12 Sensor Circuits: Conditioning and Filters

sensors

sensor

circuits

signal

Prerequisites: Sensor Circuit Fundamentals | Electronics Fundamentals

This enables: ADC and Noise Reduction | Sensor Interfacing

12.1 Overview

This section: Overview — This first route shapes small sensor signals with amplification, filtering, protection, and calculated interfaces.

This first route shapes small sensor signals with amplification, filtering, protection, and calculated interfaces.

This is part 1 of 2. Continue with Sensor Circuits: Bridges and Noise for the second focused route.

Start With the Measurement Story

Protect the Meaning of a Weak Signal

An analog-to-digital converter is a part that turns a voltage into a number. It is often called an ADC. Picture a strain sensor on a water tank. Its useful change is tiny, while motors, long wires, heat, and the power supply can add much larger unwanted changes.

Begin with the real range the sensor must measure. Record its smallest useful change, safe voltage limits, noise sources, and how fast the physical value can move. Then choose gain to use the converter range without clipping. Add a filter only when its time response still fits the job.

Test zero, mid-range, and full-range inputs. Switch nearby loads, change cable position, and apply a value just beyond the safe limit. Compare the raw voltage, the conditioned voltage, the final number, and a trusted reference. A clean number is not proof if the chain hid a fault.

One bench result cannot cover every part, temperature, or installation. The deeper sections explain bridges, amplifiers, filters, and conversion maths so each stage keeps a stated limit and test.

A raw sensor output is rarely ready for a dashboard or control loop. The first design move is to identify what must be amplified, filtered, level-shifted, isolated, or protected before the reading can be trusted.

12.2 In 60 Seconds

Signal conditioning transforms raw, weak sensor outputs into clean, properly scaled signals for ADC conversion. The key components are: amplifiers (boost millivolt signals to fill the ADC range for maximum resolution), Wheatstone bridges (detect tiny resistance changes in strain gauges and load cells with high precision), anti-aliasing filters (remove noise before digitization), and level shifters (match voltage ranges). In the thermocouple example below, signal conditioning yields about 163× finer nominal ADC code spacing than a direct sensor connection.

Chapter Roadmap

First identify why raw sensor outputs need conditioning.
Then inspect bridge circuits and millivolt signals.
Next size gain and low-pass filtering for a 0-3.3V ADC.
Finally apply the chain to thermistors, load cells, noise, grounding, and anti-aliasing.

Checkpoints recap each design decision; deeper circuit details support a first read.

Key Concepts

Instrumentation Amplifier: A differential amplifier with high input impedance and a single gain resistor; ideal for amplifying small differential signals from Wheatstone bridges and strain gauges in the presence of common-mode noise.
Wheatstone Bridge: Four resistors in a diamond configuration where one or more are sensing elements; the differential output voltage is proportional to the excitation voltage and the resistance imbalance. Using that excitation as the ADC reference can cancel excitation drift in the digital reading.
Common-Mode Rejection Ratio (CMRR): The amplifier’s ability to reject identical signals on both inputs while amplifying the difference; high CMRR (>80 dB) is critical for rejecting noise on long sensor cables.
Anti-Aliasing Filter: An analog low-pass filter before the ADC that attenuates frequencies above half the sample rate enough to meet the application’s alias-error limit.
Rail-to-Rail Op-Amp: An op-amp whose output can swing to within millivolts of both supply rails; essential for single-supply 3.3 V designs where the conditioned signal must span the full ADC input range.
Signal Offset Removal: Subtracting a DC offset from a sensor signal to center it in the ADC’s input range, maximizing dynamic range utilization for differential or bridge sensors.
Gain-Bandwidth Product: The product of an op-amp’s gain and its bandwidth is approximately constant; higher gain settings reduce the usable bandwidth, limiting the maximum signal frequency that can be accurately amplified.
Input Impedance Matching: The amplifier’s input impedance must be much higher than the sensor’s source impedance to prevent loading effects that would reduce the measured voltage and introduce gain errors.

