Resistance measuring system

A temperature measuring system comprises a sensor which is connected to a supply rail through a first lead, and which may be selectively connected by a relay through a second lead or a third lead to the inverting input of an operational amplifier. The leads have different resistance values. The output of the amplifier is connected to its input through a resistor, and its non-inverting input is connected to the rail through a potential divider. The output of the amplifier is connected to a computer through a low pass filter and an A/D converter. In operation, the output voltage of the amplifier is first measured with the second lead connected to its inverting input and then measured again with the third lead connected. From these measurements the resistance of the sensor is calculated after calculating and hence eliminating the resistance of the leads. The sensed temperature can then be calculated from the resistance of the sensor.

This invention relates to a resistance measuring system which includes a 
sensor the resistance of which varies and a circuit for measuring the 
resistance of the sensor, and also to a method of measuring the resistance 
of such a sensor. 
In such a system variations in the resistance of the two leads which 
connect respective terminals of the sensor to the measuring circuit cause 
errors in the measurement. In an attempt to compensate for the lead 
resistance variations it has been proposed to connect one terminal of the 
sensor to the measuring circuit through a third lead having a different 
resistance value to the other two leads but this does not provide full 
compensation for the lead resistance variations. 
It is an object of this invention to reduce errors caused by lead 
resistance variations. 
In accordance with one aspect of this invention, there is provided a 
resistance measuring system comprising a sensor the resistance of which 
varies, a first lead connected to one end of the sensor, a second lead 
connected to the other end of the sensor, a third lead of different 
resistance to the second lead connected to said other end, a circuit for 
measuring the resistance of the sensor, and switch means having a first 
state in which the sensor is connected to the measuring circuit through 
the first and second leads and a second state in which the sensor is 
connected to the measuring circuit through the first and third leads. 
By providing the third lead and the switch means the resistance of the 
leads may be calculated and hence the error caused by lead resistance 
variation may be reduced. 
The measuring circuit may include means for producing a first voltage 
corresponding to the combined resistance of the sensor and the first and 
second leads when the switch means are in said first state and a second 
voltage corresponding to the combined resistance of the sensor and the 
first and third leads when the switch means are in said second state. 
In accordance with another aspect of this invention there is provided a 
method of measuring resistance comprising taking a sensor the resistance 
of which varies having a first lead connected to one end thereof, a second 
lead connected to the other end thereof, and a third lead of different 
resistance to the second lead connected to said other end thereof, 
measuring the combined resistance of the sensor and the first and second 
leads, measuring the combined resistance of the sensor and the first and 
third leads, and calculating the resistance of the sensor from the two 
combined resistance measurements.

Referring now to the drawing the system comprises a supply rail 10 set to a 
voltage Vi and connected through a first lead 12 having a resistance r to 
one end of a Rosemount type 102EC 2BC platinum resistance temperature 
sensor 14 having a resistance Rt. The other end of the sensor 14 is 
connected through a second lead 16 having a resistance r to a terminal 18 
and through a third lead 20 having a resistance kr to a terminal 22. The 
three leads 12, 16 and 20 are made of identical material so that they have 
identical temperature co-efficients and the value of k is set to a 
non-unity value, for example 3. 
The terminals 18 and 22 may be selectively connected through switch means 
in the form of a pole 24a of a relay 24 to the inverting input of an 
Analogue Devices Inc. type AD 517S operational amplifier A1, the 
non-inverting input of which is connected to the rail 10 through a 
resistor R3 and to a OV rail through a resistor R4. The resistors R3 and 
R4 operate as a potential divider. Connected between the output of 
amplifier A1 and its non-inverting input there is provided a feedback 
resistor R2. The resistors R2, R3 and R4 are Vishay type S102C precision 
resistors. 
The output of amplifier A1 is also connected to the input of a unity gain 
low pass second order Butterworth filter 26 having a cut-off frequency of 
5 Hz and the output of filter 26 is connected to the input of an A/D 
converter 28. The output of the A/D converter 28 is connected to the input 
of a computer 30 which controls relay 24. The amplifier A1 together with 
the filter 26, A/D converter 28, computer 30 and resistors R2, R3 and R4 
form a measuring circuit. 
With the relay pole 24a in the position shown, the output voltage Vo of 
filter 26 is given by: 
##EQU1## 
where R1=Rt+2r, and R2, R3 and R4 are respectively the resistance values 
of the resistors R2, R3 and R4. 
The values of the resistors R2, R3 and R4 should be chosen so that the 
voltage Vo lies within the operating range of the system over the 
temperature range sensed by the sensor 14. 
The calculation of the temperature sensed by the sensor 14 will now be 
explained. 
First, with the pole 24a in a first position so that the amplifier A1 is 
responsive to the combined resistances of the first lead 12, the second 
lead 16 and the sensor 14, the following calculation is made: 
##EQU2## 
where R1=Rt+r+r and Vo=output voltage of filter 26. 
Then, with the pole 24a in a second position so that the amplifier A1 is 
responsive to the combined resistance of the first lead 12, the third lead 
20 and the sensor 14, the following calculation is made: 
##EQU3## 
where R1'=Rt+r+kr and Vo'=output voltage of filter 26. 
Then the value of Rt is calculated as follows: 
EQU r=(R1'-R1)/(k-1) (4) 
and 
EQU Rt=(R1-2r) (5) 
The temperature may then be calculated from the following law relating the 
temperature T and resistance Rt of sensor 14. 
##EQU4## 
where B=0.1 for temperatures below 0.degree. C. and B=0.0 for temperatures 
above 0.degree. C. 
The computer 30 is programmed to make the calculations shown in equations 
2, 3, 4, 5 and 6 and to calculate the temperature from the resistance 
value Rt. 
It is estimated that the lead resistance is calculated with an accuracy of 
.+-.0.25 ohm and so the error caused by lead resistance variation is 
almost eliminated.