ElecEng Handbook Electronic Engineer Reference
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Sensor Interfacing

Bridge, RTD, thermistor and photodiode conditioning calculators, plus sensor-type and signal-conditioning reference tables with wiring diagrams.

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Sensor curves, temperature coefficients and tolerances vary widely by part; linearization constants (RTD alpha, thermistor beta) come from the sensor datasheet. Treat results as engineering estimates.

Wheatstone Bridge Output

Vdiff = Vbias · ΔR / (4R + 2·ΔR) for one active arm. For a small change the output scales linearly with ΔR/R, which is then amplified and fed to the ADC.
V
Ω
Ω
Differential Vdiff
Relative ΔR/R
A real gauge has four active arms (full bridge) giving up to 4× the signal. Bridge output is differential — use an instrumentation amplifier to reject the common-mode bias.

RTD Resistance vs Temperature

R = R0 · (1 + α·T), linear model. For Pt100 α ≈ 0.00385 /°C and R0 = 100 Ω. Calibrating and using the datasheet curve is more accurate than this linear form.
Ω
/°C
°C
Resistance R(T)
Sensitivity dR/dT
Pt100 sensitivity is only ≈0.385 Ω/°C; the signal needs amplification. Lead resistance adds error — a 4-wire or at least 3-wire connection removes it.

Thermistor Divider to ADC

Vout = Vcc · Rth / (R1 + Rth). Pick the series resistor so the swing covers your ADC range; the linearity is best when R1 ≈ Rth at the temperature of interest.
V
Ω
Ω
ADC voltage Vout
Divider current
The voltage is non-linear in temperature. Use the datasheet beta/Steinhart equation to convert back to °C, or a lookup table. Keep self-heating low by limiting current.

Photodiode Transimpedance

Vout = Iph · Rf; bandwidth f = 1/(2π·Rf·Cf). The feedback capacitor Cf stabilizes the amplifier and limits noise — it sets the closed-loop bandwidth.
A
Ω
F
Output Vout
Bandwidth f3dB
Use an op-amp with input bias current well below Iph and a low input capacitance. The junction capacitance of the photodiode adds phase lag — Cf counters it but trades bandwidth.

Thermocouple Output EMF

V(emf) = S · (T1 − T0), where S is the Seebeck coefficient and T1, T0 are the hot and cold (reference) junction temperatures. K-type ≈ 41 µV/°C.
µV/°C
°C
°C
Output emf
Junction difference ΔT
A thermocouple measures a temperature difference, not absolute temperature. The cold (reference) junction must be measured — usually with an on-board sensor — and its slight Seebeck correction added. Coefficients are non-linear; for accuracy use a lookup table or ITS-90 polynomial, not just a single S.

Load-Cell Bridge → ADC Counts

Bridge differential = (mV/V) · Vex; amplified = ×G. Resolution = amplified full-scale ÷ 2^bits (one LSB), or input-referred µV/LSB = Vex·(mV/V)·G ÷ 2^bits.
V
mV/V
bit
Bridge diff (FS)
Amplified output
Resolution (LSB)
This is the ideal full-scale path through an instrumentation amplifier to an ADC. The amplifier must not saturate — keep G·Vdiff(full-scale) below the ADC's input range — and noise, bridge offset and ADC ENOB (not just bit count) degrade the real resolution.

Sensor Self-Heating Error

Power dissipated in the sensor is P = I²·R; the body warms by ΔT = P·θ, where θ is the thermal resistance (°C/W) to its surroundings.
A
Ω
°C/W
Dissipated power
Self-heating rise ΔT
Self-heating biases many resistive sensors: an RTD reads a few tenths of a degree too high unless you use low excitation, pulse the current, or do 4-wire (Kelvin) sensing. θ grows in a vacuum or with poor thermal contact — keep the sensor well coupled to what you want to measure.

