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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

Transducer driving methods and transducer driving systems

Transducer driving methods and transducer driving systems are described. According to one aspect, a transducer driving method includes providing a plurality of initial driving signals to a transducer, wherein each of the initial driving signals has a respective one of a plurality of different frequencies, identifying one of the frequencies where the transducer has a reduced impedance as a result of the provision of one of the initial driving signals having the one frequency to the transducer compared with impedances of the transducer resulting from the provision of others of the initial driving signals having others of the frequencies to the transducer, determining that the identified one of the frequencies is not acceptable for driving the transducer, as a result of the determining, identifying another of the frequencies, and driving the transducer using another driving signal having the another frequency.

Myjak, Mitchell J.↗

Characterization of the acoustic field generated by a horn shaped ultrasonic transducer

A horn shaped Langevin ultrasonic transducer used in a single axis levitator was characterized to better understand the role of the acoustic profile in establishing stable traps. The method of characterization included acoustic beam profiling performed by raster scanning an ultrasonic microphone as well as finite element analysis of the horn and its interface with the surrounding air volume. The results of the model are in good agreement with measurements and demonstrate the validity of the approach for both near and far field analyses. Our results show that this style of transducer produces a strong acoustic beam with a total divergence angle of 10 degree, a near-field point close to the transducer surface and a virtual sound source. These are desirable characteristics for a sound source used for acoustic trapping experiments

acoustic, horn, levitation, acoustic simulation↗

Nanophotonic Atomic Force Microscope Transducers Enable Chemical Composition and Thermal Conductivity Measurements at the Nanoscale [Nanophotonic AFM Transducers Enable Chemical Composition and Thermal Conductivity Measurements at the Nanoscale]

The atomic force microscope (AFM) offers a rich observation window on the nanoscale, yet many dynamic phenomena are too fast and too weak for direct AFM detection. Integrated cavity-optomechanics is revolutionizing micromechanical sensing; however, it has not yet impacted AFM. Here, we make a groundbreaking advance by fabricating picogram-scale probes integrated with photonic resonators to realize functional AFM detection that achieve high temporal resolution (<10 ns) and picometer vertical displacement uncertainty simultaneously. The ability to capture fast events with high precision is leveraged to measure the thermal conductivity (η), for the first time, concurrently with chemical composition at the nanoscale in photothermal induced resonance experiments. The intrinsic η of metal–organic-framework individual microcrystals, not measurable by macroscale techniques, is obtained with a small measurement uncertainty (8%). The improved sensitivity (50×) increases the measurement throughput 2500-fold and enables chemical composition measurement of molecular monolayer-thin samples. In conclusion, our paradigm-shifting photonic readout for small probes breaks the common trade-off between AFM measurement precision and ability to capture transient events, thus transforming the ability to observe nanoscale dynamics in materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Liquid metallic laser ultrasound transducer for high-temperature applications

This study aims to investigate a laser ultrasound (LUS) transducer for high-temperature (>100 °C) applications. For decades, many researchers have investigated efficient LUS transducers, yet studies on laser ultrasound transducers capable of performing at the high-temperature condition are rarely found in the literature. Most current LUS transducers still utilize a polymer-based composite material, that is, not stable at varying temperature conditions. This study introduces a liquid metallic (LM) LUS transducer that utilizes field's metal, which has a high thermal expansion (~3 × 10 -4 K -1 ). We hypothesized that such a high thermal expansion of the liquid metal can effectively produce laser-generated ultrasound waves, substituting for conventional polymer-based transducers. A numerical simulation predicted that the LM LUS transducer would produce higher LUS intensity (~22 dB) than that without the LUS transducer. Experiment results confirmed that the LM transducer effectively intensifies the ultrasound wave signals, obtaining a signal-to-noise gain over 30 dB. Moreover, the transducer was found capable of transmitting detectable wave packets in relatively high-temperature conditions (~400 °C), while conventional candle soot nanoparticle-polydimethylsiloxane could not perform stably at these elevated temperatures. The investigations introduced in this article are scientifically significant since we demonstrated the engineering feasibility of liquid metallic materials for LUS transducers.

47 OTHER INSTRUMENTATION↗

Pressure Transducer Measurement Variability in Deep Wells Screened Across the Water Table

Abstract Automated water level measurements collected using vented pressure transducers in deep wells screened across the water table may exhibit a greater response to barometric pressure changes than the true water level. The cause was hypothesized to be disequilibrium in barometric pressure between the wellbores and land surface due to air exchange with the deep vadose zone. In this study, vented and nonvented pressure transducers were installed and operated simultaneously in two deep wells screened across the water table. A vent tube open to the atmosphere at land surface allowed for barometric compensation of the vented transducers. Two nonvented transducers were installed in each well, one submerged in the water and one above the water surface. The difference in readings allowed for barometric compensation. Manual measurements were also collected. It was confirmed that measurements from the vented transducers exhibited greater variability in response to barometric pressure changes than the nonvented transducers and manual measurements. Comparison of the downhole barometric pressure measurements to values from a nearby meteorology station showed the response in the wells to changes in barometric pressure was time‐lagged and attenuated. Thus, the reference pressure from land surface supplied to the vented transducers was not representative of the air pressure within the wells. This caused fluctuations of the transducer readings in response to barometric pressure changes to be greater than the true water level change. This issue can be resolved by the use of nonvented pressure transducers.

