Ing. Mehran Mirzaei, Ph.D.

—The main goal of this paper is to present a novel 3D analytical method for precise and fast modeling of rotational eddy current speed sensors with cylindrical structures. An equivalent linearized model is developed using a multi-slice structure. The cylindrical structure of rotational eddy current sensors is modeled using the multi-slice linearized structure. The 3D distribution of induced eddy current in the rotating conductive rods is considered in the analytical modeling. The method of separation of variables using Fourier series is utilized for the analytical analysis of rotational eddy current speed sensors. The new calculation method is tested on the eddy current speed sensor with perpendicular coils and different rotating rods. The analytical results are compared with the calculations of 3D time harmonic and time stepping finite element methods. The measurements on the sensor prototype verified the calculations. When compared to the 3D Time Harmonic FEM, the 3D analytical method is 12-times faster.

This paper presents an axial flux eddy current sensor with a compact and simple structure for measuring the rotating speed of iron shafts. The sensor structure is optimized for high sensitivity with a novel configuration of the coils positioned perpendicularly to each other. The sensor comprises two D-shaped excitation coils and two D-shaped pick-up coils in a double-layer structure. A disc-shaped magnetic shield or core shields the coils. Two iron shafts with different material properties are considered. A new cup-shaped configuration of nonmagnetic copper and aluminum caps mounted on iron shafts improves sensitivity and suppresses susceptibility to shaft material properties and airgap variation. 2D and 3D finite element methods are utilized for the performance analysis of the sensor. The measurements are performed at speeds up to ± 3000 rpm and different excitation frequencies from 400 Hz to 4 kHz. The eddy current speed sensor has excellent linearity characteristics with a nonlinearity error of 0.15%. The geometry of the coils is further optimized and improved for maximum sensitivity and compactness. The fault-tolerant capability of the sensor is also evaluated.

This paper presents the novel structure of an eddy current sensor for linear speed measurements. The sensor has one excitation coil and two pairs of antiserially connected pick-up coils, which are located inside and outside the excitation coil. The design and modeling of the sensor are considered with an air core and with a magnetic yoke (core) to compare their performances in terms of sensitivity and nonlinearity error. The experiments and the analysis are performed at different excitation frequencies and speeds. A novel 3D analytical method is developed and utilized for parametric analysis and for the design of this sensor. The simulation results are compared with measurements up to 16.7 m/s (60 km/h). The achieved nonlinearity error is as low as 0.3%

Demagnetization factor and corresponding apparent permeability for multiwire arrays using the 3-D finite element method (FEM) are calculated in this article. The effect of distance between magnetic wires on the demagnetization factor and apparent magnetic permeability is studied for various values of relative magnetic permeability. The simulations are compared with experimental results on arrays up to 91 wires. A novel simplified equivalent 2-D model for wire arrays is presented in this article, as a fast method for calculations. The simplified axisymmetrical model consists of a set of hollow cylinders with equivalent volume. The results of the proposed simplified 2-D model fit very well the full 3-D FEM simulations and experimental results. Two different hexagonal and square arrangements for wires are considered both for the simulations and the measurements.

This paper presents a novel configuration of the eddy current speed sensor to measure the rotating speed of iron rods and shafts up to 3000 rpm. The proposed eddy current speed sensor has an axial airgap structure with one excitation coil and two antiserially connected pick up coils. The speed sensor is mounted in the end shaft part region. Different solid iron materials for rotating shaft are considered in the measurements and calculations to evaluate solid iron material effect on the eddy current speed sensor performance. 2D and 3D finite element method is utilized for the performance analysis of the speed sensor. Also, a 2D analytical method is developed for parametric analysis. A copper rod is also used to compare the speed sensor with the rotating iron shaft and copper shaft. Finally, two thin copper discs with different diameters are mounted on the solid iron shaft and their influences on the eddy current speed sensor were evaluated and measured to increase sensitivity and decrease sensor dependency on the permeability of the solid iron shaft. The achieved nonlinearity errors are about ±0.2%.

Using the equivalent 2D model for finite element method (FEM) we calculated apparent permeability μa and demagnetization factor D for permalloy nanowire and microwire arrays. The simulation results were verified by 3D FEM for arrays up to 3000 wires and experimentally for very large arrays containing up to 40 million wires. We achieved μa = 3 to 33 and coercivities Hc = 1 to 9 kA/m, which are low values for wire arrays. The μa depends mainly on the array geometry; it can be increased by increasing the distance between wires (pitch) and the wire length-to-diameter ratio L/d.