12.3 Learning Objectives

This section: Learning Objectives

By the end of this chapter, you will be able to:

Design Signal Conditioning Chains: Construct complete pipelines from raw sensor output to ADC-ready signals
Calculate Amplifier Gain: Derive required gain to utilize full ADC range for maximum resolution
Implement Wheatstone Bridges: Configure bridge circuits for precision resistance measurements
Evaluate Worked Examples: Trace step-by-step calculations for real thermistor and strain gauge interfaces
Select Appropriate Components: Compare instrumentation amplifiers and filter components for specific applications

For Beginners: Signal Conditioning

Imagine trying to listen to a friend whispering in a noisy stadium — you would need to amplify their voice and filter out the crowd noise. Signal conditioning does exactly this for sensor signals. It boosts weak electrical signals, removes unwanted noise, and adjusts voltage levels so the microcontroller can read them clearly and accurately.

12.4 Introduction

This section: Introduction — Raw sensor outputs are rarely suitable for direct connection to microcontroller ADCs.

Raw sensor outputs are rarely suitable for direct connection to microcontroller ADCs. Signals may be too weak (millivolts from thermocouples), too noisy (interference from motors), or at the wrong voltage level (5V sensors on 3.3V MCUs). Signal conditioning transforms these problematic signals into clean, properly scaled inputs for accurate digital conversion.

Start with the whole chain before choosing parts: gain, noise, safe voltage range, then ADC conversion.

Signal Conditioning Chain

Within the larger sensor pipeline, the signal conditioning block transforms weak, noisy sensor signals through four sequential stages:

Step 1: Amplification (Boosting Weak Signals)

Start by Instrumentation amplifier with adjustable gain (1-1000x). Then Formula: Gain = (Vref_ADC_max - Vref_ADC_min) / (Vsensor_max - Vsensor_min). Next Example: 10mV sensor signal amplified 330x to fill 0-3.3V ADC range. Finally Result: Maximizes ADC resolution, converts millivolts to measurable voltage.

Step 2: Filtering (Removing Noise)

Start by Low-pass RC filter or active filter removes frequencies above signal bandwidth. Then Cutoff frequency: fc = 1/(2πRC) set below noise, above signal. Next Example: 10Hz cutoff passes slow temperature changes, blocks 60Hz mains hum. Finally Result: Clean signal with interference removed.

Step 3: Level Shifting (Voltage Matching)

Start by Voltage divider or op-amp circuit adjusts signal to MCU ADC input range. Then Converts bipolar (-5V to +5V) to unipolar (0 to 3.3V) if needed. Next Protects MCU from overvoltage damage. Finally Result: Signal safely matches ADC specifications.

Step 4: ADC Conversion (Digitization)

Start by Sample-and-hold circuit captures instantaneous voltage. Then Successive approximation converts to N-bit digital value. Next Resolution: Vstep = Vref / 2^N determines precision. Finally Result: Binary number representing calibrated physical measurement.

This four-stage pipeline is the foundation of all professional sensor interfaces.

The mathematical gist. A 20.0 mV conditioned sensor span multiplied by the chapter’s illustrative 150× gain uses 3.00 V of an ideal 3.3 V, 12-bit ADC. Its code width is 3.3/4096 = 0.806 mV, or about 0.00537 C/count for a 1 mV/C bridge signal. Its 16 kohm, 1 uF low-pass has a 9.95 Hz cutoff and attenuates 60 Hz by only 15.7 dB, so additional anti-alias filtering is required for the chosen sampling rate.

12.5 Signal Processing Pipeline Overview

This section: Signal Processing Pipeline Overview — Before designing individual circuits, locate each source of measurement quality in the complete signal path.

Before designing individual circuits, locate each source of measurement quality in the complete signal path. Use Figure 12.1 to follow one physical quantity all the way to an IoT action, noting where the signal is still analogue and where it has become data.

