Consider the case when we transmit only zeros across the interface (even in the preamble): t1, t2, t3, etc., will all equal tc and Equation 7 reduces to: Equation 9: tx0 = RC ln[ 2/(1+e -(tc /RC)] A similar expression occurs for the all-ones case, where t1, t2, t3, etc.= tc /2: Equation 10: tx1 = RC ln [ 2/(l+e -(tc /2RC) ] Subtracting Equation 9 from Equation 10 yields the approximate peak jitter due to a band-limited interface: Equation 11: tjRC ≈ RC/2 ln [ (1+e-(tc /2RC))/(1+e-(tc /RC)) ] This function is plotted in fig.13 for RC up to 400ns. We can use this approximation to scale the Zero-One sum shown in fig.12 to obtain the approximate jitter transfer function of fig.14. Note how similar this plot is to fig.11 (calculated using the average jitter model of Equation 8) in both scale and shape, indicating the fundamental dependence of interface jitter upon the Zero-One sum of the transmitted audio word. Having developed expressions for jitter based upon the bit
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pattern across adjacent interface subframes, we are now in a position to simulate a band-limited interface transmission and examine the resultant jitter signal for sinusoidal audio data. Fig.15 shows a dithered sinusoidal audio signal of 997Hz and peak amplitude 0dBFS, and the corresponding jitter signal tot an interface time constant of 100ns. At first glance, the jitter signal appears to be noise-like, but when it is low-pass filtered (simulating a hypothetical PLL filter), the jitter is shown to be highly correlated with the audio (fig.16), despite an audio frequency that maximizes the number of PCM codes excited in the time domain.5 This is confirmed by computing the Fourier transform of the windowed and filtered jitter signal (fig.17), revealing strong spectral lines at the fundamental and third harmonic. (Throughout this article, the 0dB reference level m the jitter spectra is set to 1ns peak jitter.) A similar jitter spectrum computed for a -70dB dithered 997Hz audio signal is shown in fig.18, where even stronger first and third harmonics are indicated. The increasing correlation between audio and jitter signals as the audio level is reduced is expected, since the audio signal spends a proportionately longer time in the crossover region of the jitter transfer function. Meitner and Gendron6 have also found that the jitter spectrum in a decoded interface signal has a strong dependency upon audio level, but they account for this behaviour in terms of power-supply artifacts or "logic induced modulation." In truth, power-supply related jitter in an interface decoder will resemble jitter due to band limitation, though the results presented here suggest that the band-limitation model compares well to jitter measured in practical circuits.
Comparison of Measured Results with Simulations:
5 Robert A.
Finger; "Review of Frequencies and Levels for Digital Audio
Measurements,"JAES, January/February 1986, Vo134, pp.36-48.
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