A novel eddy current sensor is proposed in this paper for conductivity measurement of nonmagnetic metals. It has one excitation coil and two antiserially pick up coils. The three coils have rectangular forms with the equilateral triangular arrangement. The induced voltage of antiserially connected pick up coils is zero when all coils are far enough from conductive objects. However, the induced voltage is nonzero when one pick up coil is close to the conductive object due to the induced eddy currents in the conductive objects and unequal flux linkage in the pick up coils. The real and imaginary components of the induced voltage and their ratio are functions of plate conductivity. The experiments and 3D finite element method analysis of the triple coils sensor are conducted for conductivity measurement of nonferrous plates to estimate their conductivities. The accuracy of the eddy current sensor was tested and analyzed, showing that its error can be as low as 0.2%. Conductivity measurement is also presented using measured impedance change of single rectangular coil parallel to conductive plates with minimum accuracy error 0.4% and the results of conductivity estimation are compared with triple coils sensor.

This paper presents the design and modeling of an eddy current speed sensor for nonmagnetic moving rods with an axisymmetric configuration. The sensor consists of two antiserially connected excitation coils and one pick up coil located between two excitation coils. A novel computational approach using the combined finite difference method and Fourier series is proposed for the modeling and simulations of the eddy current speed sensor. The effects of the outer diameters of moving nonmagnetic rods and their electrical conductivities on the performance of speed sensor are originally evaluated. The results of the modeling for the eddy current speed sensor are compared with the measurements at time varying speeds and various frequencies. The comparison between modeling and experimental results shows the appropriateness of the eddy current speed sensor for the speed measurement of nonmagnetic rods.

Nanocrystalline and amorphous stress-annealed and field annealed tapes are used for cores of DC-tolerant current transformers. We analyze the influence of external DC field of arbitrary direction on the performance of these transformers. For the realistic core shapes the demagnetization is high, which leads to effective external field suppression. However, DC tolerant transformers are tolerant to the DC component of the current and not to the external field -they can be saturated by 30 mT field from permanent magnet. This means that for the practical applications in domestic energy meters some external shielding is required.

Magnetic position sensors are popular in industrial and automotive applications since they are robust, resistant to dust and oil, and can be cheap. This was traditionally accompanied by low accuracy. However, new precise magnetic position sensors have been developed which can achieve 0.015% error and 10 nm resolution. The maximum achievable range is about 20 m. DC magnetic position sensors use a permanent magnet as a field source; a magnetic field sensor measures the field from that source, which is a function of distance. As a field sensor, magnetoresistors are often used instead of traditional Hall sensors. Eddy current position sensors also work with non-magnetic conduction targets. Magnetostrictive position sensors are based on the time of flight of the elastic waves excited in the magnetostrictive material. These sensors can be several meters long and their applications range from level meters to hydraulics. Magnetic trackers and long-range position sensors utilize AC field sources, which are detectable from distances up to 20 m. Compared to optical instruments, magnetic trackers do not need a direct view. Their applications include surgery, mixed reality, and underground and underwater navigation.

Fluxgate sensors with straight wire or rod cores are used in NDT, portable gradiometers and sensor arrays and for the detection of small objects. We show that their sensitivity at the voltage output mode depends on the excitation parameters, properties of the core material and geometry, pick-up coil length, but only slightly on the pick-up coil diameter. This finding allows to design multiwire cores with large wire pitch, which decreases their magnetic interactions and thus reduces demagnetization and correlation of their noise. As a result, using N wires theoretically increases sensitivity N-times, which is not achievable with dense cores. We have demonstrated this tendency for N up to 8 and one type of permalloy wire.

This paper presents a way to calculate the shell thickness of nonmagnetic hollow cylinders for nondestructive applications. Aluminum cylinders with a solid structure and with a hollow structure are considered. The motion component of the induced eddy currents in a conductive cylinder is utilized to evaluate the shell thickness of hollow conductive cylinders at various frequencies and at variable speeds. One axisymmetric excitation coil and two axisymmetric pickup coils with antiserial connection are used. An analytical method using an axisymmetric computational model is developed for a parametric analysis of solid and hollow cylinder structures and shell thickness calculations, in which Fourier series are utilized. A 2D axisymmetric finite element method is also performed for a comparison with the results of the analytical method. The measurements at variable speeds and at various frequencies are presented with various hollow aluminum cylinders. The high linearity of the induced voltage versus the speed curve makes it possible to calculate the shell thickness of nonmagnetic hollow cylinders at different speeds.

