Strain gauges · Measurement

Load Cell Parallel Trim Resistor Calculator

Calculate the trim resistors in the output leads of up to four parallel full-bridge load cells so each contributes equally to the summed signal.

DMSKeil 2017
01

Inputs

Constant-voltage excitation; input resistances are not considered (matching is deliberately done in the output circuit). Corner-load errors from installation are not corrected.

02

Results

Enter values and run the calculation.

Method

What is calculated?

Parallel full bridges deliver the electrical mean of their outputs but load one another in proportion to their output resistances. Only with equal sensitivities and output resistances is the summed signal also the mean of the forces. Following Keil, cells are matched to the one with the largest quotient R_A/C by inserting trim resistors in the output leads of the others so that all effective sensitivities are equal.

Equations

C*₁ = C₁ / (1 + R_A1·(1/R_A2 + 1/R_A3 + … + 1/R_An)) (Keil Gl. 5.10)

C_ges = ΣC*ᵢ (Keil Gl. 5.11)

R*_Ai = Cᵢ·Q_max, Q_max = max(R_Ai/Cᵢ) (Keil Gl. 5.12)

R_AZi = R*_Ai − R_Ai (Keil Gl. 5.13)

Limits

Assumptions and typical mistake

Constant-voltage excitation; input resistances are not considered (matching is deliberately done in the output circuit). Corner-load errors from installation are not corrected.

Placing the whole trim resistor in one output lead or using datasheet instead of measured output resistances.

Inputs

What you enter – and where the values come from

Sensitivity cell 1 [mV/V]
Sensitivity C of the first load cell: output in millivolts per volt of excitation (mV/V) when exactly its rated load acts. Small cell-to-cell differences cause corner errors and are trimmed here. Source: the cell's individual test or calibration certificate, not merely the general datasheet; usually stated to four decimals.
Output resistance cell 1 [Ω]
Output resistance of the first cell, measured between its two signal leads. It determines how strongly the cells load one another in the parallel connection. Source: the datasheet gives only a nominal value (e.g. 350 Ω ± 3 Ω); for trimming measure with a precision ohmmeter to 0.01 Ω.
Sensitivity cell 2 [mV/V]
Sensitivity of the second load cell: output in mV/V at rated load per its test certificate. All cells of one scale should share the same nominal sensitivity; the small differences in the decimals are what is equalised here.
Output resistance cell 2 [Ω]
Output resistance of the second cell between its signal leads, measured with a precision ohmmeter to 0.01 Ω (not the datasheet nominal – its tolerance exceeds the trimming effect).
Sensitivity cell 3 [mV/V]
Sensitivity of the third load cell in mV/V at rated load from its test certificate; enter to four decimals so the trimming can capture the production scatter at all.
Output resistance cell 3 [Ω]
Output resistance of the third cell between its signal leads, measured with a precision ohmmeter to 0.01 Ω; the cell must be unloaded and disconnected from the amplifier.
Sensitivity cell 4 (0 = not used) [mV/V]
Sensitivity of the fourth load cell in mV/V at rated load from its test certificate. If the scale has only three cells (e.g. a vessel on three supports), enter 0 – the cell is then ignored.
Output resistance cell 4 [Ω]
Output resistance of the fourth cell between its signal leads, measured with a precision ohmmeter to 0.01 Ω. Irrelevant if C₄ = 0 is entered.
Context

What this calculator is for

Platform scales, vessel weighing and multi-support force measurement with three or four load cells on one amplifier channel, especially with wider sensitivity tolerances.

What comes next

  1. Enter the certified sensitivities and measured output resistances of all cells.
  2. The cell with Q_max gets no resistor; the others get the computed R_AZ, half in each output lead.
  3. Use the group sensitivity C_ges to scale the amplifier.
Results

How to read the results

  • The cell with R_AZ = 0 is the reference; all others get their trim resistor halved into both output leads.
  • C_ges is the sensitivity the amplifier needs for the summing scale; the group's rated load is the sum of the individual rated loads.
Result quantities

What each value means

Governing quotient Q_max = R_A/C [Ω/(mV/V)]
Largest ratio of output resistance to sensitivity in the cell group. It automatically determines the reference cell: that cell gets no trim resistor, while cells acting more sensitively are reduced to its level. The value itself is not entered in the amplifier.
Trim resistor cell 1 (total) [Ω]
Total trim resistor for cell 1; solder half into each of its two output leads. 0 = reference cell.
Trim resistor cell 2 (total) [Ω]
Total trim resistor for cell 2, half in each output lead.
Trim resistor cell 3 (total) [Ω]
Total trim resistor for cell 3, half in each output lead.
Trim resistor cell 4 (total) [Ω]
Total trim resistor for cell 4 (0 if unused or reference cell).
Effective sensitivity per cell after trimming [mV/V]
Sensitivity with which each individual cell enters the summed signal after trimming – equal for all cells, which is the purpose of trimming.
Sensitivity of the parallel group C_ges [mV/V]
Sensitivity of the complete parallel cell group in millivolts per volt of excitation, referred to the sum of rated loads. Enter it as transducer sensitivity after trimming and then verify it with test weights.
Source

Technical basis

Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 5.6 parallel connection of full bridges, eqs. (5.10)–(5.13) after [5.10].

The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.

FAQ

Frequently asked questions

Why trim the output rather than the supply circuit?

So as not to disturb existing supply-side adjustments; the output circuit also carries only tiny currents.

How accurately must R_A be known?

To about 0.01 Ω, otherwise the match is no better than the cell tolerance.

What happens without trimming?

The cell with the lowest output resistance dominates and eccentric loads are weighted wrongly.