Physical quantity passes through sensor transduction, signal conditioning, ADC conversion, digital processing and output or action. Gain, filtering and voltage matching happen before conversion. — Figure 12.1: Complete Sensor Signal Processing Pipeline: Physical to Digital to Action

In Figure 12.1, the physical quantity is transduced into an electrical signal; conditioning scales and filters it before conversion; the ADC produces codes; digital processing turns codes into evidence; and the output stage uses or transports the result. An error introduced before conversion can be labelled downstream but not reconstructed, which is why the bridge, thermistor, and gain circuits in this chapter belong inside an end-to-end chain.

Key Pipeline Stages:

Stage	Purpose	Example Components	Typical Issues
1. Physical	Measure real-world phenomenon	Temperature, light, pressure	Environmental interference
2. Transduction	Convert to electrical signal	Thermistor, LDR, piezo sensor	Sensor drift, non-linearity
3. Conditioning	Prepare signal for ADC	Op-amps, RC filters, dividers	Insufficient gain, wrong cutoff
4. ADC Conversion	Digitize analog signal	ESP32 12-bit ADC, ADS1115	Noise, quantization error
5. Digital Processing	Extract meaningful data	Averaging, Kalman filter	Algorithm complexity, latency
6. Output/Action	Use the data	Display, relay, MQTT	Communication failures, delays

The stage map explains where work happens, but a practical design must also decide what to trade. Use Figure 12.2 as a review route: inspect cost, power, speed, and complexity from top to bottom, then test whether each proposed response changes another constraint.

Sensor circuit trade-offs compare hardware filtering, duty cycling, sample averaging and modular blocks. Cost, power, speed/noise and simplicity/features require different compromises. — Figure 12.2: Sensor Circuit Design Trade-offs: Cost, Power, Speed, and Complexity

Read Figure 12.2 as paired starting strategies rather than universal answers. An RC network can cheaply limit bandwidth; duty cycling changes when measurements are available; averaging reduces uncorrelated noise while adding latency; and modular blocks contain complexity without removing it. Carry those consequences into the component calculations below so that conditioning is justified by a measurement requirement, not added as decoration.

12.6 Wheatstone Bridge

This section: Wheatstone Bridge — The Wheatstone bridge is a precision measurement circuit used with strain gauges, load cells, and other resistive sensors requiring high accuracy.

The Wheatstone bridge is a precision measurement circuit used with strain gauges, load cells, and other resistive sensors requiring high accuracy. It detects small resistance changes by comparing two voltage dividers.

The bridge makes the problem visible: a real physical change may only move the output by millivolts.

Before reading the balance rule, inspect Figure 12.3 to see why comparing the midpoint voltages of two divider branches reveals tiny resistance changes.

A Wheatstone bridge pairs three fixed resistors with a variable sensor and amplifier. The balance equation gives zero output when the bridge is balanced. — Figure 12.3: Wheatstone Bridge: Four-resistor configuration for detecting small resistance changes with high precision.

Read Figure 12.3 by tracing each supply-to-ground branch separately, then compare the two centre nodes that form the differential output. Equal ratios, R1/R2 = R3/Rx, make those midpoint voltages equal and yield 0 V. A change in the sensing arm breaks that equality, linking mechanical or thermal change to a signed voltage. The amplifier then enlarges this small difference while rejecting voltage common to both nodes, which is why the bridge is useful before a limited-range ADC. Key Properties:

Balanced condition: When R1/R2 = R3/Rx, output voltage = 0V
Sensitivity: Small changes in Rx produce measurable differential voltage
Applications: Strain gauges (weight scales), pressure sensors, temperature measurement
Advantage: A differential readout rejects interference common to both midpoint leads; matched temperature-compensating arms can reduce thermal drift, and a ratiometric ADC reference can cancel excitation drift.

12.6.1 Wheatstone Bridge Sensitivity Calculator

Calculate the output voltage of a Wheatstone bridge for a given resistance change in the sensor element.

