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Variable Inductance and Capacitance Transducers

Variable Inductance and Capacitance Transducers

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Sep 11, 2026

A transducer converts a physical quantity into a usable electrical signal. Variable-inductance and variable-capacitance transducers are generally passive transducers: they require external excitation, and the measured quantity changes an electrical parameter rather than directly generating energy.

  • Variable inductance transducer
  • Variable capacitance transducer
  • Passive transducer
  • Measurand

These devices are widely used for displacement, position, pressure, force, vibration, level, thickness, and proximity measurement. Their output is usually processed using an AC bridge, oscillator, demodulator, frequency converter, or capacitance-to-digital circuit.2

Footnotes

  1. Inductive Transducer Working & Its Applications - Overview of self-inductance, mutual-inductance, and eddy-current operating principles. ↩

  2. What is Capacitive Transducer? - Definition, passive operation, and measurement applications of capacitive transducers. ↩

Core distinction

An inductive transducer responds to changes in magnetic coupling or magnetic reluctance, whereas a capacitive transducer responds to changes in electrode geometry or dielectric permittivity.

1. Variable Inductance Transducer

A variable-inductance transducer operates by changing the inductance of a coil or the mutual inductance between coils. The inductance of a coil is approximately

L=N2RL = \frac{N^2}{\mathcal{R}}

where NN is the number of turns and R\mathcal{R} is the magnetic reluctance. Therefore, moving a ferromagnetic core, changing an air gap, or altering magnetic coupling changes LL.

The impedance of an energized coil is

Z=R+jωLZ = R + j\omega L

where RR is resistance, ω\omega is angular frequency, and LL is inductance. A change in inductance consequently produces a change in voltage, current, impedance, or bridge output.2

  • Magnetic reluctance
  • Mutual inductance
  • Self-inductance
  • Variable reluctance

Main operating methods

  1. Variable self-inductance: movement changes the inductance of one coil.
  2. Variable mutual inductance: movement changes the coupling between a primary and secondary coil.
  3. Eddy-current principle: movement of a conductive target changes the coil impedance through induced currents.

Footnotes

  1. Inductive Transducer Working & Its Applications - Overview of self-inductance, mutual-inductance, and eddy-current operating principles. ↩ ↩2

  2. Transducers: Unit 2 Course Material - Academic notes covering inductive and capacitive transducer characteristics and limitations. ↩

Working of a Variable-Inductance Transducer

  1. 1
    Step 1

    An AC voltage is applied to the sensing coil or primary winding.

  2. 2
    Step 2

    The energized coil establishes a magnetic field through its core, air gap, or nearby target.

  3. 3
    Step 3

    The measurand moves a core, changes an air gap, or changes the position of a conductive target.

  4. 4
    Step 4

    The magnetic reluctance or coil coupling changes, producing a corresponding change in self-inductance or mutual inductance.

  5. 5
    Step 5

    A bridge, demodulator, oscillator, or impedance circuit converts the electrical change into a calibrated output.

  6. 6
    Step 6

    The conditioned signal is related to displacement, force, pressure, vibration, or another physical quantity.

Linear Variable Differential Transformer

The LVDT is the most important practical variable-inductance transducer for linear displacement. It contains one primary winding, two identical secondary windings, and a movable soft-iron core. The secondary windings are connected in series opposition. An AC excitation applied to the primary induces voltages E1E_1 and E2E_2 in the secondary windings.

The differential output is

Eo=E1−E2E_o = E_1 - E_2

At the central or null position, E1≈E2E_1 \approx E_2, so the output is nearly zero. When the core moves toward one secondary, its induced voltage increases while the other decreases. The magnitude of EoE_o indicates displacement, and its phase indicates direction.

LVDT characteristics

  • Contactless operation between the core and windings gives very long mechanical life.
  • It provides high resolution because displacement is measured continuously.
  • The output is approximately linear over its specified central range.
  • It requires AC excitation and usually requires demodulation to obtain a DC output.
  • Shielding may be necessary because external magnetic fields can affect the measurement.2

Other variable-inductance arrangements

ArrangementQuantity changedTypical application
Variable air-gap sensorAir-gap length and reluctanceSmall displacement, vibration
Movable-core coilCore positionLinear position
Differential reluctance sensorTwo opposing magnetic gapsPosition and force
Eddy-current sensorCoil impedance due to induced currentsNon-contact displacement and thickness
LVDTMutual inductance between primary and secondariesPrecision linear displacement

Footnotes

  1. The LVDT Construction Process - Construction, mutual-induction operation, and practical LVDT characteristics. ↩ ↩2

  2. Linear Variable Differential Transducer - Description of LVDT construction, excitation, operation, and applications. ↩

Qualitative Comparison of Inductive and Capacitive Transducers

Relative engineering tendencies; actual performance depends on design and operating conditions.

Variable-Inductance Transducer: Advantages, Limitations, and Uses

2. Variable Capacitance Transducer

A variable-capacitance transducer uses a capacitor whose capacitance changes with the measurand. For a parallel-plate capacitor,

C=εAdC = \frac{\varepsilon A}{d}

where CC is capacitance, ε=ε0εr\varepsilon = \varepsilon_0\varepsilon_r is permittivity, AA is effective overlapping area, and dd is separation between plates.2

Capacitance can be varied in three principal ways:

  1. Changing the distance dd between plates.
  2. Changing the overlapping area AA.
  3. Changing the dielectric constant εr\varepsilon_r between the plates.
  • Permittivity
  • Dielectric
  • Fringing field
  • Guard electrode

For a small displacement Δd\Delta d with constant AA and ε\varepsilon,

ΔCC≈−Δdd\frac{\Delta C}{C} \approx -\frac{\Delta d}{d}

Thus, reducing the plate separation increases sensitivity, although excessive reduction can cause mechanical contact or electrical breakdown.

