

When is the LCD-3 review coming? =)

Tyll Hertsens's picture
When I have time to do it justice.
Brod's picture

Very interesting. I feel that THD+N is by far the most important specification for a headphone amplifier, so I will be eagerly following the progress of your testing!

schalliol's picture

I too am very interested in seeing what you're able to produce here. Once you get it up and running, it would be very cool to see amps run in different ways, i.e. a HR BUDA unbalanced, balanced and with different power supplies. People often wonder about how these configurations affect the signal, and THD+N is a great set of measurements to explore!