Set the excitation voltage and nominal arm resistance to match the proposed bridge, then vary the resistance change over the sensor’s credible full-scale range. Compare Output voltage (approximate) with Output voltage (exact): close agreement shows that the small-change approximation is safe around balance, while divergence warns that the sensing arm has moved too far into the divider’s curved response. Next compare the millivolt output with the chosen ADC input range. The calculator’s result is not yet a measurement resolution; it is the differential signal available to an instrumentation amplifier. Use the displayed magnitude to select gain with headroom for offset and overload, and retain the exact result as the check against the linear approximation used in firmware or design notes.

Check your understanding: Use the questions below to check the key idea

This section:

Physics Phoebe, Physics and measurement-foundations expert

Checkpoint: Bridge Signals

A balanced Wheatstone bridge starts at zero output voltage.
A 350ohm bridge with a 0.1% change and 5V excitation produces about 1.25mV.
High input impedance and common-mode rejection protect that tiny differential signal.

12.7 Signal Conditioning Chain

This section: Signal Conditioning Chain — Complete signal conditioning transforms raw sensor signals into clean, properly scaled inputs for ADC conversion. Complete signal conditioning transforms raw sensor signals into clean, properly scaled inputs for ADC conversion. After the bridge, the chain prepares the signal for conversion: amplify, filter, shift, buffer, sample. Before sizing individual components, inspect Figure 12.4 to see how each conditioning stage prepares the signal for the next boundary.

Read Figure 12.4 from the weak sensor output through gain, filtering, level shifting, sampling, and conversion. That order connects noise and range decisions to the final digital measurement instead of treating each circuit as an isolated recipe.

Sensor conditioning runs through amplification, noise filtering, galvanic isolation and A/D conversion to digital output. A component table links each stage to functions and applications. — Figure 12.4: Signal conditioning prepares a small sensor signal for ADC conversion through gain, filtering, level shifting, and sampling.

Signal Conditioning Pipeline: From millivolt sensor output to calibrated digital measurement.

Each stage addresses specific signal quality issues:

Stage	Function	Typical Components
Amplification	Boost weak signals to full ADC range	Instrumentation amplifier (INA128, AD620)
Filtering	Remove noise above Nyquist frequency	RC low-pass, active filters
Level Shifting	Match sensor output to ADC input range	Voltage divider, op-amp buffer
Buffering	Provide high-impedance input isolation	Unity-gain op-amp

12.7.1 Gain and ADC Resolution

Use this interactive tool to calculate ideal gain after an analog stage subtracts the sensor’s minimum output voltage. Without that offset removal, the displayed gain and resistor can clip the ADC; also check the selected amplifier’s output headroom.

12.7.2 RC Low-Pass Filter Designer

Calculate component values for an anti-aliasing RC low-pass filter given your desired cutoff frequency. Start with the highest signal frequency the application must preserve, then choose a cutoff above that band but below frequencies that would alias at the ADC’s sample rate. Enter a practical resistor and inspect the calculated ideal capacitance alongside its nearest E12 value; the standard component changes the realised cutoff, so use that realised value for the sampling check. The resistor cannot be chosen from filter maths alone: a very large value can raise thermal noise and may prevent the ADC sampling capacitor from settling, whereas a very small value increases loading and requires a larger capacitor. After selecting the pair, verify attenuation at the first unwanted frequency and confirm that the ADC sample rate still satisfies Nyquist for the filtered bandwidth. This connects the component choice to the acquisition boundary rather than treating the calculator as a parts lookup.

Low-pass filter narrated tour

Narrated audio tour. The full transcript is below. Play the tour to open the simulator. Pause, replay a beat, or read the full transcript below. Some beats explain situations this teaching model cannot show; those beats keep the existing frame and provide captions only.