This paper presents a novel structure of contactless eddy current speed sensor for linear speed measurements of flat shape type conductive objects. The sensor consists of one excitation coil and two different antiserially connected pick up coils. The sensor is designed and analyzed with an air core and a magnetic yoke (core) to compare their drawbacks and merits at different excitation frequencies and low and high speeds. 2D and 3D finite element method and developed analytical methods are utilized for parametric analysis and design of linear eddy current speed sensor. The simulation results are compared with the measurements up to 15.5 m/s.

This paper presents a new linear eddy current speed sensor with rectangular-shaped coils. The excitation coil and the pick-up coil have a perpendicular configuration without a magnetic yoke. The proposed sensor is shorter than the previous designs. The sensor works for a conductive moving target; in this paper we present calculations and an experimental verification for solid iron and aluminum moving part materials. A novel 3D analytical method is presented for the description and for the design of an eddy current speed sensor that is fast and has high precision. The source fields and the reaction fields caused by induced eddy currents are separated in our 3D analytical method, which facilitates an enhanced investigation of the features of the speed sensor. Evaluations of the effects of the moving part material and of coil lift off on the performance of the speed sensor are made with the use of a 3D analytical method. Measurements are performed for an eddy current speed sensor at different speeds up to 11.65 m/s and at different frequencies with a novel analytical model in terms of the induced voltage in the pickup coil versus speed. Simplicity and high precision are the main advantages of the proposed speed sensor. The achieved linearity error is 0.47% (measured) up to 11.6 m/s, and 0.43% (calculated) up to 117 m/s (420 km/h).

This paper presents a position sensor based on a novel configuration of linear variable differential transformer. Design and optimization of the position sensor using finite element method are presented. The measurements are also conducted to validate experimentally the sensor performance. The sensor has short air core coils and long magnetic armatures. The axis of the rectangular excitation coil and two antiserially connected rectangular pick up coils is perpendicular to the motion direction of the position sensor. The coils are located between two parallel silicon steel laminations serving as the armatures. The position sensor is optimized with compromise between minimization of nonlinearity error and maximum sensitivity. The main advantage of the proposed position sensor is the small ratio of coils dimensions to the working range. The position sensor is operated for excitation frequencies of 500 Hz, 1000 Hz, and 2000 Hz. The maximum nonlinearity error is less than 1.5% for the theoretical results and it is less than 2% for the measured results in ±90 mm position range.

We present a method for the estimation of the DC B-H curve of a straight magnetic wire which is used as a core for fluxgate sensor. An inverse technique is used as the direct precise measurement is practically impossible. 2D time stepping and 3D time harmonic finite element methods are used for numerical calculations to find a proper magnetization curve from the measurements of induced voltage into the pickup coils. Combined rational and power functions are utilized to model the magnetization curve, which is later used for numerical analysis too.

Impedance analyses of a number of solid iron conductors at 400 Hz and 1000 Hz is presented in this paper. The impedance of solid nonmagnetic conductors is well documented. However, there have been fewer studies of solid magnetic conductors, because of complications caused by strong nonlinearity. Nevertheless, some industrial applications require ferromagnetic conductors, and a simple method for expressing their impedance is desirable. Solid iron conductors of various shapes are considered here. Analytical methods are developed that take into the account the eddy currents in the solid iron and its magnetic nonlinearity. Magnetization curves of solid iron conductors were measured using the yoke method and using a permeameter. The nonlinear time harmonic finite element method is used for impedance calculations of solid iron conductors. The impedance measurement results are compared with the analytical method and with finite element calculations. Hysteresis effects on resistance and inductance are also taken into consideration. The calculated results are compared with measurements at different currents and frequencies.

Simple and precise hysteresis models with a small number of parameters allowing fast calculation are required for the magnetic analysis, as the field is calculated in a very large number of points. This paper presents a new simple method for modeling the hysteresis loops of soft magnetic materials using combined rational and power functions. Three approaches are used to model the hysteresis loops analytically. In the first approach, the upper and lower curves of the hysteresis loops are estimated and are calculated separately, using combined rational and power functions. In the second approach, the hysteresis loops are calculated using the DC magnetization curve and combined rational and power functions, applying a phase shift in the magnetic field strength variations relative to the magnetic flux density. The third approach presents a novel method for modeling hysteresis loops: first, the model is fitted to the “mean curve”, which is in the middle of the measured hysteresis curve, and as a second step the phase shift is calculated as in the second approach. A solid iron sample with a rectangular cross section is used for the measurements and the hysteresis modeling. The proposed method is also applied to model the hysteresis loops of a magnetic material with high magnetic permeability and grain-oriented steel, to show the generality of the proposed methods.