NTC Linearization Resistor

A parallel resistor Rp flattens the NTC curve around a chosen temperature T0 and makes the string more linear. Rp_opt = RT0·(β−2T0)/(β+2T0), temperatures in kelvin.
Ω
K
°C
Optimal Rp
NTC at T0
The optimal Rp linearizes the R–T characteristic around T0, trading off sensitivity and range. A steeper β narrows the linear window; to maximise the near-linear span, put T0 near the middle of your measurement range.

Sensor Johnson-Noise Floor

Vn = √(4·k·T·R·BW). Johnson noise sets the thermodynamic floor for any resistive sensor, independent of excitation.
Ω
°C
Hz
×
Input noise Vrms
Output noise Vrms
kT at 25 °C is about 4.1×10⁻²¹ J. Halve the bandwidth or the resistance to reduce noise by √2. In a bridge the effective R is the output resistance (R1∥R2∥R3∥R4). Johnson noise is unaffected by higher excitation — raise signal via gain or lock-in techniques instead.

Parallel-Plate Capacitance

C = ε0·εr·A/d. Estimate force, pressure, level and proximity sensor capacitance, and stray coupling, from plate geometry.
·
cm²
mm
Capacitance C
ε0 = 8.854 pF/m. A small gap yields large capacitance per area (ideal for touch and force), but it also boosts sensitivity to mechanical tolerance and to stray fringe fields at the plate edges.

📊 Sensor Look-Ahead Diagrams

Linearization and noise trades for common sensors.

NTC LINEARIZATION raw steep R–T with Rp (flatter, offset) T0 T

NTC linearizationAdding Rp in parallel pulls the steep NTC tail down and straightens the transfer curve around T0. The price is reduced sensitivity and a resistance offset — accept it in firmware calibration.

SENSOR NOISE FLOOR Rs + noise gain G BW Vn = √(4kT·R·BW) Rs, gain and BW set the minimum detectable signal

Noise floorThe sensor, its interface resistance and the amplifier bandwidth together set the minimum detectable signal. Widening bandwidth or gain also multiplies noise — trade them against the required resolution and response speed.

CAPACITIVE SENSOR · C = εA/d dielectric εr d C = ε₀εr·A/d slide plate ⇒ ΔA A (overlap) sense via RC time / osc freq / bridge

Parallel-plate sensorCapacitance C = ε₀·εr·A/d changes with the electrode overlap A, the gap d or the dielectric constant εr. Read it as an RC time, an oscillator frequency or a bridge imbalance — measuring a change rather than an absolute value makes stray capacitance far less important.

SENSOR SIGNAL CHAIN sensor excite+ amp/filter ADC each stage's gain/offset lands on the ADC scale — units to counts

Sensor signal chainExcitation energizes the element, conditioning turns its small change into a clean voltage, the amplifier scales it and an anti-alias filter rejects out-of-band noise before the ADC. Design the chain end to end — gain, offset, and filter each decide how many counts map to the measurand.

📊 Sensor Diagrams

Wheatstone bridge, a 3-wire RTD connection, a photodiode transimpedance amplifier and a thermistor divider feeding an ADC.

WHEATSTONE BRIDGE Vbias excitation R1 R2 R3(+ΔR) +Vdiff − (to INA)

Wheatstone bridgeFour arms, one of which changes with the measurand (strain, pressure). Balanced arms give zero differential output; imbalance produces Vdiff proportional to ΔR/R, amplified by an instrumentation amp.

3-WIRE RTD Iexc Rlead Pt100 →V1 sense lead → V2 lead in the same loop as excitation and sense cancels out

3-wire RTDExcitation and both sense lines share one lead, so its resistance drops out of the measurement. This removes lead error without needing the more expensive four-wire connection.

PHOTODIODE TIA Iph photodiode R1 C1 op-amp + to GND Vout

Photodiode TIAThe photocurrent flows through Rf, and the op-amp holds the photodiode at zero reverse bias, converting Iph to a clean voltage Vout = Iph·Rf with Rf/Cf setting the bandwidth.

