(a) Discussion. Electrical conductivity (see also Sec. 4-9.1) is related to the concentration of total dissolved solids. The purest water is a very poor conductor Pure water has a conductivity approaching very closely the theoretical minimum of approximately 0.05 gmho/cm at 25°C, which is due to the dissociation products of water itself.

(b) Measurement Techniques. Alternating current is generally used in a measuring system because direct current produces progressive changes in concentration near the

electrodes. Also, products of the electrode reactions (with direct current) may set up a voltaic cell and an appreciable back emf. Figure 4.53 shows an a-c Wheatstone bridge circuit for measuring electrical conductivity. In the figure Rx is the resistance of the electrolyte measured between two electrodes of a conductivity cell, R3 and R4 are end resistors whose function is to establish the limits of bridge calibration, and R5 is a calibrated slidewire which does not enter into the arms of the bridge, and therefore variable values cause no error in bridge readings. The condition for balance of the Wheatstone bridge is A/B = Rs/Rx, and this

condition is indicated by no current flow through detector D (a galvanometer or microammeter).

4- 7.8 Specific Weight of Compressed Water

The specific weight of water varies markedly with temperature. The effect of pressure on specific weight is less dramatic but still significant. The curves of Fig. 4.54 illustrate the effects of temperature and pressure on the specific weight (lb/ft3) of water.

The purpose of a cross-spectrum analyzer is to measure the cross spectral density, P(f), of two correlated signals, x(t) and y(t) This is done, one frequency at a time, by integrated multiplication of band-pass-filter outputs, as indicated in Fig 6.17. A comparison of Figs 6 15 and 6 17 shows that this cross-spectrum analyzer is a slight gen­eralization of an ordinary spectrum analyzer using a multiplier as a detector

In some analyzers70 72 tuned-circuit band-pass filters are used In others84 109 the input to the multiplier is the result of passing a modulated pair of signals, x(t) cos (coj t + фх) and y(t) cos (co, t + фу) (constructed by multi plying the signals by oscillator outputs), through a low-pass filter The broken line in Fig 6.17 indicates the ability to control the relative phase in the two modulations at in-phase operation gives the cospectral density, Coxy(f), with 90° between the two signal channels, the output is the quad-spectral density, Quxy(f) Then Eqs 6 6 and 6 7 can be used to determine the cross spectrum, Pxy(f) = Coxy(f) — і Quxy(f)

As in the discussion of the spectrum analyzer (Sec 6-6.2), the major parameters selected by the ex­perimentalist are the frequencies at which Pxy(f) is determined, the frequency resolution, Af (defined in Fig. 6 16), and the analysis time, T. Quantitative criteria for making these selections are given in Sec 6-7

6- 6.4 Digital Spectrum Analysis

In Sec 6-5 5 it was noted that digitizing plus sub­sequent computer analysis can be used as an alternative to continuous-signal analysis The computer programs in use give not only time-domain functions (usually computed first in the program) but also their Fourier transforms, as indicated in Table 6 14. Thus the programs discussed may be regarded as frequency analyzers too

Although not indicated m Figs 6 15 and 6 17, the incoming signal may be “conditioned” before analysis In the continuous analysis this could often consist in filtering out frequencies above and/or below those of interest in the analysis Similarly, in digital analysis it is not only customary to remove any nonzero mean values (і e, d-c components) from the signals but also to do some of the following detrending, і e, removing a linear trend in time, filtering, such as prewhitening, and normalizing signal magnitudes by dividing deviations from the mean by the signal’s standard deviation

Digital filters,11 computer arithmetic operations on the sequential data points of x(t) that have the effect of changing its spectrum, can be used to advantage Thus, in prewhitening, the filter characteristic is modified so that the spectrum is one more nearly like white noise [і e., P(f)

is made to be approximately constant] and more amenable to analysis

Computer programs usually calculate autocorrelation and cross correlation functions from the data and for values of r only up to тт, this value is generally some small fraction (typically 10% or less) of the data duration T in order to secure good accuracy Then the computer Fourier analyzes the correlation functions

1 Reduce or eliminate the unwanted signals at or near their source

2 Increase the desired signal levels

3 Filter the signals, emphasizing frequencies of interest over others

4 Correlate pairs of related signals, as in cross­correlation and cross-spectral analysis

5 Use long durations of data or many repetitions

Px(f) = 2 Cx(t) cos 2nfT dr (6 38)

pxy(f) = fTm Cxy(r) cos 2nfr dr — і f m cxy(r)

