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Shunt calibration

Zero adjustment and function test with shunt resistor

By connecting a resistor Rp in parallel to a strain gauge, a defined detuning of the measuring bridge can be achieved. This can be used for a functional test. Alternatively, this method can also be used to adjust the output signal of the Wheatstone bridge to 0 mV.

To do this, the shunt resistor is permanently inserted into the strain gauge bridge circuit, or alternatively into the connection terminals of the measuring amplifier.

By connecting a shunt resistor Rp in parallel to one of the four bridge resistors R, a resistance change ΔR results:

ΔR = R  · Rp / (R + Rp) - R      (eq. 1)

Converted as a relative resistance change, we get:

ΔR/R = - R / (R + Rp)      (eq. 2)

With the bridge equation for the DMS quarter bridge

Ud/Us = 1/4 · (ΔR1/R1)      (eq. 3)

Inserting equation 3 into equation 2, we get:

R / (R + Rp) = 4 Ud/Us      (eq. 4)

and transformed to Rp:

Rp = R · (1/4 · 1/Ud/Us  -  1)      (eq. 5)

 
With equation 5 it is now possible to calculate the required shunt resistance for a given bridge detuning Ud/Us.
With equation 5 it is now possible to calculate the required shunt resistance for a given bridge detuning Ud
For a positive effect of the shunt resistor, arrange it parallel to R2 or parallel to R4.
Rule of thumb: for approx. 1mV

Shunt resistors for 350 Ohm strain gauges

R in Ohm Ud/Us in mV/V Rp in Ohm ∼ Rp in kOhm aus E12
Series of standards
350 0,5 174650 180
350 1,0 87150 82
350 2,0 43400 47
350 4,0 21525 22

 

Shunt resistors for 120 Ohm strain gauges

R in Ohm Ud/Us in mV/V Rp in Ohm ∼ Rp in kOhm aus E12 
Series of standards
120 0,5 59880 56
120 1,0 29880 27
120 2,0 14880 12
120 4,0 7380 8,2

 

Shunt resistors for 1000 Ohm strain gauges

R in Ohm Ud/Us in mV/V Rp in Ohm ∼ Rp in kOhm aus E12 
Series of standards
1000 0,5 499000 470
1000 1,0 249000 270
1000 2,0 124000 120
1000 4,0 61500 68

 

Nonlinearity of the bridge circuit

When calculating the shunt resistance in Equation 5, the linearized form of the bridge equation was used:

ΔUd/Us = 1/4 (ΔR1/R1 - ΔR2/R2 + ΔR3/R3 - ΔR4/R4)     (eq. 6)

or for the quarter bridge with only one active strain gauge R1 with R = R1 = R2 = R3 = R4

ΔUd/Us = 1/4 (ΔR/R)     (eq. 7)

The exact solution for the quarter bridge is: (from wheatstone-bruecke.pdf)

Ud/Us = 1/4 (ΔR/R) · 1/ (1 + ΔR/2R)      (eq. 8)

The additional term 1/(1 + ΔR/2R) takes the nonlinear component into account.

or with c = 1/(1 -  2·ΔUd/Us)  and eq. 4 nd solved for Rp (from wheatstone-bruecke.pdf):

Rp = R · (1/4 · 1/Ud/Us  -  1)  · 1/c      (eq. 9)

The bridge detuning calculated with the linearized bridge equation is too large by a factor of c. 

With a linearized calculated strain of 1000 µm/m, the exact strain is 999 µm/m. The error is approximately +1 µm/m (+0.1%).

With 87150 ohm in parallel with a 350 ohm strain gauge, the bridge is detuned by 0.998 mV/V. This corresponds to a strain of 2000 µm/m at a k-factor of 2.

Another error is caused by additional series resistors. These can be, for example, the resistance of supply lines, or calibration resistors built in for the standard signal adjustment of sensors, and temperature-dependent nickel resistors built in for the drift adjustment of the E-module. The circuit diagram of the Wheatstone bridge with series resistors is shown in the following figure.

Bridge circuit with series resistor

 

Rv is composed, for example, of 2x 1 Ohm line resistance plus 2x 20 Ohm nickel series resistors plus 2x 10 Ohm fixed resistors = 62 Ohms. Considering the additional voltage divider, which leads to a reduction in the supply voltage Us at the Wheatstone bridge, the bridge equation of the quarter bridge (with R = R1 = R2 = R3 = R4) is:

Ud/Us = 1/4 · (ΔR/R) · Rv/(Rv+R) · 1/ (1 + ΔR/2R)     (eq. 10)

or c = 1/(1 -  2·ΔUd/Us) and eq. 4 and eq. 10 solved for Rp:

Rp = R · (1/4 · 1/Ud/Us · 1/c · Rv/(Rv+R)  -  1)  ·    (eq. 11)

The red parts take into account the nonlinearity of the bridge circuit, the blue parts take into account the influence of the series resistors.

 

 

 

 

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