Soft magnetic wires and microwires are currently used for the cores of magnetic sensors. Thanks to their low demagnetization, they contribute to the high sensitivity and the high spatial resolution of fluxgates, Giant Magnetoimpedance (GMI), and inductive sensors. Arrays of nanowires can be prepared by electrodeposition into predefined pores of a nanoporous polycarbonate membrane. While high coercivity arrays with square loops are convenient for information storage and for bistable sensors such as proximity switches, low coercivity cores are needed for linear sensors. We show that coercivity can be controlled by the geometry of the array: increasing the diameter of nanowires (20 µm in length) from 30 nm to 200 nm reduced the coercivity by a factor of 10, while the corresponding decrease in the apparent permeability was only 5-fold. Finite element simulation of nanowire arrays is important for sensor development, but it is computationally demanding. While an array of 2000 wires can be still modelled in 3D, this is impossible for real arrays containing millions of wires. We have developed an equivalent 2D model, which allows to solve these large arrays with acceptable accuracy. Using this tool we have shown that as a core of magnetic sensors, nanowires are efficiently employed only together with microcoils with diameter comparable to the nanowire length.

Sensitivity of precise Rogowski coils can be increased by using low-permeability magnetic core instead of air core. This allows to increase the resolution for small current values. We have studied an impact of cores with µr = 14 and 26 on linearity, frequency dependence, crosstalk from external currents and sensitivity to misplacement of the measured current. Both 3D FEM simulations and measurement were used. While we found negligible effect on crosstalk and resistance to misplacement and also on frequency characteristics, the linearity was significantly degraded. However, the linearity error in case of µr = 14, 80 mm diameter Rogowski coil with 1000 A range is still below 0.2 %, which is sufficient for energy meters.

We have calculated and plotted the apparent permeability and the demagnetization factor of single magnetic wires. We have also confirmed the accuracy of the analytical formula for the conversion between the apparent permeability and the demagnetization factor. We also show that, as regards wire geometry, the effective permeability calculated from the inductance does not provide a good estimate of the apparent permeability, but that it is close to the amplification factor for induction sensors. We extend the concept of apparent permeability to a wire array. This will allow us to design multiwire magnetic sensors, mainly induction sensors and fluxgates. FEM calculations have been verified on physical models with up to 91 wires. Finally, we show a simplified 2D model for studies of larger wire arrays, and we verify the accuracy of the model.

This letter presents a novel speed sensor based on motion-induced eddy currents in conductive moving parts. The magnetic yoke is an E-shaped ferrite core. The excitation coil is on the center leg of the E-core, and two antiserially connected pick-up coils are on the side legs. Solid iron and aluminum materials are used for the moving part in the simulations and in the measurements. Two-dimensional and 3-D finite element methods are used for a detailed analysis and for the parametric calculations of the eddy current speed sensor. Despite its simple structure, the proposed eddy current speed sensor shows high linearity. The analysis and the measurements are performed at various speeds and excitation frequencies for an evaluation of the performance of the eddy current speed sensor. The minimum linearity error is less than 0.5%.

A novel position sensor for pneumatic and hydraulic cylinder applications is presented in this paper. The solid iron core conical in shape surrounded by axisymmetric coils is an essential part of the proposed position sensor. The axisymmetric coils are used for excitation and voltage measurements. The conical solid iron core is annealed to homogenize the magnetic properties and to increase the permeability of the conical solid iron core. This improves the performance of the position sensor in terms of sensitivity and linearity. Analytical and finite element analyses are utilized along with measurements in order to analyze the performance of the position sensor. The position sensor performs measurements of excitation coil inductance and pick-up coil voltages. Various frequencies are considered for the analysis and for the measurements. The measurement results show that the maximum linearity error is about 4% for the manufactured sensor, and is calculated to have a maximum value of 1% for the theoretical model. The achievable resolution of the proposed sensor is about 0.4 mm.

