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I’ve been looking at designing a D/A converter for a while now. In my experience these are some of the hardest audio components to do right. It started with building output stages over a decade ago and at some point I even found myself in a company designing a D/A converter transistor by transistor.

However, as recent experiments have shown, I still have a lot to learn.

The reason why a D/A converter is so hard is because you have no possibility for feedback, since you’re translating into a new domain. You literally have to synthesize an output signal out of nothing according to the digital numbers handed to you.

Lots of listening tests have shown that if the output stage is good enough, you can always hear the sonic signature of a particular D/A chip, be it the architecture (switched-capacitor, steered current, R2r, etc) or even noise shaping loop structures. Oddly though, they all measure pretty much perfect. That’s an annoying discrepancy as it leaves you half blind whilst designing!

I wanted to see if I can see some of that subjective impression in measurements. As it happens I had two and a half D/A converters available.

First there is an eBay WeiLiang WM8741 D/A converter which I bought as a kit to see how the WM8741 performs in a cheap setup. The whole thing costs about $55 shipped which is mind blowing as the chip itself costs around $10 and you get some first grade opamps, a PCB, and all the components. The output stage in this one (v1.3) was designed exactly according to the wm8741 datasheet. But there were some pretty grave design errors on the PCB – the voltage regulators were different in the layout than on the schematic (yes, I did fix them).

But after complaining about these errors I was given a new board which has version v1.9. Power supply is better (i.e. not broken) and the WM8741 can now be switched into high or low rate (pin 22). But suddenly I noticed the entire analogue stage had changed, so I decided to hook both output stages to one D/A converter and measure the differences. A comparison between these output stages is in the pipeline.

Lastly, I could not resist a dirt cheap ESS9023 I2S board from diyinhk. Tapping the I2S signals from the WeiLiang board, I now had two and a half D/A converter to play with.

The WM8741 with v1.3 output stage and the ESS9023 have exactly the same output voltage (2.0 Vrms for 0 dBFS). So in this post we’ll focus on these two.

First, let’s do the standard measurements. The things you can basically read from the data sheets.

Harmonic distortion

!!! – I made a huge mistake and labeled all measurements ESS9018 instead of ESS9023. Please be assured it IS the ESS9023 all the time.

There is an immediate problem here. The wolfson 8741 output is not exactly clean, whereas the ESS9023 is pretty exemplary. Something is modulating the signal and the prime candidate is the power supply.

The THD+N reading on the AP System Two considers not only the harmonics, so we may assume the blame in the 50 Hz components for the reading on the wm8741. It is performing worse in the WeiLiang board.

Power supply rejection ratio

From the previous graph it is clear we need to look at PSRR, since the WeiLiang boards are showing a fair amount of supply disturbance.

So, we’ll probe one channel on the D/A converter output and the 5V supply rail and look at the respective spectra. First up, the WeiLiang wm8741.

There’s your problem. In the 20-400 Hz you can see the DAC follows the power supply exactly: it has 0 dB PSRR. When we get closer to the 1kHz signal region, the signal starts to modulate with the power supply components.

This is because the wm8741 is a charge distributing D/A converter. It first samples reference voltages onto a signal weighted number of capacitors and then onto the output. So, any disturbance on those reference lines is directly modulated onto the output. It looks worse than it is, given that the maximum component reaches only -75 dB, but this is definitely something that can and should be improved on the WeiLiang design.

Now, let’s to the same with the ESS9023.

Here we see a very different picture. The ESS9023, fed from exactly the same rail that feeds the wm8741, seems to almost completely reject the 50 Hz components. They don’t show up in the 50-1kHz range at all, and also don’t modulate with the 1 kHz signal. Very good news for ESS.

Frequency response

Another problem: the frequency response of the ESS9023 is pretty much ideal again, but the wm8741 is already down 3 dB by 20 kHz.

Part of this is the WM datasheet output stage, which we’ll discuss in a later blog post, another part is the 8741 sample rate. The WeiLiang v1.9 board lets you set pin 22 on the wm8741 high or low (disabling high-Z which is medium rate). Since the AP2322 can not go higher than 48 kHz, we’ll set the rate to low which makes the frequency response better. Still: advantage ESS.