‘ " m J rn J

X sin 27rfr dr = Coxy(f) — і Quxy(f) (6 39)

for the spectrum and components of the cross spectrum, respectively Equations 6 38 and 6 39 give spectral values at

fl=J_>fa=_lff3=_L

?r 1 t л 1т m ‘ m ^1 rr

Since these spectral results correspond to the less desirably shaped (sin сотт)/сотт spectral window of Fig 6 16, the so called “hamming filtering” operation is usually performed for final results

P(f) = 0 23P^f + 0 54P(f)

+ 0 23P^f <6 41)

to obtain the more desirable window shown

The environment in which an in core sensor operates is hostile to both the sensor materials and the means of transmitting signals to the readout instruments In most cases the environment includes high neutron flux (>lo’ 2 neutrons enrr2 sec1), intense gamma fields (>108 R/hr), elevated temperature (>500°F or 210°C), and high pressure (>1000 psi), along with other undesirable effects, such as vibration induced by coolant flow or boiling Although it is not reasonable to expect in-core sensors to last through the entire life of the reactor in such a hostile environment, nevertheless the sensors should be designed so they do not require removal or replacement more frequently than once every time the reactor is refueled. Most in-core neutron sensors can last through several refueling cycles.

Another factor in the design of in-core sensors is the space limitation. Power reactors have closely spaced lattices of fuel rods and fuel assemblies; seldom is more than to in. available for installing an in-core sensor. As a result, in-core sensors must be rugged enough to withstand the rigors of the nuclear radiations and the thermal and mechanical environment and small enough to fit in the available space.

At full power the thermal-neutron flux in the core of a power reactor is more than 103 times the out-of-core neutron flux. Typical values are 3 to 5 X K)1 3 neutrons cm 2 sec 1 , with peak values of over 101 4 . Materials used in the construction of in-core neutron sensors must be resistant to neutron damage during the expected lifetime of the sensors. Similarly, the gamma field is more than 103 times that in out-of-core positions, where the exposure rate is usually 3 to 5 X104 R/hr. Heating of the sensor materials by absorption of gamma energy must be considered in both the design and location of the sensor, and adequate cooling must be provided. Damage to the material from gamma exposure must also be taken into account.

The temperature in a power reactor at the location of an in-core neutron sensor is generally determined by the temperature of the reactor coolant at that location. Boiling-water reactors operate at saturated steam conditions that average 550°F (288°C). In some instances where higher pressure is used to extend unit capacity, the temperatures range up to 595°F (313°C). In pressuri/.ed — water reactors the core operating temperatures vary with load and location in the core but seldom fall below 520°F (271°C) or exceed 630°F (332°C). Gas — and sodium-cooled reactors operate at temperatures considerably higher than those in water reactors. Gas-cooled reactor temperatures range from 650°F (343°C) to 1450°F (788°C), depending on load and location in the core, and sodium-cooled reactor temperatures vary from 700°F (370°C) to 1000°F (540°C).

Water reactors characteristically operate at a higher pressure than gas — and sodium-cooled reactors because of the higher vapor pressure of water. Nominal operating pressure for boiling-water reactors is 1000 psi. Some of the early boiling-water reactors were capable of operation up to 1500 psi to obtain increased steam-flow capability at the turbine generator.

Pressurized-water reactors operate at pressures that maintain subcooled conditions in the reactor coolant system. Most pressurized-water reactors operate at 2250 psi. The external sheath or enclosure of an in-core neutron sensor must withstand these pressures without collapsing and must be watertight so moisture cannot degrade the insulation resistance of the sensor and cables. Likewise, the high operating pressure calls for careful design and installation of penetrations through the reactor vessel to preclude coolant leakage to the atmosphere.

In gas-cooled reactors operating pressures vary from 300 to 700 psi, and in sodium-cooled reactors the operating pressures are 200 psi. Pressure does not present as signif­icant a problem in designing in-core neutron sensors and cables and seals for gas — and sodium-cooled reactors as does the high operating temperature.

