Campbell Scientific CR1000 Measurement and Control System - Manual (Page 262)

Section 7. Installation
262
where,
V
S
= measured bridge‐output voltage
V
X
= excitation voltage
or,
X = 1000 (R
S
/(R
S
+R
1
)‐R
3
/(R
2
+R
3
)).
With reference to figure PT100 in Four-Wire Full-Bridge (
p. 263
), the resistance of
the PRT (R
S
) is calculated as:
R
S
= R
1
X' / (1‐X')
where
X' = X / 1000 + R
3
/(R
2
+R
3
)
Thus, to obtain the value R
S
/R
0
, (R
0
= R
S
@ 0°C) for the temperature calculating
instruction PRTCalc(), the multiplier and offset used in BRFull() are 0.001 and
R
3
/(R
2
+R
3
), respectively. The multiplier (R
f
) used in the bridge transform
algorithm (X = R
f
(X/(X-1)) to obtain R
S
/R
0
is R
1
/R
0
or (5000/100 = 50).
The application requires control of the temperature bath at 50°C with as little
variation as possible. High resolution is desired so the control algorithm will
respond to minute changes in temperature. The highest resolution is obtained
when the temperature range results in an output-voltage (V
S
) range, which fills the
measurement range selected in BRFull(). The full-bridge configuration allows
the bridge to be balanced (V
S
= 0 V) at or near the control temperature. Thus, the
output voltage can go both positive and negative as the bath temperature changes,
allowing the full use of the measurement range.
The resistance of the PRT is approximately 119.7 ohms at 50°C. The 120-Ω fixed
resistor balances the bridge at approximately 51°C. The output voltage is:
V
S
= V
X
[R
S
/(R
S
+R
1
) ‐ R
3
/(R
2
+R
3
)]
= V
X
[R
S
/(R
S
+5000) ‐ 0.023438]
The temperature range to be covered is 50°C ±10°C. At 40°C, R
S
is
approximately 115.8 ohms, or:
V
S
= ‐802.24E‐6 V
X
.
Even with an excitation voltage (V
X
) equal to 2500 mV, V
S
can be measured on
the ±2.5 mV scale (40°C/115.8 Ω/–2.006 mV, 60°C/115.8 Ω/1.714 mV). There is
a change of approximately 2 mV from the output at 40°C to the output at 51°C, or
181 µV/°C. With a resolution of 0.33 µV on the ±2.5-mV range, this means that
the temperature resolution is 0.0009°C.
The ±5 ppm per °C temperature coefficient of the fixed resistors was chosen
because the ±0.01%-accuracy tolerance would hold over the desired temperature
range.