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.
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