The velocity of the reactor coolant through the core of pressurized-water reactors averages 15 ft/sec (4.6 m/sec). Bulk boiling takes place in the core of a boiling-water reactor. The dynamic forces resulting from coolant flow and bulk boiling must be factored into the design of in-core sensors.

5- 3.1 Introduction

An intermediate power channel, shown in Fig 5.16, consists of a compensated ionization chamber (CIC), a dual-voltage power supply, a log N unit, and readout equipment Each of these units is discussed below.

5- 3.2 Ionization Chamber and Power Supplies

(a) Sensor. Compensated ionization chambers are used as neutron sensors in the intermediate-range channel. Ionization chambers operate in the mean-current mode as opposed to pulse counting, which is used at lower fluxes (see Chap. 2, Sec 2-2.3). The CIC produces a current proportional to the sum of the neutron and gamma fluxes, but, through a compensation chamber, a current is pro­duced that cancels about 95 to 99% of the gamma current (see Chap. 2, Sec 2-2.2).

(b) Power Supplies. The requirements of the power supplies for the intermediate-range power channels are essentially the same as those described for the start-up channel in Sec. 5-2.6, the only difference is the requirement of the CIC to have both positive and negative voltages. The positive high voltage is 600 to 1000 volts, whereas the negative high-voltage requirement is from 100 to 1600 volts.

High-voltage monitors must be provided to monitor and alarm on loss of positive high voltage These alarms, as described previously, are connected to the shutdown circuits.

5- 3.3 Interconnecting Cables and Grounding

Because the chamber signal generated in the CIC is a current and not a pulse, noise generated in the cable between the chamber and log N amplifier is not nearly so critical as that with a pulse channel Noise pulses are suppressed m the log N amplifier—integrator circuits No electronics are installed near the CIC in the high-radiation area. If cables with high radiation resistance are used, the operating time between cable changes can be increased.

The output signal produced in the CIC varies from about 10 15 to 102 amp Ground loops between the detector and the log N amplifier should be avoided in order to reduce stray signal pickup. The detector is insulated

LEGEND

A TO ANNUNCIATOR, MAIN CONTROL CONSOLE В TO ANNUNCIATOR, NUCLEAR PANEL

1 RELAY TRIP, FUEL-HANDLING SHUTDOWN CIRCUIT (SOURCE FLUX LEVEL, LOW)

2 RELAY TRIP, FUEL-HANDLING SHUTDOWN CIRCUIT (LOG COUNT RATE LEVEL, HIGH)

3 RELAY TRIP, FUEL-HANDLING SHUTDOWN CIRCUIT (PERIOD, SHORT)

4 RELAY TRIP, FUEL-HANDLING SHUTDOWN CIRCUIT (FISSION-CHAMBER VOLTAGE, LOW)

5 RELAY TRIP, OPERATING SHUTDOWN CIRCUIT (PERIOD, SHORT)

6 RELAY TRIP. OPERATING SHUTDOWN CIRCUIT (FISSION-CHAMBER VOLTAGE, LOW)

Fig. 5.15 — Block diagram of source

range channels 1,2, and 3

INSTRUMENT CONTROL CENTER NO
4
В TO ANNUNCIATOR, NUCLEAR PANEL 1 RELAY TRIP, OPERATING SHUTDOWN CIRCUIT (PERIOD, SHORTI 2 RELAY TRIP, OPERATING SHUTDOWN CIRCUIT (ION-CHAMBER VOLTAGE, LOW)

Fig. 5.16—Block diagram of intermediate-range channels 4, 5, and 6.

from the detector thimble by ceramic standoff insulators, which are impervious to radiation damage. The shields of the coaxial cables are connected to the chassis, which should be grounded to nuclear instrumentation ground at one point, effectively reducing or eliminating the ground loops (see Chap. 10).

The basic kinetic equations, Eqs. 1.7 and 1.8, can be solved for constant к (e. g., following a step change in reactivity). The neutron density as a function of time is:

m+1

n= £ Aje CJjt (1.10)

H J

where the values of Aj are determined by the initial values (at t = 0) n0 and C;0, and where the values of coj are the m + 1 roots of the equation:

The (3; and Aj are the delayed neutron fractions and decay- constants for the m groups of delayed-neutron emitters.

