[time-nuts] Software Sawtooth correction prerequisites?
Dr Bruce Griffiths
bruce.griffiths at xtra.co.nz
Sat May 12 18:37:14 EDT 2007
The statement that Dallas' version of the nanosecond differs by 10% from
Motorola's is somewhat disconcerting until one analyses how the delay
Aside from the contribution from internal logic propagation delays
Delay = Constant*RC,
Where R is the value of a resistor that determines the current used to
charge a capacitor and the constant is determined by resistor ratios.
Thus a naive implementation may use 256 equal resistors (r) connected in
series with a set of switches used to select the the required
resistance value (Nr) in 256 nominally equal steps.
The delay would then be proportional to N.
Unfortunately the ramp slope would vary over a range of 256 to 1 as
would the current. The current mirror used in the actual circuit may
have some dificulty in operating accurately over a current range of
256:1. Also the power dissipation in some of the resistors in the string
would vary over a large range. The large range (256:1) in the ramp slew
rate seen by the comparator would lead to significant variations in the
comparator delay. Fortunately if the effective value of the resistor
corresponding to N=0 is made somewhat larger (=Ro) than r then although
the N=0 delay will increased, the range of currents seen by the current
mirror and the corresponding slew rates seen by the comparator can be
reduced significantly improving the performance and reducing the
variation in resistor dissipation. This implementation should be
inherently monotonic despite variations in r and Ro. The effective RC
product and the corresponding delay can be designed to have a low
temperature coefficient. The RC product will vary from lot to lot and
this variation can be compensated by resistor trimming. There are other
schemes other than a series resistor string that can be used, however
most of these are not inherently monotonic and resistor trimming to
correct this error as well as the scale error may be necessary.
The attached plot of the error of a typical DS1020-15 illustrates that
the integral non linearity of the delay may amount to several
nanoseconds worst case.
This indicates that if one uses say 30ns of the range to correct for the
sawtooth error of an M12M or equivalent GPS timing receiver, that a
typical correction error due to the intergral non linearity of the
DS1020-15 may be as large as 1ns. However this can be reduced
significantly by calibration or perhaps by just calibrating the gain.
However unless an actual calibration or parameter fitting to a more
elaborate model for the INL other than just a change of scale factor the
specified data sheet maximum value for the delay it is unlikely that a
mere adjustment of the scale factor will ensure that the delay error of
every DS1021-15 that meets its datasheet specification will be less than
1 nanosecond. The optimum scale factor may also vary from wafer to wafer
as well as within the wafer.
Thus whilst it is highly likely that calibrating the delay and using a
lookup table or a model for the INL using several adjustable parameters
will allow a programmed delay error of under 1ns, it is unlikely that
merely adjusting the "gain" will reduce the programmed delay error to
under 1ns for all DS1021-15s ever produced that meet the datasheet
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