Advanced Frequency Synthesis by Phase Lock

APPENDIX X

SOME TABLES

X.1   ACCUMULATOR SHORTENING

The number of bits in each accumulator is in the first column of Table X.1 and the required value of a_HK (reduction in modulus) is in the second column [Hosseini and Kennedy, 2007, Table II]. The resulting accumulator lengths are shown in Table X.2.

TABLE X.1   Value of a_HK

n0	a
5, 7, 13, 17, 19	1
6, 9, 10, 12, 14, 20, 22, 24	3
8, 18, 25	5
11, 21	9
16, 23	15
15	19

TABLE X.2   Resulting Accumulator Lengths

X.2   SEQUENCE LENGTHS

The sequence length for n-bit accumulators in a p-section MASH-111… configuration is 2^m, where m is given in Table X.3 [Borkowski et al., 2005, Table II], if the initial condition is odd (i.e., LSB is set in the first accumulator).

This also applies to fractions containing a small LSB, 2⁻ⁿ, with no initial setting, since the register (accumulator) is then equivalent to an n-bit register with the LSB set after the first clock. In this case, m ≥ n, since m = n for the first register. None of the bits that are less significant than the nth LSB participate in the operation of the registers under these conditions.

TABLE X.3   Minimum and Maximum Values of m

Advanced Frequency Synthesis by Phase Lock, First Edition. William F. Egan.© 2011 John Wiley & Sons, Inc. Published 2011 by ...