# Inductive Displacement Sensor Operating in an LC Oscillator System Under High Pressure Conditions—Basic Design Principles

## TL;DR

A new inductive displacement sensor is designed to measure rock deformation under extreme pressure and temperature conditions, offering a cost-effective alternative to traditional sensors.

## Contribution

The paper introduces a novel inductive displacement sensor design for high-pressure environments with high-resolution strain measurements.

## Key findings

- The sensor achieves strain resolution of ~100 nm under pressures exceeding 400 MPa.
- The design balances electrical and mechanical parameters to maintain stable oscillations and high sensitivity.

## Abstract

What are the main findings?
Presentation of the basic design principles of an inductive displacement sensor for rock samples, enabling high-resolution measurements (≥10−6) in a high-pressure chamber under hydrostatic pressures of several hundred MPa and temperature variations of several tens of degrees Celsius.Discussion of the challenges and limitations related to sensor fabrication and the stability of the associated LC oscillator.

Presentation of the basic design principles of an inductive displacement sensor for rock samples, enabling high-resolution measurements (≥10−6) in a high-pressure chamber under hydrostatic pressures of several hundred MPa and temperature variations of several tens of degrees Celsius.

Discussion of the challenges and limitations related to sensor fabrication and the stability of the associated LC oscillator.

What is the implication of the main findings?
The presented sensor facilitates rock deformation measurements under pressure and temperature conditions equivalent to those at depths of several kilometres, which is critical in the context of increasing resource-extraction depths and the development of underground fuel-storage facilities.The presented sensor offers a low-cost, simple-to-fabricate solution with favourable metrological properties, providing a viable alternative to conventional sensors (e.g., resistive strain gauges), which face limitations under such conditions.

The presented sensor facilitates rock deformation measurements under pressure and temperature conditions equivalent to those at depths of several kilometres, which is critical in the context of increasing resource-extraction depths and the development of underground fuel-storage facilities.

The presented sensor offers a low-cost, simple-to-fabricate solution with favourable metrological properties, providing a viable alternative to conventional sensors (e.g., resistive strain gauges), which face limitations under such conditions.

The paper presents some design principles of an inductive displacement transducer for measuring the displacement of rock specimens under high hydrostatic pressure. It consists of a single-layer, coreless solenoid mounted directly onto the specimen and connected to an LC oscillator located outside the pressure chamber, in which it serves as the inductive component. The specimen’s deformation changes the coil’s length and inductance, thereby altering the oscillator’s resonant frequency. Paired with a reference coil, the system achieves strain resolution of ~100 nm at pressures exceeding 400 MPa. Sensor design challenges include both electrical parameters (inductance and resistance of the sensor, capacitance of the resonant circuit) and mechanical parameters (number and diameter of coil turns, their positional stability, wire diameter). The basic requirement is to achieve stable oscillations (i.e., a high Q-factor of the resonant circuit) while maintaining maximum sensor sensitivity. Miniaturization of the sensor and minimizing the tensile force at its mounting points on the specimen are also essential. Improvement of certain sensor parameters often leads to the degradation of others; therefore, the design requires a compromise depending on the specific measurement conditions. This article presents the mathematical interdependencies among key sensor parameters, facilitating optimized sensor design.