App-17
IM DL850E-01EN
Appendix
Calculation of the Shunt Resistance
To execute shunt calibration, you need to calculate the shunt resistance (Rs) and the expected strain (ε) in
advance. For “P2-Y,” use ε as given in the equation below (normally a negative value).
In the general method given for shunt calibration (the easy method), an error of 1 to 2% is introduced as the
strain value (ε) increases. Therefore, use the detailed method whenever possible.
Equation for Rs and ε When Shunt Calibration Is Executed
General Equation (Easy method)
ΔR/R = K × ε ..................... (1): Fundamental strain equation
ΔR = R − R//Rs
*
................ (2): Equation for the change in resistance when the shunt resistance is on
* In this manual, the equation for parallel resistances is expressed as follows:
R//Rs =
=
1
R
R × Rs
R + Rs
1
1
Rs
+
ε
: Strain (strain value that you want to be generated
when the shunt resistance is turned on)
K: Gauge factor
R: Bridge resistance
ΔR: Resistance change
Rs: Shunt resistance (shunt resistance you want to derive)
If ΔR from (1) and (2) is cancelled out,
Rs = R × (1 – K × ε)/(K × ε)
Equation A: General equation for calculating the shunt
resistance (includes error)
Detailed Equation
E:
Bridge voltage
V
0
:
Bridge output voltage
R
1
to R
4
: Bridge resistance (R
1
= R
2
= R
3
= R
4
)
Rs:
Shunt resistance (shunt resistance you want to derive)
R’:
Combined resistance when the relay is turned on (R’ = R//Rs)
V
0
= E × (R
1
× R
3
– R
2
× R
4
)/{(R
1
+ R
2
) × (R
3
+ R
4
)}
...................(1): Basic equation for a Wheatstone bridge
When shunt calibration is on,
V
0
= E × (R
1
× R
3
– R’ × R
4
)/{(R
1
+ R’) × (R
3
+ R
4
)}
...................(2): Equation when shunt calibration is on
R’ = R
2
//Rs..........................(3): Equation for combined resistance R’
R
1
= R
2
= R
3
= R
4
= R ........(4): Since R
1
to R
4
are equal, they are represented as R.
Also, from the basic equation of strain,
V
0
/E = K × ε/4 .....................(5): Basic equation of strain
If V
0
/E and R
1
to R
4
from (2), (3), (4), and (5) are cancelled out,
Rs = R × (1 – K × ε/2)/(K × ε)
Equation B: Detailed equation for calculating the shunt
resistance (no error)
E (bridge power supply)
R
1
R
4
R
2
R
3
R
s
V
0
