App-10
IM DL350-01EN
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
Δ
R: Resistance change
Rs: Shunt resistance (shunt resistance you want to derive)
If
Δ
R from (1) and (2) is canceled 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 (where 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 canceled 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
Rs
V
0
Appendix
