## OPERATING RANGE

4.3.1 Counter.

The operating range can be considered as that range of the measured parameter throughout which the system. indication bears a stated relationship to the true value of the measured parameter, within the boundaries of other constraints on the system such as response time and allowable fractional variation.

The upper end of the range of the counting channel is limited by counting losses in the electro­nic subsystem at high count rates. The properties of the electronic subsystem are discussed in Section VI.

The lower end of the range of the counting channel is limited by the allowable error due to counting statistics coupled with the counting sensitivity of the chamber. For example, if a mini-

_3

mum of 1 count per second is required and the counting sensitivity is 1 x 10 counts per second.

3 .

per nv, then the lower end of the range is 10 nv.

There are other effects that could, in principle, limit the. lower end of the range to a different value than that determined by statistics and counting efficiency, but they are not realized in practice. At higher gamma levels than those normally encountered at startup, gamma-pulse pile-up would be more severe, requiring a higher discriminator setting and hence resulting in a lower counting sensi­tivity than at the normal gamma level. Some examples of this effect are worked out below. The rate, r^, that a pulse pile-up will exceed a certain, amplitude, per Second, is: . (4-10)

(4-11)

where

rate that pulse pile-up exceeds the level Vj-> ,

critical voltage level.(proportional to discriminator setting),

voltage profile of a single pulse at point of interest in system,

n = pulse rate,

"o

f = mean square of spectral distribution of pulse power at point of interest

in system, and

0

a = the variance of the signal.

The above expression assumes background pulses of uniform size which is an approximation, of course; however, an appreciation of the functional dependence is afforded by the above expres­sion.     If the logarithm is taken of Equation (4-10) for the number of positive crossings due to pulse pile-up, the following is obtained: . This expression can be applied to the integral bias curve to obtain

Figure 4-2 is a plot of integral bias data taken at different gamma levels. If the equivalent count rate is plotted on semi-log paper versus the square of the discriminator setting, Figure 4-3 results. From this figure the following is obtained: The slope of each curve, S.

a.

1 (4-13)

(4-14)  ■ •U Figure 4-2. Integral Bias Curves, Detector Assembly No. 1 (Counter) Versus Gamma Flux

2 2 ‘

The terms ct„ and a are obtained from the slopes S — below as: = = — 4.61 (a 2 + a j2)

-1.96 Vе 7 ‘ 1

S2 (з x 106 R/h^ _1* 83  But since

then,

0.111 = о 2 + oy2

and „ 2 ^ 30 „ 2

ae + 7 ayl.

or subtracting 0.008

or

■ Oy 2 = 1.2 X10’3   Thus,

and

a 2 = 0.111 — 0.0012 = 0.110 03S/SINf)00 * J 3iva 3SHld  ІЛ

 Figure 4-3. Count Rate Versus Square of Critical Voltage Level

 4-9 