Full transcript — Low-pass filter (8 beats)

B1 — Office temperatureYou are preparing an office temperature sensor to reduce sixty hertz interference while preserving useful temperature changes. Model caption: Office temperature measurement: reduce 60 Hz interference while preserving useful temperature changes. B2 — Slow changes passNoise means unwanted variation. A low-pass filter passes slow changes more easily. At ten hertz, interference reduction is about fifteen point seven decibels. Model caption: Low-pass filtering passes slow changes more easily and reduces faster unwanted variation. B3 — Cutoff and lagCutoff sets the frequency limit. Lag means the output responds later. Model caption: Cutoff separates frequencies by how strongly they are reduced. Lag means the filtered output can respond later than the input. B4 — Component exampleFor a concrete design, combine a sixteen kilohm resistor with a one microfarad capacitor. Multiply sixteen thousand ohms by one millionth of a farad to get zero point zero one six seconds. Multiply that by two and by pi, about three point one four, to get about zero point one zero zero five seconds. Divide one by that result to get a cutoff of about nine point nine five hertz. Model caption: Chapter calculation: 16 kΩ with 1 µF gives about 9.95 Hz. The rounded 10 Hz example reduces 60 Hz interference by about 15.7 dB. B5 — Amplitude gainsIn the teaching model, set the cutoff to ten hertz and the filter order to one. Order controls how sharply faster changes are reduced. Set the useful signal to one hertz and the noise to sixty hertz. For the useful signal, divide one by ten, square the result, and add one to get one point zero one. Divide one by the square root of one point zero one to retain about ninety-nine point five percent of the useful amplitude. For the noise, divide sixty by ten, square the result, and add one to get thirty-seven. Divide one by the square root of thirty-seven to retain about sixteen point four percent of the noise amplitude. Model caption: Calculated amplitude gains: useful signal ≈ 99.5%; selected noise ≈ 16.4% of its own input amplitude. Asset gain readouts round these to 100% and 16%. B6 — Cutoff trade-offAt order one, estimate delay by dividing one thousand by two times pi times the cutoff in hertz. At ten hertz, divide one thousand by about sixty-two point eight to get about sixteen milliseconds. At one hertz, divide one thousand by about six point two eight to get about one hundred fifty-nine milliseconds. With the useful signal still at one hertz, divide one by one, square the result, and add one to get two. Divide one by the square root of two to retain about seventy-one percent of the useful amplitude. The lower cutoff reduces more noise, but also weakens and delays useful changes. The moving waveform illustrates smoothing; its shape is a teaching approximation. Model caption: Cutoff 10 → 1 Hz: estimated delay 16 → 159 ms. At 1 Hz cutoff, useful amplitude gain is about 71%. The trace is a teaching approximation. B7 — Smoothness and accuracyA common mistake is to assume a smoother sensor output preserves the useful temperature changes, but smoothing can reduce useful changes and delay their arrival along with reducing noise. For your office sensor, preserving the temperature information matters more than making the output seem perfectly smooth. Model caption: Smoother does not establish greater accuracy: useful changes can be reduced and delayed together with noise. B8 — Choose a cutoffChoose a cutoff that preserves useful changes and acceptable response time. Model caption: Choose a cutoff that quiets unwanted changes while preserving the useful changes and the response time your measurement needs.

This section: — These three load cells (Wheatstone-bridge force sensors) present different ways to put force into the sensing element. These three load cells (Wheatstone-bridge force sensors) present different ways to put force into the sensing element. Compare the top face, threaded ends, and cable before choosing a mount. The photos do not show the wiring needed to approve a circuit.

Round load cell with a flat metal compression pad and a cable, a physical sensor used for weight measurement. — This real example (DTB miniature load cell) shows a physical form of load cell (wheatstone-bridge weight sensor). Use the visible package, interfaces, scale, mounting, and surrounding context as evidence; a catalogue label alone does not establish deployment fit. Photo: Daraceleste; CC BY-SA 4.0

Cylindrical metal load cell with threaded mounting ends and an attached cable, showing how it fits into a weighing assembly. — This real example (HTC load cell) shows a physical form of load cell (wheatstone-bridge weight sensor). Use the visible package, interfaces, scale, mounting, and surrounding context as evidence; a catalogue label alone does not establish deployment fit. Photo: Daraceleste; CC BY-SA 4.0