The roots of со in Eq. 1.11 have the following proper­ties: For p = constant > 0, nt roots are negative and 1 is positive. The m negative roots are approximately —A! , —A2, . . ., — Am, the decay constants of the delayed-neutron emitters. P’or p = constant < 0, all m + 1 roots are negative.

Thus, for constant positive values of the reactivity, the neutron density is the sum of one positive exponential and m negative exponentials. After an interval of time large — compared to the delayed-neutron periods, the positive exponential remains

n = п0еы"‘ = n0c 7 (1.12)

The quantity T (= l/co0) is the stable reactor period or asymptotic period, and l/0Ji, l/cu2, . . ., l/cjm are the transient periods. Figure 1.1 shows the stable and transient periods vs. reactivity for 2 3 5 U with the prompt-neutron lifetime as a parameter. Note that for 5k small and positive the stable period is independent of / (for / < 10 3 see); in fact, T is approximately //5k where 1 = 1 + rav and rav is the average decay period of the delayed-neutron emitters, Tav = (l/(3)Z(ft/A;). The quantity! is the effective neutron lifetime. Figure 1.1 also shows that for large 5k the stable period is approximately //5k.

The relation between the reactivity and the stable reactor period is obtained by substituting 1/T for to0 in Eq. 1.11,

ft

1 + TAj

This is the inhour equation. Reactivity can be expressed in “inverse hours” or “inhours,” where 1 inhour is defined as the amount of reactivity that makes the stable reactor period equal to 1 hr. Substituting T = 3600 sec and the values of /3; and A; from Table 1.1 and noting that //T ^ З X 10 6 , we find the following:

1 inhour?2.4 X 10 s for a 2 3 5 U-fueled thermal reactor 5l X 10 5 for a 2 3 9 Pu-fueled thermal reactor ^ 1.4 X 10 s for a 2 3 3 U-fucled thermal reactor.

The inhour equation is shown graphically in Figs. 1.2, 1.3 and 1.4, where the reactivity is plotted against the stable — period for various values of / and for various isotopes of uranium and plutonium.

An in-line sensor or a tap to an adjacent mounted sensor must be located in a position where errors due to local disturbances, such as turbulence and vibration created by the process or adjacent machinery, are avoided For accuracy in lower pressure ranges, the sensor should include provisions for compensating for the weight of liquid in connecting lines so that the transmitted or observed pressure is that in the main piping or containment

An ANSI Piping Code recommends that the pressure take-off size not be less than %-in. pipe for operating up to
900 psi and 800°h and not less than %-in. pipe above these values. An acceptable method for installing a take-off is to weld a Weld-O-let or similar adapter to the main pipe or vessel and then drill through the adapter and pipe or vessel wall а ‘Д-іп.-diameter hole (or larger if desired) to produce a sharp clean edge at the inner wall. Actual si/e of the hole should be large enough to avoid plugging. Alignment of the axis of the opening should be perpendicular to the direction of flow to avoid false pressure readings due to impact velocity effects. Material specification and controls should comply with ASME Nuclear Piping Systems of proper class 1, 2, or 3.

The pressure sensor is mounted adjacent to the take-off in such a way as to reduce transmission of piping — or vessel-expansion strains, process heat, or system vibrations to the sensor mechanism Figure 4.22 illustrates a common

installation practice featuring y2-in.-O. D. tubing or equiva­lent pipe pitched to facilitate draining and maintenance. Full support of connecting tubing is recommended, un­supported tubing must take a lower pressure rating. Root valves at take-offs must be the same sue as the take-off. Above 900 psi and 800° F, the take-off may be swaged or reduced to allow a У2-іп. root valve, but the size at the main piping or vessel may not be reduced. Blow-down valves for drain must be at least У8-іп. pipe size. Instrument shut-off valves may be V4-in. pipe size and threaded to match standard instrument casing connections, this latter practice facilitates disassembly and routine maintenance and calibra­tion.

Measuring the dynamic characteristics of power reactors is commonly accepted to be an integral part of testing during reactor commissioning. Transient response to ex­ternally induced system changes is perhaps the most popular category of such tests. However, transfer-function and noise-spectrum measurements are also common It is not unusual for the latter to be required by AEC licensing in the interest of safety.743 The incentive for transfer — function and noise testing usually stems from the desire for a more detailed knowledge than is possible from the transient tests.

