Brief
A voltage is not a measurement until you design the whole chain.
The task was to take a non-contact displacement transducer (NCDT) — whose inductance
shifts only slightly as a target moves — and design the full instrumentation path that
turns that shift into a stable, low-noise DC voltage fit for measurement. The
requirements set the bar: a single inductive sensing element, an output proportional to
displacement, a fixed 0–100 mV range, minimised noise, quantified linearity
error, and complete signal conditioning.
The Sensor
Inductance that tracks displacement.
The NCDT is modelled as L(x) = L₀(1 + kx), where L₀ is the null-position inductance
and k the sensitivity. Deliberately, only one inductive element is placed in the
bridge — trading a little sensitivity for far less magnetic noise, permeability drift, and
inductive-mismatch error than a multi-coil arrangement.
The Bridge
A mixed L–C AC bridge converts inductance to voltage.
The sensor sits in a mixed L–C AC bridge — the variable inductance L(x), a fixed
L₀, a precision NP0/C0G capacitor C, and a precision resistor R — excited by a
sinusoidal source. The differential output works out to V₀ = Vₛ · kx / (1 − (kx)²),
which for small displacement collapses to the clean linear law V₀ ≈ Vₛ · kx.
Error Budget
Quantify the nonlinearity instead of hand-waving it.
Linearity is treated as a number, not an adjective. The small-displacement approximation
contributes ≈ 1.01% error at kx = 0.1; air-gap reluctance adds a magnetic
nonlinearity of ≈ 0.5% FS; together the design carries a total linearity error of
≈ 1.5% of full scale — stated honestly so the measurement’s trustworthiness is known up
front.
Signal Conditioning
Rectify, scale, and filter to a clean 0–100 mV.
The AC bridge output is conditioned in three stages:
- a precision full-wave rectifier (super-diode) recovers magnitude without the diode
forward-voltage error a passive rectifier would add;
- a difference amplifier (G = 15) scales the rectified signal so full-scale
displacement maps to the target 100 mV;
- a 2nd-order active low-pass filter (f_c = 20 Hz) strips the AC carrier ripple and
high-frequency noise, leaving a steady DC reading.
Value
Measurement fundamentals, done properly.
Sensor modelling, bridge analysis, an explicit error budget, and a complete
conditioning chain — the unglamorous core of instrumentation, and the difference between
reading a sensor and actually measuring something with it.