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
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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. |
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