Concept

Synchronous detection — where it appears

Measuring a carrier-borne signal by multiplying it by a reference at the same frequency and averaging, so that only the part in phase with the reference survives. It rejects noise and quadrature signals, and its accuracy depends on where the reference's phase is taken.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

Calibrated at the carrier, a matched cable allows 121 kHz where its phase allowed 16.5 kHz. computed by solving, not by drawing. A 350 Ω quarter bridge read through ten metres of screened pair, excited over leads of 0.35 Ω and 3 µH each with 500 pF between them. Solid: the worst error of a synchronous reading over strains from −2000 to +2000 µε after a calibration at +1000 µε at the operating carrier, with the reference taken from the source at the instrument; dashed, from the bridge's own terminals on sense wires; dotted, the phase measure 1 − cos φ the earlier readings of this cable used. For a 200 ppm budget: 16.5 kHz by phase, 119 kHz calibrated against the source and 121 kHz calibrated against the bridge.

What a calibration at the carrier removes

The phase a cable puts on a carrier-excited bridge is a loss of 1 − cos φ, and a loss that is the same at every strain is a gain error — which a shunt calibration at the operating carrier exists to remove. Calibrated there, a synchronous reading of a quarter bridge through ten metres of matched screened pair allows 121 kHz for 200 ppm over ±2000 µε, where the phase measure allowed 16.5; the capacitance between the conductors, which no matching could improve, stops mattering. Where the reference is taken — at the instrument or from sense wires at the bridge — moves that by 1.2 per cent. What calibration cannot touch is a screen mismatch: its leak is a fixed voltage, not a fixed gain, and a hundredth of a per cent of it takes 121 kHz back to 11.5.

applied · Bridge

A 1% mismatch in the cable reads as 3.0% of full-scale displacement, at every frequency. computed by solving, not by drawing. A capacitive displacement sensor — two 10 pF plates driven at ±5 V in antiphase facing a common electrode — read by a charge amplifier through two metres of three-conductor cable with 30 pF a metre between each excitation conductor and the sense conductor. With the two cross-capacitances mismatched by 1 per cent and the sensor centred, the reading's in-phase part (solid) is 3.00 per cent of full scale at every carrier from 100 Hz to 1 MHz: the cable is a sensor capacitance, and its mismatch a displacement. The quadrature part (dashed), which the cable's resistance makes, rises with frequency and a synchronous detector rejects it. With each conductor in its own screen the cross-capacitance is gone and so is the error.

The sensor that is the capacitance

Read a capacitive displacement sensor through the same kind of cable that limited a strain-gauge bridge's carrier, and the roles exchange. On the bridge, a 1% mismatch in the cable's capacitance was a quadrature leak that grew as the square of the carrier and could be escaped by a lower one. On a sensor of two 10 pF plates it is 3.0% of full-scale displacement, in phase, at every carrier from 100 Hz to 1 MHz — because a capacitance between an excitation conductor and the sense conductor is in parallel with the measurand and is a sensor capacitance. No detector phase separates it and no carrier escapes it; only geometry does. Screen each conductor separately and there is nothing left to mismatch.

applied · Bridge

A reference 0° behind the excitation at 20 kHz, after a calibration at +1000 µε: matched, the worst error is 5.79 ppm; with a tenth of a per cent of screen mismatch, 0.607%. computed by solving, not by drawing: the error of a synchronous reading of a 350 Ω quarter bridge through ten metres of screened pair, against the strain read, with the reference 0° from the excitation at the bridge and a shunt calibration at +1000 µε through the same reference, for a matched screen (solid) and for 0.01 and 0.1 per cent of mismatch. The calibration takes out cos(φ − θ), because it multiplies the signal at every strain. It cannot take out a voltage that does not scale with the strain, and the mismatch's leak is such a voltage: a hyperbola through zero at the calibration strain. Worst over ±2000 µε: 0%: 5.79 ppm, 0.01%: 606 ppm, 0.1%: 0.607%.

The reference that should be late

A carrier amplifier's reference is taken from the excitation because that is what the output is meant to be in phase with, and nothing says that is where it belongs. A screen mismatch's leak arrives late by the common-mode node's lag and the difference's together, 525 ns on ten metres of pair and a 350 Ω bridge, so a reference on the excitation reads sin 3.7° of it at 20 kHz: 0.607 per cent of error at a tenth of a per cent of mismatch, and 72.6 parts per million with the reference 3.7° late. The null is a delay rather than a phase and does not move with the mismatch, and a delayed reference allows about five times the carrier on any mismatched screen. How exactly it must be held narrows as mismatch times carrier.

applied · Bridge

Named alongside it

The objects these essays reach for when they reach for this one.

Measurement error Parasitics Calibration Device mismatch Strain gauge Wheatstone bridge Capacitive sensor Charge amplifier Common-mode rejection Design tradeoff Excitation Guarding

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