THERMISTOR → ADC Vcc R1 Rth GND ADC pin ● Vout

Thermistor dividerRth and R1 form a voltage divider whose output feeds the ADC. A small capacitor across the ADC pin plus a series resistor filters sampling glitches and RF noise.

THERMOCOUPLE + COLD JUNCTION metal A hot T1 metal B cold J on-board junction (T0) amp + ADC emf = S·(T1 − T0), ~µV see further measure T0 with a local diode/RTD and add the cold-junction Seebeck correction

Thermocouple & cold junctionTwo dissimilar metals join at the hot junction. The volt-µV signal is the difference between hot and the cold (reference) junction on the board; an on-board temperature sensor feeds the cold-junction compensation so the reading reflects T1 alone.

LOAD CELL → INA → ADC strain-gauge bridge (FS mV/V) Vex + − INA ×G diff o/p ADC N bit counts = G·Vdiff/2^N per LSB keep G·Vdiff(FS) < ADC span

Load-cell bridge to ADCExcite the strain-gauge bridge, amplify its small differential signal with an instrumentation amplifier, then convert with a delta-sigma ADC. The gain and ADC resolution together set how many counts one bit of load maps to.

4-WIRE (KELVIN) SENSING RTD / sensor R + self-heat I force I return sense '+' & '−' (no lead drop) ΔT = I²·R·θ — use low / pulsed I

4-wire Kelvin & self-heatTwo wires force the current, two more sense the voltage so lead resistance drops out of the reading. The bias current still heats the element by I²·R·θ, so keep excitation low and pulse it to trim the self-heating error.

RATIOMETRIC · Vexc = ADC REF Vexc R1 R2 R4 R3 + ADC code Vref = Vexc signal & reference both track Vexc → a slow droop cancels code = G·Vbridge/Vexc ∝ ΔR/R, rail noise rejected

Ratiometric excitation & ADCA bridge is usually excited from the same supply that later becomes the ADC reference. Both the bridge output and the reference scale with the supply, so a slow droop or ripple on Vexc cancels out of the final code — the reading stays proportional to ΔR/R, not to the supply rail, for less sensitivity to noise on the power line.

HALL SWITCH · B → DIGITAL OUT B Hall Ibias Vh thr hyst out Vh ∝ B·I → amp → comparator w/ hysteresis → clean on/off hysteresis band stops contact bounce & threshold chatter

Hall switch & biasA current-biased Hall plate develops a small voltage proportional to the perpendicular field (Vh ∝ B·I). An amplifier raises it, then a comparator with hysteresis converts the smooth analogue field into a clean digital on/off as the magnet sweeps by — the hysteresis band stops contact bounce and threshold chatter from stuttering the output.

📚 Sensor Reference Tables

Common sensor families and their typical signal conditioning. Values are representative — check each sensor's datasheet.

Common Sensors

TypeMeasuresOutputTyp. accuracy
Thermistor (NTC)temperatureresistance±1–5%
RTD (Pt100)temperatureresistance±0.1–1%
Thermocoupletemperature~µV/°C±0.5–2%
Strain gaugestrain / forceΔR (bridge)GF-based
Hall effectmagnetic fieldmV/G or switch±1–3%
Photodiodelightcurrent (TIA)band limited

Signal Conditioning

SensorFront-endNote
NTC thermistordivider + ADCneeds beta/Steinhart linearization
Pt100bridge + INAlead compensation (3/4-wire)
Thermocouplecold-junction + ampsmall signal, needs cold-junction ref
Strain gaugefull bridge + INAfour active arms maximize signal
PhotodiodeTIA (current→voltage)Cf sets noise/bandwidth balance

Amplifier Choice

NeedBest fitWhy
Bridge differentialInstrumentation amphigh CMRR rejects bias
Current→voltageLow-bias op-ampfA–pA bias, low noise
Small DC mV signalChopper / zero-driftremoves offset & drift
AC / pulsed sensorAC-coupled ampblocks offset, shapes bandwidth