## Shunt calibration

### Zero balance and function test with shunt resistor

By the parallel connection of a resistor Rp to a strain gauge, a defined detuning of the measuring bridge can be brought about.
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. For this purpose, the shunt resistor is permanently inserted into the strain gauge bridge circuit, or alternatively into the connection terminals of the measuring amplifier. The parallel connection of a shunt resistor Rp to one of the four bridge resistors R results in a resistance change ΔR:

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

Reshaped as a relative change in resistance you get:

ΔR/R = - R / (R + Rp)      (Gl. 2)

With the bridge equation for the strain gauge quarter bridge

Ud/Us = 1/4 · (ΔR1/R1)      (Gl. 3)

Setting equation 3 into equation 2 results in:

R / (R + Rp) = 4 Ud/Us      (Gl. 4)

and reshaped as Rp:

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

With Equation 5, it is now possible to calculate the required shunt resistance for a given bridge detuning Ud / Us.

For a negative effect of the shunt resistor set it parallel to R1 or parallel to R3.

For a positive effect of the shunt resistor, it is arranged parallel to R2 or parallel to R4.

Rule of thumb: for approx. 1mV/V bridge detuning on a 350 ohm bridge you need approx. 100 kOhm.

### Shunt resistors for 350 ohm strain gages

R in Ohm Ud/Us in mV/V Rp in Ohm

∼ Rp in kOhm from E12
standard series

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 gages

R in Ohm Ud/Us in mV/V Rp in Ohm ∼ Rp in kOhm from E12
standard series
120 0,5 59880 56
120 1,0 29880 27
120 2,0 14880 12
120 4,0 7380 8,2

### Shunt resistors for 350 ohm resistors

R in Ohm Ud/Us in mV/V Rp in Ohm ∼ Rp in kOhm from E12
standard series
1000 0,5 499000 470
1000 1,0 249000 270
1000 2,0 124000 120
1000 4,0 61500 68

### Non-linearity 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)     (Gl. 6)

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

ΔUd/Us = 1/4 (ΔR/R)     (Gl. 7)

The exact solution for the quarter bridge is:

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

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

or with c = 1/(1 -  2·ΔUd/Us)  and eq. 4 and resolved according Rp:

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

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

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

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

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

### Bridge circuit with protective resistor Rv is composed, e.g. from 2x 1 ohm line resistance plus 2x 20 ohms nickel resistor plus 2x 10 ohms fixed resistor = 62 ohms. Taking into account the additional voltage divider, which leads to a reduction of the supply voltage Us at the Wheatstone bridge, results for the bridge equation of the quarter bridge (with R = R1 = R2 = R3 = R4):

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

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

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

The red components take into account the non-linearity bridge circuit, the blue components take into account the influence of the series resistors.