Section 3
3-4
Theory of Operation
The factory calibration of the analyzer consists of measuring the output V at
several gas concentrations, and determining the coefficients for a fifth order
polynomial (H
2
O uses a third order polynomial) F(V) that relates V to gas
concentration, with a zero gas concentration in the reference cell.
F(V) = a
1
V + a
2
V
2
+ a
3
V
3
+ a
4
V
4
+ a
5
V
5
3-3
Coefficients a
1
thru a
5
are factory-determined for the specific gas, and are
unique to each analyzer.
The calibration function F(V) is only valid for the
temperature and pressure at which it was determined, and a zero gas
concentration in the reference cell.
It has been found empirically that
(absolute) temperature affects the gas concentration in a linear fashion, while
pressure affects the signal output V in a linear fashion. Therefore, the
expression relating signal output to gas concentration with a zero gas
concentration in the reference cell (absolute mode) is
C
F V
P
P
T
T
o
o
=
3-4
where P is barometric pressure in the cell (kPa), P
o
is standard barometric
pressure (101.3 kPa), T is IRGA temperature (
°
C or
°
K), and T
o
is IRGA
calibration temperature (
°
C or
°
K).
The situation is a little more complicated in differential mode. If we place a
nonzero CO
2
mole fraction in the reference cell, then infrared radiation will
be absorbed, transmittance will decrease, and
ν
r
should decline. This decline
is prevented however, by an automatic gain control circuit that increases the
detector gain by an amount necessary to hold
ν
r
constant. This provides
span stability over the long term, but the ouput voltage must now be
corrected for the gain increase before the calibration polynomial can be
applied.
How much is this gain increase? The detector output signal
ν
r
is
proportional to photon flux, so to hold v
r
constant, the gain must be inversely
proportional to the reduced photon flux that results when CO
2
is added to the
reference cell. Transmittance is proportional to the photon flux, so
the gain
increase is proportional to 1/
τ
r
, where the subscript r refers to the
transmittance of the reference cell. Therefore, to correct for the gain
increase, we find the transmittance of the reference cell given the reference
cell CO
2
mole fraction, and multiply the analyzer output voltage by
τ
r
.
To find
τ
r
, we assume that the sample and reference cells are optically
identical when they contain the same absorbing gas concentrations. If the
