Теплый пол
28 ноября, 2020
If the flux is constant for t < о and differs from this constant value by 0(t) for t> o; i. e.,
ф(0 = фо 
for t<0 

ф(0 = ф0 + 0(t) 
for t>o, 
(347) 
then the expected value of the signal from an ac system is, from Equations (338) and (347),
/• со
<S(t> = АкФ0 I v2(x) dx •’o
At the input to the integrating circuit the expected value of voltage is, from Equations (339) and (347), ■ ■
ф (tx)v2(x)dx
(349)
The application of Equation (348) to an actual case is usually quite difficult, leading to a large quantity of algebraic manipulation during which mistakes are very probable. An alternative method, that lends itself to some approximation and considerable simplification, is as follows.
Equation (349) is used to obtain the expected value of voltage at the input to the integrating circuit. This expression is replaced by a simpler one that should give essentially the same output; a knowledge of the properties of integrating circuits is useful here. This simpler expression is then vised as the driving function in the differential Equation (32) of the integrating circuit to obtain the expected value of the signal, <S(t)> . Examples of this procedure are included in Subsection 3. 2. If an exact answer is desired, use either Equation (348), or Equations (349) and (32) with no approximations.
5. 2. 1 Required Bandwidth
The required bandwidth of the subsystem is dependent upon the bandwidth of the information to be processed. The shape of the information pulse that is available from both the incore and the outofcore detectors has been described previously. The expression given was:
І = 
0 d ( 1 — — amperes, T T / 

where 
Po = 
charge of either sign/unit length of track in the gas 1 — oul  , cm / 
d = 
gas gap (cm), 

T = 
transit time of the electron or positive ion across the gas gap (seconds), and 

t = 
time after pulse initiation (seconds). 
In the above expression, the time required to accelerate the ion pairs to their average drift velocity is assumed to be negligible. This information pulse is applied to the interconnecting cable for transmission to the remote amplifier input.
In the outofcore subsystem, the interconnecting cable is modified RG6A/U coaxial cable. Because of the almost ideal transmission characteristics of the RG6A/U cable (attenuation/100 ft = 2. 9 dB at 100 Me), the information pulse is transmitted to the amplifier input essentially unchanged in shape. For the incore subsystem, the interconnecting cable is 40 feet of stainless steel — quartz — stainless steel prototype incore cable in addition to the RG6A/U mentioned above. The transmission characteristics of the prototype incore cable are far from ideal. * The attenuation
For an experimental comparison of these cables, see Section V.
per 100 feet of the prototype incore cable is, typically, 6 dB/100 ft at 22 Me. This high frequency attenuation causes an increase in the rise time of the information pulse from on the order of 10 nsec to 0. 15 psec. The upper and lower frequency breakpoints of the electronic subsystem are made to conform to the requirements of this information pulse.
Though the spurious signals arising from gamma and alpha pulses are not rejected by
/
amplitude discrimination, they are effectively suppressed, since the response is proportional to
the square of the pulse amplitude. However, the MSV gamma signal does exceed the electronic
noise level, and is the predominant source of spurious signal in the system at high gamma levels.
Shown in Figure 44 is the gamma contribution to the MSV signal level at a measured gamma flux
level of 3 x 10° R/h and the projected level at 2.5 x 10 R/h. Also shown in this figure is the
3 1 1
counting channel output at a counting sensitivity of 0. 67 x 10 sec nv.
Figure 44. MMSVM Neutron Flux Threshold
The local amplifier serves three functions:
a. It provides a characteristic impedance termination for the signal cable from the remote amplifier,
b. It provides additional gain for driving the squaring circuit, and
c. It contains the attenuation networks necessary to divide the six decades of flux coverage into twelve ranges. Its gain is nominally 50, but it is adjustable over a ±30 percent range from its nominal value.
7. 1. 3 Inverter
The inverter is a unity gain amplifier whose function is to receive the signal from the local amplifier and provide two outputs to the mean square analog, one output 180 degrees out of phase with the other.
7.1. 4 Mean Square Analog
The mean square analog is a piecewise linear circuit whose output current varies as the square of the input voltage. By passing the current through a 10, 000ohm resistor, a voltage is obtained that is fed to a unity gain dc amplifier which provides the readout signal and operates the trips. A capacitor in parallel with the IQ, 000ohm resistor controls the averaging time constant of the system. .
This section contains a discussion on some of the properties of a counting channel comprising a detector, logarithmic countrate meter, and period meter. The properties considered are:
a. Variance of the countrate indication,
‘ b. Probability of false trip from the countrate indication,
c. Variance of the period indication, and
d. Probability of false trip from the period indication.
The derivations are based on the assumption of constant average counting rate (infinite period), but the results should be valid for finite periods greater than the longest timeconstant in the system.
2. 1 VARIANCE OF THE COUNTRATE INDICATION
The logarithmic countrate meter considered is of the multiplediode pump type (Cooke^ Yarborough), of which one section is delineated in Figure 21, and in which R is the same for
Figure 21. One Section of MultipleDiode Pump Type of Log CountRate Meter
each section, C^/C ^ is the same for each section, and of any section is — Jq ^f °* preceding section. That is,
(Rcf)k = 10(RC()(k+D
and
(RCT)k — 10(RCT)(k,
where к is the section number and starts at 1 for the section with the lowest frequency breakpoint. All sections of the multiple pump are driven from the output of a scaleoftwo circuit.
Let the average counting rate, r, at the input of the scaleoftwo be such that the output of the k— diode pump is onehalf of its saturation value; i. e.,






