Measuring Jitter
We have intentionally left our jitter specification blank. It's not because jitter is unimportant. On the contrary, we care deeply about jitter because it produces non-harmonic distortion, which is the reason they are perceived as fatiguing, metallic, and harsh. However, to measure it reliably down to the picosecond level (one trillionth of a second) remains exceedingly difficult, and even if it could be done, a single number is inadequate unless its frequency-domain behavior is also understood. So rather than attempting to present a singe definitive number, we limit ourselves to presenting certain characteristics of jitter that seem relevant to auditory perception.
Sometimes, the jitter of the master clock is presented as a performance metric of a DAC. But it merely represents a lower bound, not the actual sampling jitter of the DAC. What we're really after is the sampling jitter, measured at the analog output of the DAC, which is what ultimately matters to the sonic quality.
Jitter Sidebands
One direct way of measuring jitter is simply to monitor the DAC output with an ADC. If the jitter is sufficiently small, which is usually the case, then it would manifest itself in the frequency domain as double sidebands, centered around the signal. From the amplitudes of these sidebands and the frequency of the signal, we can then estimate the amount of timing jitter.
To illustrate how this jitter spectrum might look like in the frequency domain, we generated a 1 KHz, 50 ps rms (141 ps peak-to-peak) sinusoidal jitter in software, modulating the sample time of an 11.025 KHz signal (sampled at 44.1KHz, 24 bits). This simulated signal was then fed into the Audio Precision APx525 analyzer for FFT. Since the signal is from a numerically-generated simulation, we do not see the noise floor, which is well below the lowest limit of the plot. But we do see the telltale sign of jitter -- the double sideband centered around the main signal, which in this example is at +/- 1 KHz and -112 dB from the signal. As evident in this plot, the sidebands are not harmonically related to the signal, which is the reason they are perceived unnatural and objectionable.
Some Assumptions
In actual measurements, as we search for jitter on the order of picoseconds, we run into the limitation of measuring instruments. It is not easy to tell what portion of jitter is from the DAC under test or the ADC of the measuring instrument. Fortunately, the jitter of an ADC is usually lower than that of a DAC. The ADC does not need to go through the process of recovering the clock from the incoming data. Its timing-critical conversion stage can be driven almost directly from a pristine clock source without suffering much degradation in quality. As we will see, it turns out that the ADC of the APx525 performs exceptionally well in this regard, and we can assume that its jitter is usually less than that of the DAC under evaluation.
We also assume that, for the most part, the DAC jitter is dominated by frequency-coherent jitter than random jitter. As we have seen already, frequency-coherent jitter will produce discrete tones centered around the signal in the frequency spectrum. By contrast, random jitter will produce a flat frequency spectrum, which is indistinguishable from white noise in the FFT analysis. It is generally recognized that the human ear is more perceptive to the presence of discrete tones than white noise. So we consider only that which exhibits frequency-coherent behaviors.
Another assumption we make is that low-frequency jitter (below about 100 Hz) is masked by the signal and is below the threshold of hearing. In the frequency domain, the low-frequency jitter sidebands congregate near the main tone, and if sufficiently low in frequency, it appears as skirts around the main tone. Research by Julian Dunn indicates that jitter below 100 Hz is at least 40dB less audible than jitter above 500 Hz. This is consistent with well-known research on auditory masking, which has demonstrated that the presence of a large tone masks smaller tones at nearby frequencies.
With the above assumptions, we used the ADC of the APx525 analyzer to sample the analog output of the D1 DAC, being mindful of the fact that what we are measuring is not merely the DAC but the DAC plus the ADC. To increase the sensitive of measurement, we use a high-frequency signal, 11.025 KHz, a quarter of the sample rate, 44.1KHz. And to expose as much frequency-coherent jitter as possible, we used very long FFTs, 1024K points, averaged 4 times.
Moreover, to test if the jitter is sensitive to data patterns, we varied the frequency and magnitude of the signal over hundreds of points, in effect, varying the pattern of 1's and 0's in the data. The results show that changing data patterns do not alter the jitter spectrum of the D1 DAC in any noticeable way.
USB Interface Jitter Measurement (16 bits)
We have a keen interest in measuring the jitter of the USB interface because its level of jitter is typically much worse than the SPDIF interface. If left untreated, the degradation in sonic quality is readily audible. So we wanted to see if our multi-stage jitter reduction circuit would be effective on the USB interface. The FFT plot of the D1 DAC output (16-bit, 11.025 KHz signal) shows that there are no jitter sidebands visible above the noise floor, around -135 dB, which means that if they exist, they are buried under the 16-bit quantization noise. If there were a single jitter-induced tone at -135dB, the corresponding jitter would be 4 ps rms.
Here is the same measurement, zoomed in along the frequency axis. Notice the slight spreading around the signal, about +/-20Hz. This spreading is a characteristic sign of low-frequency jitter. As mentioned above, such a low frequency jitter is masked by the presence of the strong nearby tone and is well below the threshold of audibility.
SPDIF Interface Jitter Measurement (24 bits)
We've already mentioned that these measurements are ambiguous because they not only represent the D1 DAC's performance but also that of the ADC of the APx525. Before proceeding further, it would be illuminating to digress for a moment to see the loopback performance of the Audio Precision APx525 analyzer. In a loopback setup, the analyzer essentially measures itself, with its DAC output connected to its ADC input. With 24-bit data, the noise floor is low enough to reveal numerous discrete tones. Although these discrete tones are quite low in amplitude, all below -132 dB, their behavior is complex. We see several discrete tones that appear to be jitter sidebands (positioned symmetrically around the signal), but also many others that are not jitter-related. Based on this plot alone, it would be impossible to separate the contributions of the DAC from those of the ADC.
Finally, we look at the jitter spectrum of the Anedio D1 DAC through the SPDIF interface. Shown here is the spectrum of the D1 DAC output, measured using the APx525 ADC. Notice that practically all the discrete tones in the APx525 loopback measurement is now gone, suggesting that it was the APx525 internal DAC that produced most of the discrete tones. The FFT spectrum of the D1 DAC plus the APx525 ADC looks remarkably clean. The only discrete tones that are symmetrically positioned around the signal are at +/-1 KHz, -150 dB, which translates to about 0.7 ps rms jitter.
At this point, measuring jitter down to the picosecond level can only be tentative because we can see only part of the picture. The FFT-based jitter measurements cannot distinguish between white noise and random jitter-induced noise. Yet these measurements, limited as they are, show that the multi-stage jitter reduction implemented in the Anedio D1 DAC performs their job effectively and consistently for both USB and SPDIF interfaces.