The possibility that the denominator of Eq. 6.18 will approach zero and result in an unstable oscillatory system is one important reason for measuring and understanding G(s). On the other hand, for reactors known to be quite stable, measurements of G(s) can give H(s) if Eq 6.18 is
used. The term H(s) gives information about reactor and plant parameters, such as the constants in Eq 6 17

Transfer-function measurements in power reactors are not restricted to rod-oscillator tests. The next section shows that a considerable variety of methods involving variables other than just reactivity and power are used Table 6.7, listing the many power-reactor transfer-function and related spectral-analysis experiments, gives an idea of the wide applicability of the techniques given in Table 6 8

In power-reactor dynamics it is often desirable to know transfer functions among a variety of variables, not neces­sarily just between reactivity and power. Thus it is not uncommon to simultaneously measure a number of transfer functions, or spectral-density functions, by simultaneously measuring pairs of system variables over a period of time In the experiments listed in Table 6 8, the primary interest is

usually in the neutron-flux fluctuations, but other fluctua­tion variables have also been analyzed, namely, pressure, flow, acoustical noise, temperature, gamma flux, valve position, and pump speed. These, along with the reactivity and power, represent principal variables of interest in dynamics analyses.

A counter is an ionization chamber designed to de liver a current pulse for each ionizing event 1718 A number of features are common with those of the more general ionization chamber In fact, superficially, chambers designed for the current and counting modes are mdis tinguishable There are commercial chambers designed to perform in both the current and counting modes, which, if the application is not demanding, can serve as well as a detector limited to a single mode

The difference stems from basic differences in the signal, і e, a pulse vs direct current. For large pulses that are easily distinguishable from one another, the ionization of each ionizing event must be collected quickly This is accomplished by careful design In, addition, the gas fill of

the chamber must be selected to maximize electron mobility There are a number of gas mixtures that are better in this respect than pure inert gases A high performance counter would use one of these gas mixtures

Because the signal is a pulse, the insulation quality of the chamber is not as critical The pulse height depends primarily on the capacitance, C, and resistance, R, of the system in which the counter is used Thus, if the time constant, RC, of the output circuit is 100 or more times the pulse rise time, negligible attenuation occurs Since a typical installation might have a capacitance of 2000 pF, a counter with a pulse rise of 0 2 ptsec requires an output resistance of only 10,000 ohms to meet this test The insulation resistance then needs to be 106 ohms or more for satisfactory performance, a criterion that is easily met The faster the pulse rise, the less a high resistance is required If an electronic amplifier is introduced, the analysis is somewhat different from the above, however, the result is similar

In a counter the internal structure is given particular attention Capacitance is minimized (see Fig 2 4) The distances between electrodes is optimized to the range of the ionizing event Since discrimination between unwanted ionization events is usually required, some of the theo­retical pulse height may be sacrificed for this end

Practical counting rates are determined by the pulse rise time If some resolution loss can be tolerated, say less than 10%, the maximum counting rate would be about 1/IOt, where r is the rise time In a counter with a 0 2-qsec rise time, this corresponds to 5 X 105 counts/sec, a typical counting rate

The lower limit on counting rates is not a function of the counter structure but of the radiation background in which the counter is placed and of the electronic dis crimination However, because of poor statistics, it is not good practice to rely on counting rates of less than 1 count/sec A state-of-the-art fission counter is good for five and a half decades in a gamma field of 10s R/hr with only small losses in counting efficiency In general, higher gamma fields can be tolerated if losses in efficiency are acceptable The trend is to develop counters with faster rise times and with corresponding improvements in maximum counting rate and gamma tolerance

The use of a counter is somewhat more involved than the use of an ionization chamber Not only must the counter be operated on a voltage plateau, but counts from the desired events must be separated from counts at tributable to undesired events Figure 2 12 shows how this is done with a pulse height discriminator

Pulse height discrimination is one of the simpler methods of separating wanted pulses from unwanted pulses It has found many applications in reactor start up systems and is easiest to apply when the wanted pulses are larger than the unwanted pulses The usual way of determining the effectiveness of a counter and of the counting svstem is by an integral bias curve The discriminator setting corre sponds to the number of counts, expressed in counts per second, of greater pulse amplitude In practice, only a single curve is measured Figure 2 12, however, has been con structed by measuring alpha and gamma curves in the absence of neutrons An arrangement such as that shown in Fig 2 13 can be used to measure these curves A knowledge of the integral bias curves is indispensable in selecting and using a fission counter

