# Dual-modulus Prescaler - The Solution

The Solution

The solution is the dual modulus prescaler. The main divider is split into two parts, the main part N and an additional divider A which is strictly lesser than N. Both dividers are clocked from the output of the dual-modulus prescaler, but only the output of the N divider is fed back to the comparator. Initially, the prescaler is set to divide by M + 1. Both N and A count down until A reaches zero, at which point the prescaler is switched to a division ratio of M. At this point, the divider N has completed A counts. Counting continues until N reaches zero, which is an additional N - A counts. At this point the cycle repeats.

begin{align} &f_o = f_rleft\ Rightarrow &f_o = f_rleft(MN+Aright) end{align}

So while we still have a factor of M being multiplied by N, we can add an additional count, A, which effectively gives us a divider with a fractional part. Only the prescaler needs to be constructed from high-speed parts, and the reference frequency can remain equal to the desired output frequency spacing.

The diagram below shows the elements and arrangement of a frequency synthesizer with dual-modulus prescaler. (Compare with diagram on main synthesizer page).

One can compute A and N from the formulae:

begin{align} N &= leftlfloorfrac{V}{M}rightrfloor\ A &= V - MN end{align}

where V is the combined division ratio V = MN+A. For this to work properly, A must be strictly less than M, as well as less than or equal to N. These restrictions on values of A imply that you can't get every division ratio V. If V falls below M(M - 1), some channels will be missing.