UNCLASSIFIED
TM-CAL-009
WHEATSTONE BRIDGE NULL METHOD
Ratio-Based Precision Resistance Measurement Without Meter Calibration
Prepared by: Mervyn Martin, KO6NNH
Merced, California  •  26 May 2026
Amateur Radio / Electronics — Not for commercial calibration use

Table of Contents

  1. Chapter 1 — General Information
  2. Chapter 2 — Theory of Operation
  3. Chapter 3 — Materials and Construction
  4. Chapter 4 — Assembly Procedures
  5. Chapter 5 — Calibration Procedure
  6. Chapter 6 — Tuning and Adjustment
  7. Chapter 7 — Verification
  8. Appendix A — Calculations and Formulas
  9. Appendix B — Example Results

CHAPTER 1 — GENERAL INFORMATION

1-1. SCOPE

This manual covers construction and use of a Wheatstone bridge for precision resistance measurement. At null balance, accuracy depends only on the ratio of precision resistors and is independent of meter calibration, supply voltage variation, or meter sensitivity. This method can measure resistance to ±0.01% with 0.01% ratio-arm resistors.

CHAPTER 2 — THEORY OF OPERATION

2-1. BRIDGE BALANCE CONDITION

The Wheatstone bridge consists of four resistors in a diamond configuration with a battery across one diagonal and a null detector across the other.

Bridge balance (null condition)Rx = Rs × Rb / Ra

At null: Rx is the unknown, Rs is the standard (decade box), Ra and Rb are the ratio arms (precision fixed resistors). No current flows through the detector at balance; its internal resistance does not affect accuracy.

Bridge Configurations
Ratio Rb/RaRx RangeNotes
1:1 (equal arms)1 Ω–10k ΩHighest accuracy
10:110–100k ΩExtends range
100:1100 Ω–1M ΩHigher ratio, lower sensitivity

CHAPTER 3 — MATERIALS AND CONSTRUCTION

3-1. BILL OF MATERIALS

Wheatstone Bridge Components
QtyItemSpecification
2Precision ratio-arm resistors (Ra, Rb)1kΩ 0.01% or 0.1%
1Decade resistance boxTM-CAL-008 or commercial
1Galvanometer or null detector1 μA sensitivity preferred
11.5 V battery or USB powerStable DC supply
1Push-button switchFor galvanometer protective circuit
4Binding postsFor Rx unknown connection

CHAPTER 4 — ASSEMBLY PROCEDURES

  1. Wire bridge: battery+ → junction of Ra and Rx. Battery− → junction of Rb and Rs.
  2. Galvanometer: one terminal to junction of Ra/Rb, other to junction of Rx/Rs.
  3. Add protective switch (normally open) in series with galvanometer. Close briefly to check null; prevents galvanometer deflection from extreme imbalance.
  4. Connect unknown Rx to external binding posts.
  5. Mount all components in labeled enclosure.

CHAPTER 5 — CALIBRATION PROCEDURE

  1. Connect unknown resistor to Rx terminals.
  2. Set decade box (Rs) to estimated value of unknown.
  3. Briefly close galvanometer switch. Observe deflection direction.
  4. Adjust Rs: if galvanometer deflects right, Rs is low (increase); if left, Rs is high (decrease).
  5. Iterate until galvanometer reads zero with switch held closed (null balance).
  6. Calculate: Rx = Rs × (Rb / Ra).
  7. Read Rs value from decade box. Apply ratio-arm correction if Rb ≠ Ra.

CHAPTER 6 — TUNING AND ADJUSTMENT

Verify ratio arms Ra and Rb are equal by null test: replace Rx with a shorting link, set Rs = 0, check galvanometer reads null. If not, ratio arms are unequal; measure them with 4-wire method and apply correction factor.

CHAPTER 7 — VERIFICATION

  1. Measure a 0.01% certified reference resistor. Compare result against certified value. Error should be <0.05%.
  2. Measure three different unknown resistors on the decade box range. Compare bridge result vs. direct 4-wire DMM measurement.
  3. Log date, ratio arm values, and results.

APPENDIX A — CALCULATIONS AND FORMULAS

Unknown resistance at nullRx = Rs × Rb / Ra
Equal-arm bridge (Ra = Rb)Rx = Rs
Bridge sensitivity (for galvanometer selection)IG = E × ΔR / (4 × R × RG) (small imbalance, equal arms)

APPENDIX B — EXAMPLE RESULTS

Bridge Measurement Log
Rx (nominal)Rs at nullRatioRx (measured)4-Wire Check
100 Ω99.87 Ω1:199.87 Ω99.86 Ω
1k Ω999.2 Ω1:1999.2 Ω999.1 Ω
10k Ω9982 Ω1:19982 Ω9981 Ω
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