With a knowledge of the gamma background, possibly by measuring the integral bias curve, one can select the operating point to eliminate any desired function of the

unwanted counts There is, of course, a corresponding loss of efficiency since the neutron integral bias curve has a slope This loss of efficiency is so well known that it is commonly equated with gamma discrimination Ideally, and in some radiation detecting instruments, this is nearly the case, the wanted counts form a horizontal line (zero slope) In this ideal situation there is no loss of efficiency One way to approach this ideal is to use a thin coating of sensitive material Figure 2 14 shows the effect of sensitive material thickness on discriminator response It is seen that very thm films do approach the ideal

Unless the chamber size were increased (with a con sequent increase in gamma sensitivity) a great loss in sensitivity would occur if very thin films were used Thus, most practical designs favor a thicker film of sensitive material, typically 1 to 2 mg/cm2, as a workable com promise The very thin films, however, are advantageous if absolute measurements must be made

4-8.1 Humidity and Dew Point

(a) Definitions. Absolute Humidity. The number of pounds of water vapor in one pound of dry air.

Relative Humidity. The ratio, usually expressed as a percentage, of the partial pressure of water vapor in the actual atmosphere to the vapor pressure of water at the prevailing temperature.

Percentage Humidity. The quotient of the number of pounds of water vapor carried by 1 lb of dry air divided by the number of pounds of water vapor which 1 lb of dry air would carry if it were completely saturated at the same temperature, multiplied by 100.

Dew Point. The temperature at which a given mixture of air and water vapor is saturated with water vapor.

Dry-Bulb Temperature. The temperature of an atmo­sphere. The qualification “dry-bulb” is used to distinguish the normal temperature measurement from the temperature measured by the wet bulb.

Wet-Bulb Temperature. The dynamic equilibrium tem­perature attained when the wetted surface of an object of small mass (bulb of a thermometer) is exposed to an air stream. Evaporation of water causes cooling, which is counterbalanced by heat absorbed from the air.

(b) Measurement Methods. Condensation. The sur­face in contact with the atmosphere is cooled until condensate (dew) appears. A variation of this method is to cool a sample by adiabatic expansion so that condensation appears as a fog. The expansion ratio to produce a fog and the initial temperature allow calculation of the dew point.

Dimensional Change. Most organic materials change dimensionally with changing humidity. A typical instru­ment uses human hair arranged so its expansion with increasing humidity actuates a mechanism. For many materials the expansion is, to a close approximation, a linear function of the relative humidity. Animal mem­branes, wood, and paper have also been used to sense relative humidity.

Thermodynamic Equilibrium (Wet-Bulb Thermome­ter). The bulb of a thermometer is wrapped in a cloth wick that is kept wet with water. The wrapped bulb is exposed to an air stream, and the temperature observed is the wet-bulb temperature. This reading, in combination with a reading of the air temperature (dry-bulb tempera­ture) is a measure of the moisture content of the air. Variations of this basic design use ceramic sleeves instead of cloth wicks. In one design, the wick is eliminated, and the temperature of the air stream is measured after cooling by saturation from a water spray. The basic design is known as a wet — and dry-bulk psychrometer. A sling psychrometer has glass thermometers in a frame designed to be swung through the air rapidly to secure sufficient air velocity.

64.0
57.0
50 100 150 200 250 300 350 TEMPERATURE, °F 50.0
PRESSURE, psi 6000 5000 4000 3000
48.0
C3 45.0
44.0
43.0
40.0
300 350 400 450 500 550 TEMPERATURE, °F

Fig. 4.54—Effects of temperature and pressure on the specific weight of water. (Courtesy Bailey Meter Company.)

Absorption (Gravimetric). A measured volume of air is passed through a water-absorbing material, such as phos­phorous pentoxide. The gain in weight of the absorbent is the moisture content of the known volume of air. In a variant of this technique, the change in pressure when the absorbent is brought into contact with air in a sealed vessel is measured.

