Sensor Guide

Pressure Sensor and Analog Scaling: 4–20 mA, Live Zero, and Error Budgets

Treat scaling as a complete measurement interface: transfer function, electrical loading, loop headroom, diagnostics, conversion accuracy, and verification.

18 min · Intermediate · Updated October 12, 2026

One Signed Model for Voltage and Current

A linear transmitter is defined by two electrical points and two engineering points. Keep all values in canonical units internally and retain signs. This avoids separate, error-prone equations for zero-based, live-zero, offset, bipolar, and reverse-acting ranges.

Formula reference

Two-Point Scaling

X = X1 + (E - E1)(X2 - X1)/(E2 - E1)E = E1 + (X - X1)(E2 - E1)/(X2 - X1)m = (X2 - X1)/(E2 - E1)Span fraction = (E - E1)/(E2 - E1)

Variable definitions

E: measured voltage or current
X: pressure or other engineering quantity
E1, E2: electrical endpoints
X1, X2: engineering endpoints; Both endpoint spans must be nonzero

Use the Analog Sensor Linear Scaling Calculator for signed forward and inverse conversions, or the Pressure Sensor Scaling Calculator for pressure-specific voltage, current-loop, calibration, and receiver-resistor workflows.

Choose the Electrical Interface

Interface	Typical Use	Design Checks
0–5 V or 0–10 V	Simple local interface	Ground offset, cable noise, ADC overvoltage, source impedance
0.5–4.5 V or 1–5 V	Powered voltage output with diagnostic headroom	Supply/reference behavior, ratiometric assumptions, output loading
4–20 mA	Long cable and industrial transmitter	Compliance voltage, receiver burden, loop grounding, fault bands
Reverse acting	Level, valve, pressure, or position convention	Signed slope and endpoint labeling

4–20 mA Live Zero and Receiver Design

For a nominal 4–20 mA transmitter, 4 mA is 0% span, 12 mA is 50%, and 20 mA is 100%. Dividing current by 20 mA is wrong because it treats the live-zero offset as measurement span. The receiving resistor converts loop current to voltage, but it is also a series burden.

Formula reference

Current-Loop Relationships

x = (I - 4 mA)/16 mAP = Pmin + x(Pmax - Pmin)VR = I × RVavailable ≥ VTX,min + Imax(Rwire + Rreceiver + Rprotection)

Variable definitions

x: signed fraction of calibrated span
Rreceiver: current-to-voltage resistor
VTX,min: minimum transmitter terminal voltage; Use worst-case supply, maximum current, hot wiring resistance, and protection drops

Example: a 0–10 bar transmitter at 12 mA reports 5 bar. A 250 Ω receiver produces 3 V at 12 mA and 5 V at 20 mA. At full scale it consumes 5 V of compliance; that voltage must remain available after cable, protection, and transmitter drops.

Fault Bands and Out-of-Range Values

Do not assume every value below 4 mA means an open wire, or that every value above 20 mA means overpressure. Transmitters use device- and standard-specific underrange, overrange, alarm, startup, and fault behavior. Consult the datasheet and system convention.

Preserve the raw electrical reading and a calculated engineering value, then add a separate quality state. Early clamping hides wiring faults and makes commissioning harder. Protection must also tolerate credible open-circuit, reverse-polarity, surge, and overvoltage conditions.

ADC Range, Loading, and Resolution

Choose the receiver resistor and analog gain so normal and diagnostic ranges fit inside the ADC input and protection limits.
Include resistor tolerance, reference error, ADC gain/offset/INL, amplifier error, source impedance, settling, noise, and temperature coefficients.
Verify acquisition settling for multiplexed ADCs; a high source impedance can cause code-dependent error even when DC loading appears acceptable.
Use anti-alias filtering based on the required signal bandwidth, not simply the sample rate.
Keep raw codes and calibrated engineering results separate so diagnostics remain traceable.

The Sensor ADC Resolution Calculator estimates code span and engineering resolution, but nominal LSB size is not total measurement accuracy.