Cylindrical load cell with threaded ends, a red band, side connector and yellow protective cap for mounting in a weighing system. — This real example (RELC load cell) shows a physical form of load cell (wheatstone-bridge weight sensor). Use the visible package, interfaces, scale, mounting, and surrounding context as evidence; a catalogue label alone does not establish deployment fit. Photo: Daraceleste; CC BY-SA 4.0

The first cell is a short cylinder with a broad top contact and a cable leaving above it. The second has a threaded boss on each side and a cable leaving the barrel. The third is taller, with a threaded upper section and a side fitting. Each needs a different load path and space for the cable. Check the maker’s mounting and electrical data for the exact unit before connecting any one of these to the filter and amplifier discussed in this chapter.

Checkpoint: Gain and Filtering

A 10mV to 30mV sensor span is only 20mV, so a 3.3V ADC can need gain near 165x.
A 12-bit converter has 4096 levels; amplification decides how many counts the sensor actually uses.
A 10Hz RC cutoff can pass slow temperature changes while reducing 50Hz or 60Hz interference.

12.8 Thermistor Signal Conditioning

This section: Thermistor Signal Conditioning — Thermocouple example: 40 µV/°C over 0–500 °C gives 20 mV full scale.

HVAC Thermistor Conditioning

Scenario: You need to measure room temperature (15-35C) using an NTC thermistor in a conditioned bridge. Assume the bridge produces a 10-30mV differential signal over that range. This is an illustrative front-end model; check the thermistor curve and actual ADC input range before building it. Before sizing gain for the HVAC example, inspect Figure 12.5 to anchor the calculation in the differential amplifier that must handle the thermistor’s millivolt signal. Package pins and circuit limits remain part of the design even when the arithmetic is correct.

Gold metal-can AD520J integrated circuit with two rows of leads, an early instrumentation amplifier. — Figure 12.5: The INA128 selected in this exercise is a modern instrumentation amplifier; the photographed AD520J is an earlier member of the same single-chip component class, built to amplify small differential sensor signals before conversion. Photo: Mister rf, CC BY-SA 4.0

Read Figure 12.5, begin with the paired input pins that receive the small differential signal, then relate the gain-setting and output connections to the ADC range. The photographed component represents the amplifier class; the specified INA128 and its datasheet values govern the actual circuit below. Given:

Conditioned bridge output: 10mV at 35C, 30mV at 15C (20mV span)
Illustrative ideal ADC: 12-bit, 0-3.3V input range; the ESP32’s actual calibrated range depends on attenuation
Target: Use most of the available ADC range without clipping
Noise environment: Office with fluorescent lights (60Hz interference)

Steps:

Calculate required gain: To map 20mV range to 3.3V range: Dividing the 3.3V ADC range by the 20mV sensor span requires gain 165. Use a design gain of about 150, leaving 0.3V of nominal ADC headroom.
Design instrumentation amplifier: For the INA128, gain is G = 1 + 50 kΩ/R_G. A target gain of 150 needs R_G = 50,000 Ω/(150 − 1) = 335.6 Ω; use a 332 Ω standard resistor for nominal gain 151.6.
Design a first analog noise filter: A 10Hz cutoff attenuates 60Hz by only about 15.7dB. It is a first stage, not a sufficient anti-alias guarantee for 1 sample/s storage. Sample faster, apply a suitable analog anti-alias filter for the ADC rate, then digitally low-pass and decimate to 1 sample/s: $f_c = 10 \text{Hz (illustrative first stage)}$ $RC = \frac{1}{2\pi f_c} = \frac{1}{2\pi \times 10} = 15.9 \text{ ms}$ R = 16k ohm and C = 1uF give about 9.95Hz; verify the complete filter’s stopband and settling against the chosen sampling rate.
Remove offset before gain: Subtract the 10mV baseline in the conditioned differential input, then amplify its 0-20mV span by 150 to obtain 0-3.0V. A passive divider cannot subtract a 1.5V offset, and an INA128 needs supply and input/output headroom consistent with its data sheet.

