Sensors & Measurement · Study deck

Bridge Linearity and Instrumentation

Picture a strain gauge that changes slightly while its display stays at zero.

Physics Phoebe is your guide for this deck.

sensorcircuitsbridge

After studying this chapter

Learning objectives

You will be able to:

Explain why bridge circuits cancel large sensor baselines before amplification.
Estimate quarter-bridge output voltage from gauge factor, strain, and excitation voltage.
Choose instrumentation-amplifier gain from the worst-case differential signal and ADC range.
Use common-mode rejection and dummy gauges to suppress cable noise and thermal drift.

Major section

Start With the Measurement Story

An analog-to-digital converter is the circuit that turns a measured voltage into a digital number.

This proves one measurement chain and range, not every installation; the deeper sections cover bridge balance, linearity, gain, common-mode limits, and calibration.
A bridge circuit can reveal a tiny physical change, but only if the weak differential signal survives imbalance, noise, and loading.
The long folded track is the active element: bonding it to the test surface makes strain lengthen or compress that path, producing a very small resistance change.

Major section

Tiny Signals on Large Baselines

The Wheatstone bridge subtracts a matched reference so that, at rest, the output is zero and only the change appears as a small differential voltage.

Intuition: the bridge is two voltage dividers side by side.
In a single divider with another 350 Ω resistor, the midpoint sits near 2.500 V.

A bonded metal-foil strain gauge with a fine serpentine sensing grid and soldered leads

Major section

Tiny Signals on Large Baselines (continued)

A simple half-bridge divider is not globally linear.

As |DeltaR| grows relative to R + R0, the quadratic and higher-order terms stop being negligible.
A real part makes the gain concrete.
The AD620 instrumentation amplifier sets its gain with one external resistor: G = 1 + 49.4 kΩ / RG.

Major section

CMRR and Thermal Cancellation

The wanted signal is the difference between the two bridge midpoints.

It amplifies the difference and rejects the common-mode part.
A quick noise budget shows why common-mode rejection matters.
With a plain single-ended amplifier at gain 100, the noise would try to become 10 V and would slam the output into a rail.

Deck summary

Key takeaways

An analog-to-digital converter is the circuit that turns a measured voltage into a digital number.

The Wheatstone bridge subtracts a matched reference so that, at rest, the output is zero and only the change appears as a small differential voltage.
A simple half-bridge divider is not globally linear.
The wanted signal is the difference between the two bridge midpoints.

Retrieval practice

Recall check 1 of 4

Physics Phoebe says: answer from memory, then check your reasoning.

Q1Why is a Wheatstone bridge preferred over a single voltage divider for a strain gauge whose resistance changes by only about 0.1%?

AThe bridge increases the strain gauge's gauge factor so its resistance changes more.

BThe bridge subtracts a matched reference so the large steady baseline cancels to zero.

CA bridge eliminates the need for any amplification at all.

DA bridge converts resistance to current, which ADCs read directly.

Show answer

Answer: B Cancelling the baseline first lets the amplifier and ADC work on the small differential signal instead of the offset.

Retrieval practice

Recall check 2 of 4

Physics Phoebe says: answer from memory, then check your reasoning.

Q2A quarter-bridge with GF = 2.0 and Vex = 5 V is loaded to 500 microstrain. Approximately what raw bridge output (before amplification) should you expect?

AAbout 1.25 mV before amplification.

BAbout 250 mV, because that is the standard bridge output.

CAbout 5 V, equal to the excitation.

D0 V, because a quarter-bridge cannot produce an output.

Show answer

Answer: A ΔR/R = 2.0 × 0.0005 = 0.001, and Vout = 5 × 0.001 / 4 = 1.25 mV.

Retrieval practice

Recall check 3 of 4

Physics Phoebe says: answer from memory, then check your reasoning.

Q3A bridge can produce 3.75 mV at overload and feeds an ADC limited to 3.3 V. Which is the highest safe gain listed?

A100

B500

C1000

D2000

Show answer

Answer: B 500 × 3.75 mV = 1.875 V, below the 3.3 V ADC limit.

Retrieval practice

Recall check 4 of 4

Physics Phoebe says: answer from memory, then check your reasoning.

Q4A long cable runs from a bridge sensor to its amplifier and picks up 50 Hz mains hum on both conductors equally. Why does an instrumentation amplifier suppress this interference?

AThe amplifier low-pass filters everything above DC, removing the hum by frequency.

BThe bridge shorts the hum to ground before it reaches the amplifier.

CThe hum appears as a common-mode voltage on both inputs.

DMains hum cannot couple onto sensor cables, so there is nothing to reject.

Show answer

Answer: C Interference shared by both wires is common-mode and is rejected; only the differential signal is amplified.

Print reference

Answers

Answer key.

B · Cancelling the baseline first lets the amplifier and ADC work on the small differential signal instead of the offset.
A · ΔR/R = 2.0 × 0.0005 = 0.001, and Vout = 5 × 0.001 / 4 = 1.25 mV.
B · 500 × 3.75 mV = 1.875 V, below the 3.3 V ADC limit.
C · Interference shared by both wires is common-mode and is rejected; only the differential signal is amplified.