Footnotes

  1. What is Capacitive Transducer? - Definition, passive operation, and measurement applications of capacitive transducers. ↩

  2. FDC1004: Basics of Capacitive Sensing and Applications - Capacitor equations, sensing structures, fringing fields, and practical capacitive-sensing considerations. ↩

Working of a Variable-Capacitance Transducer

  1. 1
    Step 1

    Arrange two conductive electrodes with a controlled gap, overlap, or dielectric region.

  2. 2
    Step 2

    Connect the capacitor to an AC bridge, oscillator, charge amplifier, or capacitance-measurement circuit.

  3. 3
    Step 3

    The measurand changes plate spacing, overlap area, dielectric thickness, or dielectric permittivity.

  4. 4
    Step 4

    The capacitance changes according to C=εA/dC = \varepsilon A/d.

  5. 5
    Step 5

    The circuit converts the change into voltage, current, frequency, phase, or digital code.

  6. 6
    Step 6

    The electrical output is related to displacement, pressure, level, humidity, force, or another measurand.

Constructional forms

1. Variable-gap type

One plate is fixed and the other is movable. Displacement changes dd:

C=εAdC = \frac{\varepsilon A}{d}

This type is useful for small displacement, vibration, pressure diaphragm, and acceleration measurements.

2. Variable-area type

The separation remains approximately constant while the overlapping area changes:

C=εA(x)dC = \frac{\varepsilon A(x)}{d}

It is often designed to obtain a more nearly linear relationship between displacement xx and capacitance.

3. Variable-dielectric type

A material enters or leaves the electric field, changing εr\varepsilon_r. This arrangement is useful for liquid level, moisture, material composition, and proximity sensing.2

Footnotes

  1. What is Capacitive Transducer? - Definition, passive operation, and measurement applications of capacitive transducers. ↩

  2. FDC1004: Basics of Capacitive Sensing and Applications - Capacitor equations, sensing structures, fringing fields, and practical capacitive-sensing considerations. ↩

Signal conversion

A capacitive sensor may be connected to:

  • An AC bridge, where imbalance represents ΔC\Delta C.
  • An oscillator, where capacitance changes oscillation frequency.
  • A charge amplifier, where charge variation is converted to voltage.
  • A capacitance-to-digital converter, where the result is digitized directly.

For a simple RC oscillator, frequency commonly varies with capacitance according to a relationship of the form

f∝1RCf \propto \frac{1}{RC}

The exact relationship depends on the oscillator topology. Modern capacitive sensing systems use shielding, driven guards, differential electrodes, and calibration to reduce parasitic capacitance.2

Footnotes

  1. FDC1004: Basics of Capacitive Sensing and Applications - Capacitor equations, sensing structures, fringing fields, and practical capacitive-sensing considerations. ↩

  2. Capacitive Sensors - Non-contact capacitive measurement, electrode geometry, and distance dependence. ↩

Variable-Capacitance Transducer: Advantages, Limitations, and Uses

Common examination error

Do not state that a capacitive transducer always measures only displacement. Displacement is measured by changing gap or area, but pressure, level, humidity, and composition can also be measured by changing dielectric properties or by mechanically deflecting an electrode.

3. Comparison

FeatureVariable inductanceVariable capacitance
Basic parameterSelf-inductance, mutual inductance, or coil impedanceCapacitance
Governing relationL=N2/RL = N^2/\mathcal{R}C=εA/dC = \varepsilon A/d
ExcitationUsually ACAC, oscillator, charge, or digital excitation
Main mechanical actionCore movement, air-gap change, magnetic couplingGap change, area change, dielectric change
Typical outputDifferential voltage, impedance, or frequencyBridge voltage, frequency, charge, or digital code
StrengthsRugged, reliable, good industrial performanceHigh sensitivity, compact, low power, non-contact
Main error sourcesStray magnetic fields, temperature, core nonlinearityStray capacitance, cable effects, humidity, contamination
Typical examplesLVDT, variable-reluctance sensor, eddy-current probeParallel-plate displacement sensor, capacitive proximity sensor
Best suited toIndustrial displacement and positionFine displacement, proximity, level, dielectric measurement

How to Write a Short Examination Note

  1. 1
    Step 1

    State that it is a passive sensor whose inductance or capacitance changes with the measurand.

  2. 2
    Step 2

    For inductive types, mention magnetic reluctance or mutual induction. For capacitive types, write C=εA/dC = \varepsilon A/d.

  3. 3
    Step 3

    Mention the coil and movable core for an inductive device, or electrodes, gap, and dielectric for a capacitive device.

  4. 4
    Step 4

    Show how displacement or another physical quantity changes the electrical parameter and how the circuit produces output.

  5. 5
    Step 5

    Include sensitivity, ruggedness, excitation requirements, stray effects, and environmental limitations.

  6. 6
    Step 6

    Conclude with two or more practical uses, such as LVDT position measurement or capacitive level and proximity sensing.

Revision Flashcards

1 / 7
Question · Term

What is the principle of a variable-inductance transducer?

Click to reveal
Answer · Definition

The measurand changes self-inductance, mutual inductance, magnetic reluctance, or coil impedance.

Memory aid

Inductive sensors depend on magnetic path: think core, coil, and reluctance. Capacitive sensors depend on electric-field geometry: think area, gap, and dielectric.

Knowledge Check

Question 1 of 4
Q1Single choice

Which equation represents the capacitance of an ideal parallel-plate capacitor?

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