Result:

Conditioned, amplified signal: 0V (at 35C) to 3.0V (at 15C), assuming the amplifier can swing to those endpoints
Ideal 3.3V, 12-bit ADC code width: 3.3V / 4096 = 0.806mV
Ideal temperature code width: 0.806mV / (150 x 1mV/C) = 0.00537C per code, before noise, nonlinearity, drift, and calibration error

Key Insight: In this idealized example, a 150x front-end gain spreads the 20mV bridge span over 3.0V, using about 91% of a 3.3V ADC range. This improves nominal code spacing, but it does not by itself improve measurement accuracy.

Putting Numbers to It

Amplifier Gain Calculation for Maximum ADC Resolution: A thermocouple outputs 40μV/°C with 10mV output at 250°C. You need to measure 0-500°C range with ESP32’s 12-bit ADC (0-3.3V). What gain maximizes resolution without clipping?

Sensor output range (0-500°C):

V_{sensor} = 40\mu V/°C \times 500°C = 20{,}000\mu V = 20\text{ mV (full scale)}

Required gain to fill 3.3V ADC range:

\text{Gain} = \frac{V_{ADC\_{max}}}{V_{sensor\_{max}}} = \frac{3.3V}{0.020V} = 165

Instrumentation amplifier (INA128) gain formula:

G = 1 + \frac{50k\Omega}{R_G}

Solving for $R_G$ :

R_G = \frac{50\,000\Omega}{165 - 1} = \frac{50\,000\Omega}{164} \approx 304.9\Omega

Use a standard 309 Ω resistor (1% tolerance) for nominal headroom: $G = 1 + 50\,000\Omega/309\Omega \approx 162.8$ . The ideal 20 mV full-scale signal then becomes about 3.256 V, leaving about 0.044 V below the 3.3 V ADC limit at nominal values. Check component tolerances and input range in the real design.

ADC resolution after amplification:

\text{ADC step size} = \frac{3.3V}{2^{12}} = \frac{3.3V}{4096} = 0.806\text{ mV/count}

Temperature resolution:

\Delta T = \frac{0.806\text{ mV/count}}{162.8 \times 40\mu\text{V/°C}} \approx 0.124°C\text{/count}

Comparison to direct connection (no amplification):

Signal span without amplification: 20mV → uses about 25 ADC counts (20mV / 0.806mV)
Temperature code width: 500°C / 24.82 counts ≈ 20.14°C per count (about 163× wider)

With proper amplification, the nominal ADC code spacing is about 0.124°C/code instead of 20.14°C/code. This is about 163× finer nominal ADC code spacing; actual accuracy and precision depend on noise, thermocouple compensation, calibration, and amplifier limits.

Thermocouple example: 40 µV/°C over 0–500 °C gives 20 mV full scale. An ideal 12-bit ADC at 3.3 V gives direct spacing of 20.14 °C per code; with nominal gain 162.8, spacing is 0.124 °C per code. Code spacing is not accuracy.

Check your understanding: Use the questions below to check the key idea

12.9 Strain Gauge Bridge Gain

This section: Strain Gauge Bridge Gain

12.10 Continue to Part 2

This section: Continue to Part 2 — Continue with Sensor Circuits: Bridges and Noise.

Continue with Sensor Circuits: Bridges and Noise.

Find help

Search reviewed answers

3 reviewed answers.

Where should I start in a module?

Open the module page from the sidebar to see its chapters in order. Use the module map to return to a topic you need.

Modules and paths

Reviewed 2026-10-16

What can I try when a project does not work?

Check the symptom, then work through the diagnostic steps. Keep the error message and the smallest example that reproduces it.

When you are stuck

Reviewed 2026-10-16

How do interactive examples work?

Use the interactive guide to check how examples and simulations work before changing your project.

Interactive examples guide

Reviewed 2026-10-16