14th March 2000 - Understanding A/D and D/A converter measurements

On March 14th Julian Dunn was introduced to a packed meeting as "a world expert in audio D/A and A/D conversion, and the world expert on jitter"; his presentation lived up to this introduction in every way.

Since the widespread introduction of digital audio during the seventies and eighties it has become clear that many of the measurements traditionally made to assess and characterise analogue audio systems do not translate well to the digital domain. Concepts such as the frequency response of a filter can cross this divide; there are, however, phenomena such as quantization noise and jitter which not only are absent from a wholly analogue system, but which are not accurately characterised by digital equivalents of analogue test equipment and procedures. The audible flaws that result from these phenomena are not, therefore, accurately predicted by such measurements. Therefore, new measurement techniques which address these areas directly are required.

Julian defined some of the building blocks from which these tests are constructed. The first of these is a reference signal level 0dBfs, defined as the power of a sinusoidal signal which peaks at digital full scale. This simple definition has a number of interesting subtleties.

Firstly, it was pointed out that this definition allows valid digital signals whose level is greater than 0dBfs, which at first sight seems counter intuitive. Secondly, a sinusoidal signal may peak at digital full scale without any of its sample values ever taking on that full-scale value, since the signal peak may not coincide with a sampling point. Thirdly, a problem occurs when trying to determine the analogue equivalent of a 0dBfs reference tone since the presence of any dc offset introduces signal clipping. For this reason the analogue reference level must be calculated using a lower-level test tone (eg -20dBfs).

These points call into question the method used to measure the level of a digital audio signal. The possibilities include rms, peak and quasi-peak meters. The rms measurement is mathematically well-defined, but by its nature does not reflect the values of the signal peaks which are often of interest. The quasi-peak meter requires attack and decay constants to be specified in order to be unambiguous. An accurate (quasi-) peak meter is required to interpolate between the signal values to find the true signal peaks, since the sample points do not necessarily coincide with those peaks. It is not sufficient for a peak meter to record the maximum (absolute) sample values.

It was stated that 997Hz is a useful choice of frequency for reference/test tones since it does not share any factors with any of the sample rates in common usage. This results in the signal having no repeated sample values (assuming adequately small quantization step size) in any given one-second period, and furthermore ensures that at least some of the samples during that second will lie close to the true signal peak.

An essential component of both ADC and DAC devices is a band limiting filter, and the next part of the presentation discussed their measurement. Such a filter has three regions of interest: the passband, the stopband, and the transition between them.

The passband can be analysed with a swept sinusoidal test tone; the input level is maintained constant, and the output level then reflects the frequency response of the filter. The passband ripple of a good quality converter was shown by this measurement to be <0.1dB. This ripple seems at first sight to be insignificant but it was shown to lead to a prominent pre- and post-echo in the impulse response.

Measurement of the stopband response differs for ADC or DAC devices. For an ADC the method is to stimulate the device with a signal above the Nyquist limit and inspect the ADC output for alias components. The total power of any such aliases is then indicative of the filter response to the high frequency input signal. For a DAC the stimulus is in-band, and any out-of-band image components are measured to compute the response.

Wideband measurement of this response with a noise stimulus and FFT post-processing was shown to be much faster but less sensitive than using a sinusoidal sweep. However, this technique is useful for measurement of the transition band where extreme sensitivity is not required.

The next target for Julian's armoury was measurement of noise in digital audio systems. Noise is introduced in converters as Johnson (thermal) noise, quantization noise and conversion errors.

It was pointed out that idle-channel measurements are often meaningless since many DACs appear anomalously quiet when presented with continuous "digital black." For this reason noise measurements are made in the presence of a signal which is subsequently filtered from any measurements using a notch filter.

If this signal is dithered appropriately then its noise content is known and may be subtracted from the measurement. This allows an accurate measurement of the noise of, for example, a 16-bit DAC to be made despite the fact that it is swamped by the noise in the test signal.

A further complication comes from the proliferation of metering standards and weighting filters. It was shown that different choices can make over 11dB difference to the quoted result. In particular the quasi-peak meter has its roots in telecommunications where impulsive noise is a significant problem, and reads 4.5dB higher than an rms meter for white noise. For this reason it is essential to quote both the meter and weighting used for the measurement. AES-17 suggests that an rms meter and a modified CCIR468 weighting should be used.

Noise spectra are frequently displayed as FFT plots scaled such that a 0dBfs tone is indicated as 0dB on the vertical axis. Such plots do not give direct readings of noise power or noise spectral density due to the mathematics of the FFT, but the scaling can be corrected for such measurements given additional information of the sample rate and the window used for the analysis.

Next, high level non-linearities were tackled. The typical analogue-domain measurement is one of THD+N but this is inappropriate for digital systems since the harmonic products of a high-frequency test signal are outside the system passband. Instead, AES-17 describes a two-tone intermodulation measurement at 18kHz and 20kHz. The levels of the first-order intermodulation products at 2kHz and 16kHz are measured and combined.

Finally sampling jitter effects were examined and two possible tests were described. First the sample clock can be measured directly. This is often difficult as the sample clock may not exist outside the device under test; even if it does the measurement itself is prone to influence the system and is also insensitive.

The alternative is to measure the effect of the jitter on a known test signal and make inferences about the jitter from these effects. The principal disadvantage of this method is that it can become difficult to separate jitter effects from other distortions and as a result sometimes only an upper bound on the jitter present can be reliably judged. The intrisic jitter of a device was demonstrated to result in sidebands appearing either side of a high-frequency test tone. Measurement of these sidebands allows an upper bound for the jitter to be determined by integration of these sidebands.

A method for determining the jitter transfer function of a DAC was demonstrated. An AES3 signal representing a high frequency sinusoid was subjected to a deliberate jitter signal. The jitter transfer function of the DAC was then determined by stimulating it with this signal and examining its output. Since the jitter applied was sinusoidal its effects could, in this case, be separated from other distotion mechanisms since they appear as tonal components in a FFT plot. The results from a sweep of such sinusoidal jitter tests were plotted and showed a characteristic first-order roll-off.

A similar test was conducted for a sample rate converter (in which the sample clock is not available for direct measurement) and the results compared with those from the DAC.

The evening concluded with further demonstrations and a lively question and answer session.

Christopher Hicks