This paper presents the design and modeling of a linear eddy current speed sensor with a flat type structure and an air coil configuration. The theory of the eddy current speed sensor is based on utilizing the speed component of the induced currents in a solid moving conductor under stationary or alternating source fields. The stationary part comprises one rectangular excitation coil and two antiserially connected rectangular pick-up coils on the left and right sides of the excitation coil in the direction of the trajectory of the moving part. The moving part is considered firstly as a rectangular conducive ferromagnetic solid iron plate, and secondly as a rectangular aluminum plate. A 3D analytical model using Fourier series is developed to analyze the linear speed sensor in Cartesian coordinates. In addition, the 3D numerical finite element method is used for simulations of the linear speed sensor, and the results are compared with the results for analytical methods. The effects of iron permeability on the speed sensor are calculated for a rectangular ferromagnetic solid iron bar or conductor. The experimental results are presented for a linear speed sensor for a rectangular ferromagnetic solid iron plate and also for a rectangular aluminum plate, at variable speeds. The calculation and the experimental results show that the speed sensor outputs differ completely for solid iron conducive plates and for aluminum conducive plates, due to the different electrical conductivities and magnetic permeabilities.

This paper presents the design and optimization of a novel eddy current speed sensor for rotating rods and cylindrical shafts. The sensor consists of one excitation coil and two pick-up coils. All coils are stationary; we consider air coils, and we also use a magnetic yoke. We utilize a copper coating on an iron rod to increase the sensitivity, and we compare the performance with the performance achieved for an uncoated iron rod. 3D FEM is utilized for analyzing and for optimizing the design of the proposed sensor. The main advantages of the novel sensors are their simplicity, their low cost and their robust configuration. A linearity error of 0.5% has been achieved. The level of accuracy is limited by mechanical factors. A 1D analytical model has also been developed for rapid analysis and optimization of the sensor. An aluminum rod was also used in the measurements for a comparison with the results achieved with the iron rod.

This study presents an analysis and the design of a new flat-type position sensor with an external armature. One excitation coil and two antiserially connected pickup coils are used in the stationary part. Solid iron segments or steel lamination segments are used for the moving armature. The proposed position sensor was modelled using linear movement. A two-dimensional finite-difference method was developed and was used for fast analysis for optimising the sensor. The induced eddy currents in the solid armature were taken into account in the finite-difference analysis. The finite-difference calculations were compared with 2D and 3D finite-element method simulations and with experimental results. The sensor has a total error of 0.23 mm root-mean-square for 36 mm range without any compensation. Unlike previous designs, the authors’ new sensor has no moving coil.

This paper presents the design and analysis of a new eddy current speed sensor with ferromagnetic shielding. Aluminum and solid iron are considered for the moving part. One excitation coil and two antiserially connected pick up coils are shielded by a thin steel lamination. 3D time stepping finite element analysis is used to analyze the sensor performance with different magnetic materials and compare with experimental results. The compactness, simplicity and excellent linearity with different magnetic materials for the moving part show uniqueness of the proposed speed sensor. The shielding increases sensitivity and reduces the influence of close ferromagnetic objects and interferences on the sensor performance.

Magnetic position and speed sensors are rugged and durable. While DC magnetic sensors use permanent magnets as a field source and usually have only mm or cm range, inductive sensors use electromagnetic induction and they may work up to a distance of 20 m. Eddy current inductive sensors equipped with magnetoresistive sensors instead of inductive coils can operate at low frequencies, allowing detection through a conductive wall. In this paper, we make an overview of existing systems and we present new results in eddy current velocity and position measurements. We also present several types of inductive position sensors developed in our laboratories for industrial applications in pneumatic and hydraulic cylinders, underground drilling, large mining machines, and for detecting ferromagnetic objects on conveyors. While the most precise inductive position sensors have a resolution of 10 nm and linearity of 0.2%, precision requirements on the industrial sensors which we develop are less demanding, but they should have large working distance and large resistance to environmental conditions and interference.

This paper presents the analysis and design of a transformer position sensor for pneumatic cylinder considering temperature stability. Two solenoid coils as excitation coil and pick up coil around cylinder are used for position transducer. The effects of temperature of aluminum cylinder and iron rod with different ferromagnetic materials on position sensor performance are analyzed and measured. We found that the effect of temperature dependence of shell resistivity is dominant, while the effect of permeability change is negligible. Based on the simulations and measurement we suggest simple method of temperature compensation.

Novel eddy current speed sensor with axisymmetric coils and solid iron rod as moving part is presented. The analysis is performed for both dc and ac coil currents and for variable iron rod translational speed. The coil inductance and induced voltage results using the analytical method and finite-element method calculation are compared with the measured values. Two different coil configurations are used for simulations and measurement.

