Interface Bandwidth Limitation: Consider the sub-frame carrying an audio word value of 255 in fig.6. In the upper diagram, the unfiltered subframe represents the signal transmitted; in the lower diagram, the received signal at the interface decoder has been filtered with an RC time constant of 200ns. If we define zero-crossing time tx as the time taken for the received interface signal to cross the 0V detection axis after a transition has occurred at the transmitter, then tx depends upon the voltage at the receiver at transmitter transition time, and inter-symbol interference occurs; ie, zero-crossing time depends on the values of previous pulse widths. This phenomenon is shown more clearly in fig.7, which has an expanded time scale; the zero-crossing time at the end of cell 4 is smaller than that at the end of cell 6 (where the voltage at the receiver has had time to fall to a lower value). When both transmitted and received signals are known, we can compute the change in zero-crossing times at each subframe cell boundary by searching for the change in polarity of the filtered signal.
A simple computer program was written to perform this task, using the filtered data shown in the bottom half of fig.& The calculated results (fig.8) indicate that in this example, the zero-crossing time variation across the filtered subframe is about 50ns; when a series of ones are transmitted, the peak voltage received at the end of the interface falls, resulting in a reduction in zero-crossing time. The variation m zero-crossing time results in a modulation of edge timing in the clock recovered from the interface signal, and this edge modulation is clearly dependent upon the number of ones and zeros transmitted in each subframe: instantaneous recovered clock jitter is dependent upon the audio-word value transmitted over the interface. |
We will now develop an expression for the detected zero-crossing time at a given transition with a known history of previous transition times. Consider fig.9, which shows the exponential rise of a filtered transition with time-constant RC. The transmitted signal has a peak "driving" voltage Vd, while the received voltage has an initial value V0 at the time of the transition. If we denote the transition time as 0s, then the behaviour of the received signal following the transition can be described by a simple exponential time equation: Equation 2:
V =
Vd -(Vd-V0)e
-t/RC
Setting V to zero and rearranging gives the zero-crossing time: Equation 3: tx = RC ln [ 1+ |V0/Vd| ] The zero-crossing time evidently has a dependency upon the initial voltage V0 at transition time, and this in turn will depend upon previous pulse widths. If the previous transition in the interface signal occurred at-tl seconds, then V0 can be written in terms of t1 and V1 (the voltage at the previous transition): Equation 4: V0 = -Vd + (Vd +V1)e -t1/RC Substituting into Equation 2: Equation 5:
V = Vd
(1-2e -t/RC+e
-(t+t1)/RC)
This process can be continued with the next transition time at -(tl+t2) seconds, the next at -(tl+t2+t3) etc. to give: Equation 6:
V=Vd
[
1-2e-t/RC
(
1-e
-t1/RC Hence, we can write the zero-crossing time tx for the transition at 0s in terms of the previous pulse widths t1, t2, t3...: Equation 7:
tx=RC ln
[
2(1-e
-t1/RC Using Equation 7, we can now compute the zero-crossing time at each transition in a filtered interface signal containing several subframes. This yields a signal with a sampling rate equal to the maximum rate of interface transitions; ie, 5.6MHz. In our simulations, we want to map the zero-crossing times of the filtered interface signal to jitter on the recovered dock at the output of the ADIC. However, |
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