[time-nuts] Fine delay generator

[Tim Shoppa]

Bruce Griffiths <bruce.griffiths at xtra.co.nz> wrote:
> An LTC1407A-1 dual simultaneous sampling ADC allows sample rates up to
> 1.5MHz with adequate linearity if driven differentially.
> However an inverse tangent calculation is required for each measurement
> - this could easily be done in an FPGA within a few tens of nanosec.

Arctan is the mathematical solution, but by using some extra knowledge
(that the amplitude of both sin and cos can be measured
but are not necessarily exactly equal to the level of DAC resolution) and the
common sense that at some parts of the cycle, cos is changing very slowly
and sin is changing very rapidly, or the other way around, resolution
can be substantially improved (nearly a factor of two).

Giving the slowly changing phase the same weight in the calculation
as the rapidly changing phase is unwise. It is wise to calibrate
the amplitudes and relative phases of sin and cos generators using
the same DAC's as you're going to use to do the measurement.

We were doing all this 30 years ago using CAMAC crates and PDP-8's,
no FPGA for arctan but we spent a good amount of effort in
weighting the calculation to extract
every bit of time resolution given our relatively coarse DAC resolution.

Much of this is in the 1940's Radiation Lab series, there
are extensive sections on sin/cos wave generation, and they
do note when doing the time measurment that you want to move
the trace so you are using the rapidly changing phase.
Of course they weren't necessarily using 10MHz sin/cos generators
back then, mostly they were using custom-wound nonlinear wire-wound pots
and motors driving shafts to make the phases :-).

Tim.