processor, the Audiolab 8000 DAC, reveals no jitter error at all (fig.30); this is due to the superb PLL performance of this model, offering a (claimed) cloud-loop cutoff frequency of just 13Hz, where all audio-frequency interface.jitter will be attenuated to inaudible levels. (Note that the noise seen at 400Hz in this diagram is due to a ground-loop problem in the test apparatus.)

The greatest differences between 100% and impulsive DAC fitter errors occur when the signal frequency is low. Figs.31 and 32 show simulations and measurements, respectively, for a 0dBFS, 100Hz audio signal jittered by 10ns, 4kHz sinusoidal jitter. The jitter error is about 30dB higher in the impulsive (Bitstream) DAC. Thus, audible noise modulation can occur when impulsive DACs are jittered while reproducing low-frequency audio signals, and this may well be the reason some reports have suggested that Bitstream DACs lack "dynamics" and "rhythm and pace,"15

bitmap image
(a)
bitmap image
(b)
bitmap image
Fig.29 Meridian 203 Bitstream DAC: measured jitter error spectra for
(from top to bottom):
a) 10,001Hz at 0dBFS audio, no jitter;
b) 10,001Hz at 0dBFS audio, 10ns peak, 1kHz jitter;
c) 2001Hz at 0dBFS audio, 10ns peak, 1kHz jitter.

bitmap image
Fig.30 Audiolab 8000 Bitstream D/sC: measured litter error spectra for I 0,001 Hz at 0dBFS audio, I 0ns peak, 1 kHz jitter. Note the absence of error sidebands at 9kHz and 11 kHz.

since most of the rhythmic content in music occurs at low frequencies and can be high peak level.

In addition, practical low-bit DACs often possess high levels of high-frequency quantization noise that has been shaped away from the audio band, and if very high frequency jitter is introduced into such a conversion process, intermodulation products can fall back down into the audio band, causing further degradation of dynamic range and noise modulation).16 (Our simulations employ a sampling rate of 44.1kHz, and thus can not model such secondary jitter artifacts.)

Analogy to Phase-Intermodulation distortion in Audio Amplifiers: Amplitude errors caused by timing.jitter at the ADC or DAC gateway can be examined i n a wider perspective by comparing the jitter-error mechanism with artifacts found in analog electronics. Hawksford17 has shown that jitter errors in DACs can be compared to slew- rate limiting in transimpedance amplifiers located at DAC outputs. The jitter-error mechanism can also be likened to phase-intermodulation distortion (PID) in analog amplifiers. Otala18 19 has shown that PID occurs when open-loop amplitude non-linearity in a feedback amplifier is mapped to a closed-loop phase non-linearity. Cordell20 refined the PID model by writing the timing error t(x) in the phase-distorted output voltage x from a feedback amplifier in terms of the normalized open-loop non-linearity e(x) and closed-loop cutoff fco;

Equation 22:

t(x) = e(x) / 2πfco

If we substitute typical values of e(xmax) = 1% (0.01) and fco = 1MHz for an IC operational amplifier, we find that the peak timing error is equal to 1.6ns. This is of the same order of magnitude as the jitter found in digital audio interfaces. It


15 Martin Colloms, Hi-Fi News &Record Review, October 1989, pp.83-85.
16 B. Adams, 'Comments on 'Chaos, Oversampling and Noise-Shaping in Digital-to-Analog Conversion',"JAES, October 1990, Letter to the Editor, Vo138, pp.766-768.
17 M.O. Hawksford, "Digital-to-Analog Converter with Low Inter--lc Transition Distortion and Low Sensitivity to Sample Jitter and Transresistance Amplifier Slew Rate," presented at the 93rd AES Convention, San Francisco, October 1992.
18 M. Otala, "Feedback-Generated Phase Intermodulation in Audio Amplifiers," presented at the 65th AES Convention, February 1980, Preprint 1576.
19 M. O 'Phase Modulation and Intermodulation in Feedback Audio Amplifiers," presented at the 68th/LES Convention, March 1981, Preprint 1751.
20 R.R. "Phase Intermodulation Distortion - Instrumentation and Measurement presented at the 70th AES Convention, October 1981, Preprint 1842.


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