Build an Error Budget

Separate offset terms from span terms and random noise from bounded specifications. Convert each contributor into a common engineering unit at the operating point. A two-point calibration can correct initial offset and gain but does not erase nonlinearity, hysteresis, repeatability, temperature drift, aging, or dynamic response.

Formula reference

Error References

eX,electrical = |m| × eEeX,span ≈ |X - X1| × espanWorst-case bound = Σ|ei|Independent random RSS = √Σ(ei²)

Variable definitions

m: signed engineering units per electrical unit
eE: input-referred electrical uncertainty
espan: fractional span error; Use RSS only for independent random terms with compatible confidence

Calibration and Verification Workflow

Confirm pressure reference, absolute/gauge/differential convention, units, and endpoint order.
Measure electrical zero after warm-up and check the raw diagnostic state.
Apply traceable points across the range in both directions to expose hysteresis.
Fit offset and gain, then inspect residual error rather than reporting only a high R² value.
Repeat at temperature and minimum/maximum supply or loop voltage.
Verify receiver burden and cable drop at maximum current.
Inject underrange, overrange, open-wire, and recovery conditions.
Store calibration coefficients with units, date, configuration, and traceability.

Use the Sensor Calibration Calculator for fitted slope, intercept, residuals, and inverse conversion.

Common Mistakes

Treating a 4–20 mA span as 20 mA instead of 16 mA.
Assuming 0 mA represents 0% process value.
Clamping raw readings before fault classification.
Ignoring receiver burden in the compliance budget.
Taking the absolute value of a reverse-acting slope.
Calling ADC resolution the same thing as accuracy.
Correcting two endpoints and claiming nonlinearity is removed.
Mixing gauge, absolute, and differential pressure references.
Ignoring source impedance and ADC acquisition settling.
Combining maximum errors with statistical RSS without justification.

Scope Boundary

This guide covers substantially linear analog pressure and sensor interfaces. It does not replace transmitter safety certification, intrinsic-safety design, hazardous-area installation rules, fluid-system analysis, nonlinear sensor compensation, SIL calculations, or device-specific alarm conventions. Verify critical systems with datasheets, applicable standards, traceable calibration equipment, environmental testing, and fault injection.

Support reference

FAQ

How do I scale a sensor signal into engineering units?

Define two electrical endpoints and their corresponding engineering endpoints, then use signed linear interpolation. Preserve the endpoint order so direct-acting and reverse-acting sensors use the same equation.

Why is the active span of a 4–20 mA loop 16 mA?

The measurement span is the upper endpoint minus the lower endpoint: 20 mA minus 4 mA equals 16 mA. The 4 mA offset is the live zero, not part of the active span.

What does live zero mean?

Live zero means the lower measurement endpoint is represented by a nonzero signal, normally 4 mA. It provides operating current and leaves signal space below the normal range for diagnostics defined by the transmitter and system.

How do I convert 4–20 mA to voltage?

Place a precision receiver resistor in the loop and use V = IR. A 250 ohm resistor produces 1–5 V at 4–20 mA, but its voltage drop consumes loop compliance voltage.

What is loop compliance voltage?

It is the voltage available to overcome the transmitter minimum operating voltage plus wiring, protection, receiver, and other series drops at the required current. A loop can scale correctly on paper yet saturate if this budget is insufficient.

Should values below 4 mA or above 20 mA be clamped?

Do not clamp them before diagnostics. Preserve the raw value, classify normal, underrange, overrange, or fault behavior using the device specification, and clamp only a separate user-facing control value when the application requires it.

How do I handle a reverse-acting sensor?

Keep the signed electrical and engineering spans. Do not apply an absolute value to the slope; a negative slope is valid when increasing signal represents decreasing process value.

Is a two-point calibration enough?

It corrects offset and gain for a substantially linear sensor. It does not remove nonlinearity, hysteresis, temperature drift, noise, loading, aging, or dynamic error, which require separate characterization.