Then individual pulses from the (k1)^, k—, and (k +l)^ pumps are






and






respectively, where Tk ^ ^RCf]k, тк = (RCjk , and V is the voltage swing of the output of the scaleoftwo. To obtain these expressions, note that the charge delivered to C, each time the scaleoftwo output swings in the positive direction, is
R (1 + 0. 5 rT)
and this charge leaks off through R with a timerconstant, r, hence,
» . VT—eVr.
t (1 + 0.5 ГТ) ‘
By combining Equation (27) with the relations,
. 05 r T(k_ 1} » 1 ,
0. 5 r Tk. = 1 ,
, . 0 5 rT(k+ 1) <<1 ’
Equations (24), (25), and (26) are obtained.
Now rewrite Equations (24), (25), and (26) as
An individual pulse from the log countrate meter is a fraction, A, of the sum of these three pulses:
AvfeV (213)
(Actually, the total pulse is a fraction of the sum of the outputs of all of the individual sections; however, the terms below (к — 1) and above (k+ 1) contribute an insignificant amount of energy to the total pulse and can be neglected. )
2
Now the variance, a„ , of a voltage, S, that consists of a linear superposition of randomly •Э (11
arriving pulses of the form v (t) and an average arrival rate of 0. 5 r is given by’ ‘
(Equation (214) is true for pulses whose arrival satisfies Poisson’s distribution; pulses from a scaleoftwo do not. However, it is shown in Appendix A that the variance obtained by the use of Equation (214) is in error by less than a factor of 2 and is on the large side.) Substitution of Equation (213) into Equation (214) yields the variance,
and this can be combined with Equation (23a) to obtain
The average voltage from one diode pump is given by
0. 5 r VTt 1+ 0. 5 r Tt ’
It should be remembered that the manner in which Equation (218) was obtained imposes the following restrictions:
a. It is valid when the counting rate is such that the k— pump is half saturated,
b. It is approximately valid for noninteger values of k,
c. It is too large by a factor less than /2 because of the slight regularity in the output of the scaleoftwo, and
d. It is invalid for к = 1 or к = N (where N is the number of pumps in the circuit).
For к = N (high count rate, N— pump half saturated, all other pumps saturated), the
standard deviation is
The average output voltage is
S
and the fractional standard deviation is
This expression is subject to restriction c. of the preceding paragraph.
The characteristics of the two cables are compared with each other, and with some representative types of standard coaxial cabies.
5. 2. 3.1 NickelClad Copper — Quartz — Stainless Steel Cable
With a 21rfoot length of this cable, a determination of the attenuation characteristics versus frequency was made (see Figure 51). It is shown in this illustration that the cable starts to attenuate at approximately 200 kc/sec, and exhibits a 3 dB attenuation at a frequency of approximately 1. 4 Mc/sec. The attenuation then falls with a continually increasing negative slope, and has an attenuation factor of 57 dB at a frequency of 100 Mc/sec.
The transient pulse characteristics of this cable were investigated by inserting a pulse with a 1 msec width at the sending end of the cable, and determining the rise time of the pulse at the receiving bnd of the cable. Figure 52 shows these response characteristics. Note that the rise time of the pulse at the receiving end of this cable is 0. 312 psec, with a sending end pulse rise time of 14 nsec (uncorrected)[6] or 7. 7 nsec (corrected). If the cable is considered a single time constant system, the upper 3 dB frequency is determined as
f = = Ml x 10+6 = L із Mc/SeC. .
7 r 031
The range of the outofcore Campbell system is < 1 x 10^ to 1 x 101^ nv (see Figure 821).
Gamma may limit the minimum measurable neutron flux in some applications. The detector can
be used to 300°C, and is limited because it is made with aluminum. A titanium detector of
similar design could be used; it would operate up to 1000°F (tested) and beyond (untested). The 19
specified life is 10 nvt. The same Campbell channel electronics is used as in the incore system, with the exception of the polarizing voltage supply (the larger detector requires higher voltage).
■v I
VT* 
APPENDIX
To apply the above general results, it is necessary to obtain an expression for the pulse generated at the amplifier uulput by the detection of a single neutron, and this can be derived from the energy spectral density of the pulse or from a knowledge of the time constants of the circuit.
For example, consider a system whose linear portion (cable plus amplifier) has a single lowfrequency break at шa single highfreauency break at and a midfrequency
transfer impedance of Z^, and whose detector is a neutronsensitive ion chamber. The energy
spectral density of a current pulse from the detector is flat and eaual to Qe / я between the angular frequencies 2 я/Tj and я/Те, where Qg is the product of the fraction of the chamber potential through which the electrons travel and the total charge of one sign released in the chamber by the detection of one neutron, T is the ion collection time, and is the electron collection time. So if ^>2я/Т4 and и:ц<тт/Те (see Figure 32), the energy spectral density of v(t) is the product of Qe2/W and the square of the absolute value of the transfer function of the linear portion of the system:
Qe2zi22 “2/wL2
E(u>, v) = , (350)
and the pulse itself is given by
This expression for v(t) can be used in any of the preceding equations.
The bandwidth of the electronic subsystem is a function of the circuit components, and is defined in the following manner: The lower halfpower frequency is defined as the lower frequency at which the current gain of the subsystem is down to 70. 7 percent of the midband value; the upper halfpower frequency is defined as the upper frequency at which the current gain of the subsystem is down to 70. 7 percent of the midband value. The bandwidth is defined as the difference of the upper halfpower frequency and the lower halfpower frequency. The lower halfpower frequency is determined by the equation:
2* RL CC
where
f j = lower halfpower frequency in cps Rl = load resistance of a stage in ohms, and
= coupling capacitance to this load resistance in farads.
These components are the same components as those which provide the appropriate RC clipping. The minimum RC clipping time that can be used is determined by the characteristics of the leading edge of the information pulse. In general, in order to restrict the losses of pulse height in an RC clipping circuit to the order of 25 percent of the peak input pulse or less,, the clipping time must be at least ten times the rise time of the information pulse. As described earlier, the rise time of the slowest information pulse (the pulse from the incore detector assembly) is approximately 0. 15 psec. It is therefore necessary that the clipping time be not less than 1. 5 psec to keep the loss in height to 25 percent. A clipping time of 2 psec was selected. This results in a calculated lower halfpower frequency of approximately 21 kc/sec in the first stage of the remote amplifier and in the first stage of the discriminator.
The upper halfpower frequency is determined by the highfrequency components or characteristics of the circuitry. These components and characteristics are, in general, the parallel interstage resistance, the shunt capacitance, and the frequency characteristics of the active devices used. On the basis of the parallel resistance and shunt capacitance, including the stray capacity, the upper halfpower point will be in the region of 15 Mc/sec to 30 Mc/sec.
Considering a single stage with the type of transistor used in the amplifier stage of the
subsystem, the upper halfpower frequency due to beta falloff will be 7 Mc/sec minimum.
With five similar stages, the upper halfpower point will be reduced by the additional breaks, and
(71
as described in Petit and McWhorter, ‘ ’ the new upper halfpower frequency f’2 is given by
f2 — 
0. 833 f2 yflT 

