If noise having a Gaussian amplitude distribution is passed through a nonlinear device (3uch as a squaring circuit), and if the resulting. voltage or current is passed through a relatively narrow bandpass filter, the statistical properties of the output voltage or current approximate those of a random noise voltage or currentThese conditions are satisfied by a Campbell system operating at high reactor fluxes, for then the average pulse spacing is much less than the pulse width, ensuring a Gaussian amplitude distribution at the squaring-circuit input; also, since t, the time constant of the averaging circuit after squaring, satisfies the relation

(3-109)

T

the filter after squaring has a relatively narrow bandpass. Hence we can use the expression for the frequency with which a random-noise voltage crosses a given level. This rate of crossing is given^ approximately by

where

rT = rate, per second, at which signal crosses the value ST with positive slope,

. f2 = 1/(2 7T t ) .

<S> = expected value of signal

= Ak<*Qe 2g122 “H2

2 + WL

ST = trip level setting, and

dg2 = variance of signal,

, (Ak»)2 (q6Z12)4 ^h4

4T (“h* “l)3

Neglected in this analysis are the effects of internally generated noise within the subsystem or system components, and the susceptibility of these components to externally generated noise. These effects tend to increase the probability of false trips and, therefore, the results of this analysis will relate to a more stable subsystem or system than can generally be achieved in practice.

The Campbell subsystem covers its range with a linear scale in PERCENT POWER and a 10-position range switch. If the following operating conditions apply:

dnd if the level is allowed to reach 67 percent of the full-scale value, the false trip probability, r™,, will be as tabulated in Table 3-1 for the various ranges (the equivalent neutron flux is based

A. IQ ‘ О

on an assumed subsystem sensitivity of 8. 1 x 10 volts /nv). If the level is allowed to reach only 63 percent of the full-scale value, the false trip probability will be as tabulated in Table 3-2 for the various ranges. From the value of rT (Events/year) in Tables 3-1 and 3-2. it can be seen that the probability of false trip for either operating option is very small. A determination of the variation of r^, as a function of operating level for the most sensitive range and a trip setting of 96 percent of full scale has been made as follows:

Thus, the "one false scram per year" yardstick occurs when the MMSVM is operated at an approximate scale reading of 108 on its most sensitive range. ‘

TABLE 3-2 OPTION 2 ANALYSIS (<S>___ = 63 PERCENT OF FULL SCALE) ——— Шал — _ Operating Range (nv eq’uiv.) Upper Trip Point (nv equiv. ) ,x-—— max <s> . % ^S^max 10"10v2 (sT — <S>) Trip 10”10v2 as 10”12v2 (sT — <S»2 logioX ” n. log1Qe rT = A • X (Events/year) 2„s2 1×108-2. 64×108 None Not Applicable 2.64×108-8. 33X108 lxlO9 1. 95 6. 75 1. 35 13. 15 -52. 9 -22. 9 2. 89X10"15- 9 8. 33xl08-2. 64ХЮ9 3.16xl09 0. 99 21.4 4. 2 21. 1 -195.5 -84.6 2. 89X10"77-6 2. 64xl09-8. ЗЗХЮ9 lxlO10 0. 99 67.5 . 13. 5 66.9 -205 -88.8 2.89X10"81-8 8.33xl09-2. 64X1010 3.16X1010 0.835 214 42 179 -272 -118 2.89X10"111 2.64xlOl0-8. ЗЗхІО10 lxlO11 0.835 675 135 563 -286 -124 2.89×10"117 8.33xl010-2. 64X1011 3.16ХІ011 0.45 111 22 49. 9 -972 -422 2. 89X10’414 2.64xl0n-8.33xl0n lxlO12 0.45 350 70 158 -983 -427 2.89X10"419 8.33×101!-2. 64xl012 3. 16X1012 0.425 1110 220 470 -1100 -476 2. 89X10"468 2.64×1012-8. ЗЗхІО12 lxlO13 0.425 3500 700 1490 -1103 -476 2.89ХІ0"468