5.6MHz is too high a sampling rate with which to efficiently compute the effect of such a jitter signal upon any reasonable length of audio data. .

In order to reduce the jitter sampling rate to a useful value, we take advantage of the following argument: In a practical interface receiver circuit the PLL will usually employ a loop filter with a break frequency of <20kHz. If we assume that the audio sampling rate is much greater than the PLL loop frequency, then the zero-crossing time to jitter-mapping operation can be performed by computing a running average of the zero-crossing times across two subframes. Thus, the jitter value associated with a pair of adjacent subframes can be written:

Equation 8:

tjRC = RC/M ∑ M-1m=0 ln [ 2(1 -e -tm1/RC
-e -(tm1+tm2)/RC -e -(tm1 + tm2 + tm3)/RC + ... )]

where M is the number of transitions averaged across two subframes, and tm1, tm2, etc., are the pulse widths prior to the mth transition.

Note how the effect of previous transitions upon the zero- crossing time at a given transition diminishes as we move fur ther away from the transition. This allows a further reduction in jitter computation time, since we can limit the transition history taken into account without compromising accuracy.

Before examining the results of simulations that calculate the jitter on a band-limited interface, let's consider the idea

bitmap image
Fig. 10 Jitter transfer function over audio range -32,000 to +32,000 in steps of 100 for interface time constant of 100ns.

bitmap image
Fig. 11 Expanded view of the central portion of fig. 10.

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Fig. 12 Zero-One sum for twos-complement-coded 16-bit audio word (compare to fig. 11).

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Fig. 13 Maximum peak jitter plotted against interface RC time constant.

of a jitter transfer function. Equation 8 indicates that the instantaneous jitter value associated with each interface signal frame depends upon the time between transitions (ie, pulse widths) during that frame. The pulse widths (either half or full cell width) in mm depend upon the position of ones and zeros in the transmitted interface signal.

Given that each audio sample value is represented by a unique bit pattern when biphase-mark-encoded by the interface transmitter, it is possible to calculate a jitter value for each audio sample value transmitted across the band- interface and represent instantaneous interface jitter as a deterministic function of audio sample value.

Fig.10 shows such a mapping for 16-bit audio sample values in the -32,000 to 32,000 range, in steps of 100, for an RC time constant of l00ns. Here we have assumed that both channels carry the same audio value, and that the parity sub-code bit is active; the 64 zero-crossing times at each cell boundary across the frame are calculated and then averaged to obtain a jitter value for the audio sample value. Fig. 11 displays the same transfer function, but with an expanded horizontal scale over the -400 to 400 audio word range, in steps of one.

The largest change in zero-crossing time occurs as the audio word value moves through zero; ie, changes sign. This is due to the twos-complement representation of the audio word within each subframe. The jitter exhibits a staircase-like transfer function as the audio word value moves away from zero; in fact, the zero-crossing time exhibits a strong dependence upon the difference between the number of zeros and ones in the 16-bit audio word. Fig.12 shows such a "Zero- One sum" across the -400 to 400 word range, with clear similarities to fig.11 (the sum extends to ±17 for the 16-bit audio word, because the parity subcode bit is active). With this approximation we can develop a simpler expression for


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