# What is the relationship between measuring force, sensor output signal and amplifier output voltage?

### 1. Units

Measuring force [N, kN or MN]
Sensor output signal [mV]
Amplifier output voltage [V]

### 2. Sensor output signal related to the measuring force

To determine the sensor output signal, it is necessary to specify the nominal force [N, kN or MN], the nominal characteristic value [mV / V] and the bridge supply voltage [V].

If the sensor is loaded with the nominal force (100%), the following voltage is available at the output of the sensor:

USig [mV]=Excitation voltage [V]* nominal rating [mV/V]

Example:
A load cell rated at 1.0 mV / V provides an output of 10 mV at 10 V DC and at rated load (100%). Since the output signal of the sensor is proportional to the applied load, the signal voltage can be solved with the aid of a simple ratio equation (rule of three).

Example:
If the above-mentioned sensor has a nominal force of 1000N, the output of the sensor will have a signal voltage of 5 mV (10mV / 1000N * 500N) with a measuring force of 500N.

Alternatively, the signal voltage can also be calculated in one step:

USig [mV] =
Excitation voltage [V] * nominal rating [mV/V] * measuring force [N,kN or MN] / nominal force [N,kN or MN]

Example:
USig = 10V* 1,0 mV/V * 1000N / 500N = 5mV

### 3. Amplifier output voltage relative to the sensor output signal (amplifier input signal)

The amplifiers are adjusted by default to the sensors. It is assumed that 10V should be present at the amplifier output when the sensor is loaded to 100%.

If the associated sensor has a nominal rating of 1.0 mV / V, as in the above example, then the gain is preset to 1000.

The calculation is as follows:

Amplification [V/V]

=  amplifier output voltage at 100% [V] / sensor output signal at 100%  [V]

= 10V / 0,01V

By changing the above equation, the amplifier output voltage can also be calculated for a given sensor output signal:

amplifier output voltage [V] = sensor output signal [V] * amplification [V/V]

In the example above:

amplifier output voltage [V] = 0,005V * 1000 = 5V

### 4. Amplifier output signal related to the measuring force

For amplifiers set as standard, the amplifier output signal can be calculated without the above formulas using a simple ratio equation (rule of three).

Amplifier output voltage [V] = (10V * measuring force [N,kN or MN]) / (nominal force [N,kN or MN])

In the above example this would be:
amplifier output voltage [V] = (10V * 500N) / 1000N = 5V

As described under point 2 it is assumed that the amplifier output should be at 10V when the sensor is loaded to 100%. If a different assignment is desired, then the sensor output signal can be recalculated with the aid of a ratio equation (rule of three), since the output signal of the sensor is proportional to the applied force. The gain can then be determined using the above formula.