A novel eddy current speed sensor is developed to measure the rotational speed of conductive objects. The sensor consists of one excitation coil and two pick-up coils around a rotating cylinder or rod. The sensor does not use magnetic yoke. For the analysis and experimental verification, we used 30 mm diameter non-magnetic aluminum and also magnetic solid iron cylinders. The calculated and measured speed ranges are up to 1200 r/min. A 2-D analytical method is developed to calculate sensor performance. A 2-D finite element is also used for simulations to compare results with the 2-D analytical method. A 3-D finite-element analysis is required to take into account significant 3-D effects due to the air coil configuration. The experimental results are presented at different steady-state speeds. The calculation results are compared with measurements to validate theoretical models and sensor performance. The eddy current speed sensor shows high linearity even at low speeds. For ferromagnetic rods, we suggest a novel double-layer configuration: non-magnetic conductive ring or shell on top of the iron rod minimizes the influence of the permeability changes. The main advantage of the novel sensor is that it has neither mechanical nor electrical contact to the rotating rod

A novel transformer-based sensor for a pneumatic cylinder enables measurements of the piston position to be made through a thick conductive cylinder. Unlike existing industrial solutions, which are mainly based on a moving magnet, our sensors do not require modifications to the parts inside the cylinder.

In this paper, two different solid iron materials are used for two different size rails. The internal impedances, resistances and inductances of the rails are evaluated and analyzed with time harmonic and time stepping finite element methods. Two solid iron materials have different B-H curves and electrical conductivities. The analysis will be presented for different currents at different frequencies, 10 Hz - 10 kHz. The inductance analysis using finite element method is also performed under simultaneous large DC signal and small AC signal.

In this paper, combined rational and power functions are used to represent magnetization curves of high magnetic permeability ferromagnetic materials. The proposed functions cover much wider range of magnetic fields than functions currently used in simulation software packages. The objective is to present simple functions for approximation of magnetization curves with minimum number of unknown constants. The calculated functions are finally compared with measured magnetization curves to validate the precision in a wide field range from 10(-2) to 10(6) A/m.

Magnetic field in the perpendicular direction cannot be sensed by thin film sensor due tolarge demagnetisation. We show that an array of nanowires has much lower demagnetization coefficient than magnetic film. This feature can be used to add third dimension to two-dimensional magnetic sensors.

The impedance of rectangular and circular shape solid iron conductors is studied in this paper. 2D analytical model is presented for linear iron materials with different relative magnetic permeability and the results are compared with finite element method (FEM). Experiments are performed to measure the impedances. Nonlinear time harmonic FEM results are compared with experimental results for detailed evaluations. Different solid irons are considered for measurement and simulations.

The position of the piston in pneumatic cylinder with aluminum wall can be measured by external inductance sensor without modifications of the aluminum piston and massive iron piston rod. For frequencies below 20 Hz the inductance is increasing with inserting rod due to the rod permeability. This mode has disadvantage of slow response to piston movement and also high temperature sensitivity. At the frequency of 45 Hz the inductance is position independent, as the permeability effect is compensated by the eddy current effect. At higher frequencies eddy current effects in the rod prevail, the inductance is decreasing with inserting rod. In this mode the sensitivity is smaller but the sensor response is fast and temperature stability is better. We show that FEM simulation of this sensor using measured material properties gives accurate results, which is important for the sensor optimization such as designing the winding geometry for the best linearity

In this paper, temperature sensitivity of inductance position transducer of a pneumatic cylinder system is presented. The magnetic solid iron rod and aluminum piston position changes the inductance of the tubular coil around the aluminum pneumatic cylinder. The measurement and finite element method are used to evaluate inductances versus piston position at different frequencies. Temperature effect on the coil inductance is analyzed. Temperature of the iron rod and the aluminum cylinder are changed for the temperature sensitivity analysis. The measured iron rod temperature dependence is in the order of 0.45 %/°C at 100 Hz and 0.27 %/°C at 200 Hz. Finally a small compensating solenoid coil is used at one side of the cylinder (entrance side for piston) to compensate temperature dependency effects

In this paper, experimental works and theoretical analysis are presented to analyze the influence of the conductor permeability on the precision of yokeless current sensors. The results of finite-element method (FEM) fit well the measured field values around the conductor. Finally we evaluate the difference in magnetic fields distribution around non-magnetic and magnetic conductor. The calculated values show that the permeability of the ferromagnetic conductor significally affects the reading of the electric current sensors even at DC.