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ISSN 1748-0221
11:59 - Friday, 29 September 2023
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    JINST Instrumentation Theses Archive

2023 JINST TH 005    

Ph.d. degree
Indian Institute of Science, Bengaluru, India, 2019

Pankaj Sagar

Supervisor: R. Karunanithi

Cryogenic Instrumentation using Planar Inductor based Eddy Current Sensors


  • Instrumentation for particle accelerators
  • Detection of defects
  • Data acquisition circuits
  • Data acquisition concepts


Cryogenic sensors have become vital in the measurement of crucial parameters in the modern scientific research. My thesis dissertation addresses the design, development and testing of PCB-based planar inductors and associated cold electronics for different types of sensors working at cryogenic temperatures. PCB-based sensors utilize commercial FR4 fabrication processes involving layered bonding processes and selective etching to produce the required structure. Sensors that perform three different operations but use planar inductors are presented here.
The first sensor that was designed as a multilayer planar inductor-based eddy current proximity/displacement transducer. The first part of the work on the sensor involved the study of the behavior of PCB (FR4) based multilayer inductors at low temperatures. Structural analysis of the sensor was done using Ansoft structural analysis software. The structural changes (warping) that were observed in the simulation studies were experimentally verified using the variation of capacitance between the layers of the inductors when the sensor was cooled. This data was also compared with the Ansoft Maxwell models of the same sensors. The second part of the work used the designed multilayer inductor to develop a proximity sensor capable of working down to 4.2 K. Proximity/displacement of a metal surface/ target in the range of 0-5 mm could be measured using this sensor. The use of a cold electronics-based LC oscillator operating at 4.2 K using thermal cycled stable components was also reported. Effective realization of inductor-based sensors require the signal conversion and signal conditioning elements to be as close to the sensing element as possible. This required me to develop electronic circuits which are capable of working at cryogenic temperatures without any drastic changes in parameters or at least predictable changes in parameters. A detailed study of performance analysis of unbuffered inverter-based LC development is also discussed. This is a part of the sensor system used in the proximity sensor as well as an angular displacement sensor. The effect of temperature variation on cold electronics-based LC oscillators is analyzed. This variation in temperature causes the oscillator to change its operating frequency. Certain additional harmonics are also introduced into the output waveform at lower temperatures. Variation in the output of the oscillator is studied from 300 K to 4.2 K. The frequency modulated (FM) oscillator output is a function of displacement. Calibration of the developed sensor at cryogenic temperatures was performed to ascertain the sensitivity and repeatability. Impedance analysis of the planar multilayer inductor is presented and its Q-factor is determined. Experimental results of the noise characteristics of the oscillator at various temperatures are also discussed. The developed sensor has good thermal stability, sensitivity, and repeatability at cryogenic operating temperatures.
The second sensor was a cryogenically operated (down to 4.2 K) multilayer planar inductor array-based eddy current angular position/rotation transducer. An array of four multi-layered coils is used to divide the 360° into four sectors of 90° each. Switching between each of the inductors is done by a cold electronics-based multiplexer circuit coupled to an unbuffered inverter LC oscillator that has been described in the previous section. The angular displacement is a function of the frequency of the cold electronic LC oscillator. The pickup coil forms the inductor of the oscillator which is operated down to 4.2 K and uses thermal cycled stable components. The design and optimization of the rotor components are also discussed in detail. The change in frequency as a function of angular displacement was calibrated at cryogenic temperatures. The developed sensor was found to have good thermal stability, sensitivity, and repeatability over the entire cryogenic range.
The final section describes different methods to measure the Residual Resistivity Ratio (RRR) of Nb samples. RRR is an important parameter that dictates the purity and in turn the performance of the Superconducting Radio Frequency (SRF) cavity at low temperatures (≤ 4.2 K). The usual method of 4-wire electrical resistance measurement is both destructive in nature and produces a non-local (average) measurement of electrical conductivity. Here, a non-contact and local RRR measurement technique utilizing eddy current principle is presented utilizing multilayer planar inductor sensing element. Three different approaches are explored; all utilizing the impedance variation of the sensing coil and correlating it directly with the RRR of the sample. The initial approach uses the slope of lift-off lines generated by the impedance variation when the conductivity of the Nb sample changes. The ratio of the slopes of the lift-off lines become equal to the ratio of the conductivity of the metal (RRR). The second approach correlates the inductance variation of the sensing coil with the RRR of the sample. Here the sensing element is coupled to a multiplexed cold electronics-based LC oscillator.
The changes in inductances are converted to changes in frequency and hence a calibration chart relating frequency to RRR is obtained. The third approach utilizes the direct relation of the eddy current penetration depth of the conductivity of the metal. If a sample's conductivity increases, the penetration depth changes (decreases). So, in order to maintain a skin depth equal to the thickness of the sample, frequency has to be reduced. From the value of absolute inductance at these inflection frequency points, RRR can be calculated. It should also be noted that the principles used to measure the RRR of Nb samples can be extended to measure the conductivity change of any nonmagnetic metals at cryogenic temperatures. Here, a different approach is undertaken to utilize cold electronics-based dual switched oscillator circuits to measure the impedance changes associated with the sensing element. Two different oscillator circuits are used in tandem to achieve the above. This switched oscillator circuit technique is used to determine the impedance of a cryogenic sensing coil at 295 K and 77 K with different metal targets kept at specific distances. Experimental data is compared with that of an impedance analyzer circuit and measurement errors are also presented.

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