# Frequency synthesis, all-digital type

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PLL solutions to the make-me-a-frequency-to-order problem.
a counter-based logic (which gets F_ref / N_one), and phase-lock
to a voltage-controlled oscillator F_vco, with its own divider

F_ref/N_one  = F_vco/N_two

There are reasons to prefer that both N_one and N_two be even
numbers (last stage is a divide-by-two so you get 50% duty cycle
square waves).  There's still a large candidate pool of N_one
and N_two values, though.

So, if  you wanted to trim the frequency up a few parts per million,
how do you select the new N values?  If there's ten bits in the
counters, there's a million ( 2**20) candidates to check to find the best
one...

The only simplification I see, is that one can make a rank 2**10 matrix
of the combinations, and note that the equation we want amounts to:

F_ref * N_two = F_vco * N_one

which is the equation of a straight line in the N_one, N_two
coordinate system, going through (0,0) (which are NOT divisors,
you just have to disallow the divide-by-zero "solution").

There's a well-known algorithm for drawing the best line in such
a two-dimensional array, the Bresenham line-drawing algorithm,
so it's a little better than 2**20 cases to consider; more like 2**10
points that 'fit' that line equation nearly.

Still, its a bit tedious to brute-force search for the best-match ratio; is there
a better way?   And, how does one extend the scheme if there are
fractional-N tricks (pulse swallowing, basically) used for fine tuning?

Re: Frequency synthesis, all-digital type

Continued fractions is a good way to convert a real number to a
ratio of integers.

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