Linearity

Not much to see here. Both are exemplary.

Listening tests

Now it would seem that the ESS9023 is in the lead against the WeiLiang board. A WM8741 chip can perform much better than this, but in order to do so it is clear that the power supply and the output stage will need serious work. And the ESS9023 has both of those integrated with no need for external components.

This is where the story would end, if we didn’t have ears or if we had learnt that good measurements guarantee good sound. Since that’s not the case, I hooked up the wm8741 WeiLiang v1.3 and the ESS9023 for an A-B comparison. Here are my notes.

Wow. That’s just confusing. The ESS had passed every test with flying colours but when listening to it, I found myself bored or distracted – anything but captured by it. The wm8741 was a bit of a diva: a bit of a morning temper and when finally warmed up really good on good material, and really bad on bad material. But over the course of the next two days, I couldn’t bring myself to disconnect the wm8741 because it was addicting, even knowing it was very flawed and could be so much better. When I finally broke loose of its grip and got the D/A converters back on the Audio Precision, I thought of one more test to run: the TIM test.

Now this needs some clarification as it is not as well-known as it should be. Whom better to quote than Bob Metzler in the Audio Measurement Handbook [pp. 41-42]:

Many audio workers have felt that some audible distortion mechanisms were triggered by changing program material, but not evident with steady-state stimulus such as a single sine wave. […] The most popular technique was proposed by Schrock and Otala. The signal […] consists of a band-limited square wave (typically around 3 kHz) plus a high frequency sine wave “probe tone” of one-fourth the peak-to-peak amplitude of the square wave. The rise and fall sections of the square wave stress any portions of the circuit which have slew rate limitations, and intermodulation products of the
sine wave with the fundamental and various harmonics of the square wave will indicate problems.

This is the reason why I wanted an Audio Precision with IMD plug-in so badly: I wanted to do this test. Let’s look at the result.

What do we have here? Although the IMD for the ESS9023 is mostly lower than that of the wm8741, there are two very weird kinks in the sweep (and I’ve re-run this with hundreds of measurements, it’s not a measurement glitch). I normally don’t like kinks in sweeps – I would prefer higher values of distortion as long as the sweep is smooth.  The kink at -37 dBFS is therefore odd but not as concerning as what happens near 0 dBFS – it shoots up!

A level of -10 dB of intermodulation cannot be for real, right?

As it turns out, it can.

 

The IMD pictures show that at high amplitudes, the ESS9023 is modulating just about anything with everything. The reason for this could be anything, but my money is on internal biasing inside the chip that cannot follow the fast shifts in operating points. Either cascodes run out of current, some common-mode loop cannot keep up with the differential loop, or what have you. The time domain plot shows that at every slope of the square wave the circuit is upset and starts to drift about, even though the smaller sine waves are still being reproduced.

Interestingly, this leads more weight to the case for digital volume control, as the distortion is only so pronounced at the very top of the digital range. However that is with just three sine waves, the lowest of which is 3 kHz. Music is a bit more complicated than that so the problem may well be far worse for actual audio signals.

It should not be possible for the signal to influence the operating point so gravely – that’s where the ‘small signal linearity’ axiom is built upon. It is just this that vacuum tube circuit excels at (and why I started building those). Running at several hundred volts, a few volts of signal would not upset any part of the circuit, which explains why they’ve survived in special applications (microphones and high end) up until this day.

It seems very contradictory that the ESS9023, which performs flawlessly on sine waves, falls over with a test signal like this. I’m afraid it is perfectly understandable that if an engineer is asked to design to specifications such as THD, SNR and cost, those are the only places that will receive attention and optimisation, often with some very clever tricks to shine under those measurement conditions. Some times at the cost of the aspects that have not been specified or will not be checked. Almost never on intent though.

And it’s not just ESS – I’ve already measured other D/A converters from other brands that show the same behaviour. And you don’t need an Audio Precision to notice when something goes so bad. Just take the IMD test signal and look at the waveform or the spectrum.

The lesson should not be to design only by ear – that leads absolutely nowhere. But neither should one design audio circuitry just to put nice numbers on a data sheet. Maybe there is a middle way?