Absorption (Conductivity). The amount of water ab­sorbed by a quantity of a hygroscopic salt varies with temperature and humidity. The absorption changes the electrical conductivity between two electrodes in contact with the salt. The conductivity, when corrected for temperature, usually automatically, can be interpreted as relative humidity. An on-line sensor and readout is com­mercially available using the technique of surface conduc­tivity measurement of an inert non-conductor at or near the dew point. An intermeshed grid embedded in the surface of a nonporous epoxy-filled glass cloth exhibits a specific
resistivity at a given ambient moisture concentration and temperature. Sensor surface temperature is measured by a thermocouple embedded in the sensor surface

Electrolysis. The moisture in a measured flow of air is absorbed by phosphorous pentoxide and simultaneously decomposed by electrolysis. By Faraday’s law, the electro­lytic current is directly proportional to the rate of decomposition of water and hence to the moisture content of the air.

Heat of Absorption. The absorption of water vapor on a solid absorbent releases heat. A measurement of tempera­ture change when water vapor is alternately absorbed and desorbed is interpreted as moisture content.

Vapor Equilibrium. A saturated solution of a hygro­scopic salt is maintained at the temperature at which it is in vapor-pressure equilibrium with the atmosphere. The tem­perature of the salt converts directly to dew-point tempera­ture. Conductivity of the solution is used to control heating and to maintain the equilibrium temperature.

Absorption (Infrared) Water vapor and most other compounds absorb radiation in certain portions of the infrared region. A measurement of the infrared absorption can be interpreted in terms of moisture content.

6- 7,1 Error Sources

When the transfer function, G(f), between x(t) and y(t) is measured, the transducers of the signals to the analyzer may have a frequency dependence In addition, the analyzer may have a transfer function of its own, e g, if its amplifier gams are frequency dependent As a consequence significant corrections may have to be applied to transfer function measurements to obtain the ideal function desired Calibration, using known sinusoidal amplitudes or white noise generators, is frequently necessary

Unwanted signals, such as random noise (as from instrumentation or a digitizing process) or periodic signals (as in 60-Hz hum), are usually introduced by the devices measuring a system Moreover, the system itself may mix unwanted signals with the signals observed at the transducer inputs Since all these effects influence accuracy, they must be eliminated or lessened Some techniques for coping with the problem are

6- 7.2 Frequency Limits

There are three important frequencies in a transfer function or spectrum measurement the highest frequency of interest (fmax)> the lowest frequency of interest (fmin), and the resolution (Af)

Regarding fmax, it is not unusual for a characteristic of an instrument transfer function or excitation device to be such that there is considerable attenuation of frequencies above some particular frequency value If the frequency content is significant above the maximum frequency of physical importance, then the higher frequencies are usually attenuated by a low pass electronic (or digital) filter The electronic filter is designed to give an attenuation of 3 db or more at frequencies of 2fmax and above The digital filter selects the digitizing time interval, At, such that

2fmax = fN = 42)

where fjsf is the so called “Nyquist frequency” which sets an upper limit m digital analysis

The lowest frequency measured, fmin» is usually con siderably greater than 1/T, where T is the duration of the measurement, consequently the measurement is effectively averaged over many cycles (An exception to this is sinusoidal excitation at fmin with an amplitude well in excess of system noise levels, the duration of the measure ment may be kept as small as l/fmin in this case ) Usually a high pass filter is used to prevent frequencies below fmin from entering the analyzer

Reference has already been made to the resolution Af in Eq 6 37 and Fig 6 16 Continuous spectra are averaged over Af In excitation with discrete frequencies, the interval between frequencies is effectively the resolution The value of Af is usually selected to be just small enough to obtain the detail required in the spectrum Too small a value is disadvantageous from the standpoint of accuracy, as is seen in Table 6 16 Two common situations affecting a choice of Af are

1 The gross variation of a nonresonant spectrum over a few decades of frequencies is desired, m which case Af can be as large as a half to one octave, thus giving about 3 to 5 points per decade of frequency

2 The details of a resonant peak in the spectrum are desired, in which case Af must be somewhat less than the width of the peak to obtain several points across the peak

Table 6.16—Statistical Errors of Correlation and Spectral Measurements1 1 зС
Expressed in Terms of Signal Bandwidth (B), Duration of Data (T),
and Resolution of Analyzer (Af)

Function (computed from Standard deviation of function Condition of x and у having zero means) Function applicability

Cospectrum or quad-spectrum _______________ .

(T Af)H [16]