where 
f2 = 
singlestage upper power halffrequency, and 
n = 
number of identical stages, 

and 
f2 “ 
(0.833) (7) = 2 5 Mc/sec 2. 29 
6.2.3 
Actual Measured Bandwidth 

An experimental determination of the frequency response characteristics of the amplifier is shown in Figure 61. This response curve indicates an experimental lower halfpower frequency of 35 kc/sec and an experimental upper halfpower frequency of 3. 1 Mc/sec. 
4. 4.1 Measured Sensitivities
The following sensitivities are obtained directly from measured signal and flux levels. The units for dc sensitivity are the usual. The counting sensitivity is given for three values of gamma flux background.
a. DC Sensitivity
DC Sensitivity (Neutron) DC Sensitivity (Gamma)
Counter 
1. 9 x 
10 a 
= 2. 9 x 10"16 a/nv 
9. 
4 x 10" a ■ ■ 
= 3. 2 x 10"13 a/R/h 
No. 1 
6. 6 x 
109 nv 
2. 
9 x 106 R/h 

Counter 
1. 9 x 
10"6 a 
= 2. 9 x 10"16 a/nv 
1. 
2 x 10"6 a 
= 4. 1 x 10"13 a/R/h 
No. 2 
6. 6 x 
10‘9nv 
2. 
9 x 106 R/h 
Counter 1 00 x 104 cps = L52xl0’3 1.22 >: 106 cps = 0. 68 x 10’3
No — 1 6.6 x 106 nv 1.80 > 109 nv
Discriminator setting = 3.5 (arbitrary scale), 40 feet of 50ohm incore cable, 85 feet of standard 75ohm cable (RG6A/U) terminated in 75 ohms.
18[3] 
18* 
•19* 
18* 
19** 
c. Mean Square Outputs of Detector Assemblies
OutOf — Core Chamber NA04
NOTE 1. The mean square output/cycle below breakpoint
2
due to ionic mobility in the < V > distribution curve of the ion produced signal is fourtimes that above the breakpoint. All sensitivities quoted are below this breakpoint.
NOTE 2. The fraction of the applied field through which the charge falls is about onehalf if only electron motion is contributing to the signal; i. e., if the bandpass of the circuit lies above the breakpoint due to ion transit time in the power spectral density curve. It is unity if both electron and ion motion contribute to the signal; i. e., if the bandpass of the circuit lies below the breakpoint due to ion transit time in the power spectral density curve. .