Galvanically isolated voltage measurements are becoming increasingly important for the characterization of converter systems with fast switching Wide-Bandgap (WBG) semiconductors. A very high Common Mode Rejection Ratio (CMRR) $\mathbf {>\,80\,}$ dB for frequencies up to several tens of MHz is required to accurately measure, e.g., the high-side gate-source or drain-source voltage in a half-bridge, or voltages on floating potentials as, e.g., found in multi-level converters. Common to all listed measurement scenarios is the fast changing reference potential, which acts as Common Mode (CM) disturbance. This article derives the minimum necessary CMRR at different frequencies to constrain the time-domain measurement error below a certain limit. Thereby, only the switched voltage and the voltage transition rate ( $\mathbf {\text{d}\mathit{v}/\text{d}\mathit{t}}$ ) of the CM disturbance are to be considered and not the actual converter switching frequency $\mathbf {\mathit{f}_\text{sw}}$ . Afterwards, a galvanically isolated measurement system with a CMRR $\mathbf {>\,100}\,$ dB up to $\mathbf {100}\,$ MHz and an analog measurement bandwidth of $\mathbf {130\,}$ MHz is presented. Critical design aspects to achieve this performance are investigated. Compared to commercially available isolated voltage probes, the presented measurement system does not require any additional equipment like an oscilloscope to perform and visualize measurements, since the data is already digitized/sampled and thus can be transmitted directly to a host device (e.g., computer or monitoring system) with corresponding Graphical User Interface (GUI) software. Experimental verification in frequency- and time-domain confirms that the performance is on par with the best commercially available isolated voltage probes.

This work introduces a novel sensing concept based on reaction forces for determining the position of the levitating magnet (mover) for magnetic levitation platforms (MLPs). Besides being effective in conventional magnetic bearings, the applied approach enables operation in systems where the mover is completely isolated from the actuating electromagnets (EMs) of the stator (e.g., located inside a sealed process chamber) while levitating at an extreme levitation height. To achieve active position control of the levitating mover by properly controlling the stator’s EM currents, it is necessary to employ a dynamic model of the complete MLP, including the reaction force sensor, and implement an observer that extracts the position from the force-dependent signals, given that the position is not directly tied to the measured forces. Furthermore, two possible controller implementations are discussed in detail: a basic PID controller and a more sophisticated state-space controller that can be chosen depending on the characteristics of the MLP and the accuracy of the employed sensing method. To show the effectiveness of the proposed position-sensing and control concept, a hardware demonstrator employing a 207 mm outer-diameter (characteristic dimension, CD) stator with permanent magnets, a set of electromagnets, and a commercial multi-axis force sensor is built, where a 0.36 kg mover is stably levitated at an extreme air gap of 104 mm.

This work provides an analytical method, based on the Amprian model of permanent magnets (PM), for a fast calculation of the magnetic flux density in three-dimensional space applying Biot-Savart law, and the calculation of the forces using Lorentzs law. The applied approach enables the characterization regarding forces, torques, and stiffnesses of the levitating PM for any arbitrary position in space. Furthermore, it permits the extension of the investigation to any shape and configuration of ironless magnetic bearings (MB). In order to demonstrate the simple use of the analytical model, in this paper, the dimensions of an ironless axial MB employing PMs are optimized with a multi-objective Pareto analysis which reveals the physical limits concerning maximum achievable levitation height with respect to given constraints on, e.g., the required force and tilting stiffnesses, and the MB robustness defined by the maximum allowable payload on the levitating magnet. Moreover, the optimized axial MB and a corresponding test bench are realized to validate the proposed model with experimental results. For sake of completeness, it should be mentioned that in a later stage the optimized MB can also be scaled with simple scaling laws if the demanded specifications, e.g., concerning desired maximum levitation height or payload capability would have changed.

This paper provides a comparative analysis between a force sensor and an eddy current sensor, focusing on their usability to determine the position of a circular levitating permanent magnet (PM) mover within an axially symmetric magnetic levitation platform (MLP) with an exceptionally large air gap. The sensors enable closed-loop control, which is essential for accurately and stably maintaining the mover’s radial position. For the considered MLP, a change in radial position in principle results in a tilting of the mover, i.e., a deviation from the parallel alignment relative to the stator. As both the radial position and the tilting angle affect the sensors’ (force and eddy current) output voltage, an observer must deduce the radial position from the output sensor’s voltage, requiring a comprehensive MLP dynamic model and calibration of the models for both sensing approaches. The paper discusses the advantages and weaknesses of each sensor concept, exploring operational principles and performance in levitation tests. The force sensor exhibits versatility, proving functional across various application scenarios, such as when the mover is sealed in a conductive, non-magnetic chamber. In contrast, due to its high-frequency operation, the eddy current sensor is more straightforward to characterize, simplifying its behavior relative to the mover’s slower dynamics. Measurements are conducted to validate the models, showing the eddy current sensor’s robustness against disturbances and imperfections in the MLPs and its immunity to cross-axis interference. Conclusively, in levitation experiments where the mover is vertically distanced at 104 mm from the stator, the eddy current sensor achieves a position tracking precision about ten times better and a signal-to-noise ratio (SNR) ten times higher compared to the off-the-shelf force sensor, confirming its better performance and reliability; however, it cannot be used in applications where conductive objects are present in the air gap. Furthermore, additional experiments are conducted on the MLP using the eddy current sensor to show the controller’s robustness and dynamic reference tracking capability, with and without a payload.