To be suitable for a dynamics test, a control rod must be capable of introducing sufficient reactivity at a suitably fast rate. An estimate of the required magnitude of the reactivity perturbation may be obtained from

the zero-power transfer function for one group of delayed neutrons:

n0dp As(s + P/A)

Feedback effects are usually important for w < P/А. The plateau in the frequency response between w = X and w = /?/Л has a magnitude

dn/n0dp = /P (7.1.2)

In individual cases, the full-power frequency response gain may be smaller or larger than this, but this value is useful for making a rough estimate of the reactivity perturbation needed in the test. Solving for dp (expressed in cents), we obtain

dp (in cents) = (dn/n0) x 100 (7.1.3)

Thus a reactivity perturbation of ~ 1 cent would be used to obtain a power swing of ~ 1 %. The reactivity required in a test will depend on the back­ground noise level and the length of time available for testing. Usually, a power variation of a few per cent will give good results in a reasonably short time and will cause insignificant interference with normal operation. This would require a reactivity perturbation of a few cents. If it is necessary to use smaller reactivity perturbations, the testing time must be increased. For example, if the reactivity perturbation magnitude is decreased by a factor of 10, the testing time would have to be increased by a factor of 100 (see Section 4.9) to obtain the same noise error.