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4.6 Sinusoidal reactivity and frequency response 45
Comparisons of frequency response results for a model with six precursor groups
and one with a single precursor group provide a means to identify an effective
1-group precursor decay constant that causes the best agreement between the six-
group model and the one-group model. Fig. 4.11 shows such a comparison for an
1
effective one-group decay constant of 0.08 s .
The magnitudes for the two models are in good agreement except for small dif-
ferences for frequencies between 0.01 and 1 rad/s. The phase differences are
more apparent, showing differences between 0.001 and 10 rad/s. The agreement
for a one-delay group decay constant of 0.08 s 1 is about as good as possible.
10 3
1 precursor group
6 precursor groups
10 2
10 1
%power/cent 10 0
10 −1
10 −2
10 −3
10 −4 10 −2 10 0 10 2 10 4
(A) Frequency (rad/s)
0
1 precursor group
6 precursor groups
−20
Phase (deg) −40
−60
−80
10 −4 10 −2 10 0 10 2 10 4
(B) Frequency (rad/s)
FIG. 4.11
(A) Comparison of frequency response magnitudes for one delayed neutron precursor group
and six delayed neutron precursor groups. (B) Comparison of frequency response phase
angles for one delayed neutron precursor group and six delayed neutron precursor groups.
