Page 404 - Instrumentation Reference Book 3E
P. 404
Detectors 387
the bridge current is flowing and the same gas
mixture is in the reference and sample cells. Let
Ro be resistance of filament at ambient tempera-
ture, R1 working resistance (Le., resistance when
a current Z flows), Z current through one filament
(Le., half bridge current), and T wire temperature
above ambient.
Then, at equilibrium, energy input is equal to
heat loss
I~R~ (18.1)
K~
T
=
where K] is a constant proportional to the ther-
mal conductivity of the gas as most of the heat
loss is by conduction through the gas. A simple
expression for the working resistance is
Figure 18.3 Cutawaydrawing of 4-filament diffusion
katharometer cell. R1 = Ro(1 +aTj (18.2)
where cv is the temperature coefficient of resist-
which may be supplied from either a regulated- ance of the filament material. Then, from equa-
voltage or regulated-current power supply. The tions (18.1) and (18.2):
circuit for a constant-voltage detector is shown in
Figure 18.4. The detector is balanced with the Z2R1Roa = Kl(R1 - Ro) (18.3)
same gas in the reference and sample cells. If a
gas of diffe;ent thermal conductivity enters the Then
sample cell, the rate of loss of heat from the
sample filaments is altered, so changing their
temperature and hence resistance. The change in
resistance unbalances the bridge, and the out-of-
balance voltage is recorded as a measure of the
change in gas concentration. The katharometer
can be calibrated by any binary gas mixture, or
for a gas mixture which may be regarded as bin-
ary, e.g., carbon dioxide in air.
A theory of the operation of the katharometer (18.4)
bridge follows. This is simplified but is insuffi-
ciently rigid for calibrations to be calculated.
Small variations in the behavior of individual From equation (18.3), if R1 - Ro is small com-
filaments also mean that each bridge must be pared with R1, then K1 must be large compared
calibrated using mixtures of the gas the instru- with 12Roa and the term Z2Roa can be ignored.
ment is to measure. Then
Assume that the four arms of the bridge (Fig-
ure 18.4) have the same initial resistance Rl when R1 = Ro + (Z2R&/K1 j (18.5)
Figure 18.4 Circuit for 4-filament karharometer cell.