McDonald, John P.↗

Final Report on Development of Microwave Resonant Cavity Transducer for Fluid Flow Sensing: Development of Microwave Cavity Flow Meter for Advanced Reactor High Temperature Fluids

We are investigating a microwave resonant cavity transducer for flow sensing in the vessel of a high temperature fluid advanced reactor (AR), such as a molten salt cooled reactor (MSCR) or a sodium fast reactor (SFR). This transducer is a hollow metallic cylindrical cavity, with one of the flat walls of the cylinder flexible enough to undergo microscopic deflection due to dynamic fluid pressure. Membrane deflection leads to a shift in the microwave resonant frequency, which can be detected with a spectrum analyzer. We have developed a continuum electromechanics model of the microwave resonant cavity transducer performance. The deflection of the membrane is calculated using equations from the theory of plates and shells for deflection of radially constrained thin circular disk under uniform load. The microwave frequency shift is calculated using the equations from the microwave cavity perturbation theory. The transducer model was validated with proof-of-concept experimental data of water flow sensing with a Brass 360 right circular cylinder with 22.2mm diameter and 203µm thick wall. The cavity was excited through a subwavelength hole in TE 011 mode with resonant frequency f ≈ 17.8GHz. Subsequently, we have performed a preliminary proof-of-principle test of flow sensing in high temperature liquid sodium in environment. For this test, we have developed a cylindrical resonator with the same dimensions as for the Brass 360 cavity. The resonator for high temperature liquid sodium test was machined from stainless steel 316 and electroplated with silver on the interior surfaces. We have also developed and insertion probe consisting of a 50cm WR-42 brass waveguide enclosed in a protective SS316 tube. The cavity was excited through a subwavelength hole on the side of the wall of the cylinder in the TE 011 mode with resonant frequency f ≈ 17.8GHz. The liquid sodium setup consists of a cylindrical vessel with a center feed line, where a transducer inserted through the top cap of the vessel measures velocity of the impinging liquid jet. The sodium flow sensing study was performed in a liquid sodium vessel at 340°C temperature and ambient pressure. The flow rate was changed by varying sodium pump power, and a frequency shift of several hundred kHz was observed. The transducer was removed after 70 days of testing. No visual damage was observed, and the electromagnetic response remained the same. As a calibration experiment, we have assembled a water vessel with a center feed, and with dimensions similar to those of the liquid sodium setup. Water flow sensing was performed before and after liquid sodium test. The responses in both cases are similar and agree with COMSOL computer simulations. Because long-term (multi-year) experimental tests of transducer resilience to harsh environment are not practical, we have developed a probabilistic model of creep to estimate transducer resilience to the harsh environment. The probabilistic model considers diffusion creep under the condition of high temperature and low stress, where the stress and temperature are allowed to be random variables with Gaussian distributions. Using the probabilistic model, we estimate inelastic membrane deflections due to creep for several temperature ranges. We conclude that for temperatures less than 650°C, creep has negligible long-term effect on the transducer performance.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Effect of sintering temperature on adhesion of spray-on piezoelectric transducers

Conventionally sol-gel spray-on transducers require a high-temperature (> 700 ◦C) sintering process; however, this process can affect the microstructure of the substrate material. For mechanical elbows and valves utilized for fluid transport in the energy sector, the components are designed to have a specific microstructure, and deviations from these specifications can create weak points in the system. For this reason it is important to investigate how the temperature of the deposition process affects the substrate. This paper investigates the effect of high-temperature and low-temperature (< 150 ◦C) processing conditions on the surface composition of the substrate. Furthermore, the resultant transducers from high- and low-temperature fabrication processes are compared to determine if a low-temperature processing method is feasible. For these studies a sol-gel spray-on process is employed to deposit piezoelectric ceramics onto a stainless-steel 316L substrate. Energy-dispersive X-ray spectroscopy is utilized to determine the composition of the substrate surface before and after transducer deposition. Results indicate that the high-temperature processing conditions may alter the surface composition of the metal due to a diffusion of the metal into the ceramic, which results in a metal surface that is bonded to the ceramic. Furthermore, it is shown that low-temperature processing of spray-on transducers is a viable method for transducer fabrication where the resultant transducers meet the industry minimum requirement of 30 dB signalto-noise ratio. In parallel simulation calculations, finite-element method (FEM) studies were performed to model the adhesive strength of the low-temperature processed transducer to the substrate surface. Comparisons between the simulations and experiments suggest that the bond strength is much greater than the commercial gel bonds and closer to hardened epoxy glue bonds. These results indicate that spray-on transducers fabricated under lowtemperature processing conditions are a viable solution for leave-in-place monitoring of structures.

M. Sinding, Kyle↗

Second Annual Report on Development of Microwave Resonant Cavity Transducer for Fluid Flow Sensing

We are investigating a microwave resonant cavity transducer for flow sensing in the vessel of a high temperature fluid advanced reactor (AR), such as a molten salt cooled reactor (MSCR) or a sodium fast reactor (SFR). This transducer is a hollow metallic cylindrical cavity, with the flat wall of the cylinder flexible enough to undergo microscopic deflection due to dynamic fluid pressure. Membrane deflection leads to a shift in the resonant frequency, which can be detected with a spectrum analyzer. Because the transducer is intended for immersion in a high temperature corrosive fluid, understanding of material degradation is crucial for estimation of transducer performance lifetime, and development of measurement interpretation algorithms. We conducted a preliminary computational investigation of relevant damage mechanisms of a stainless steel 316 cylindrical resonator in FLiBe salt. The two main damage mechanisms, creep and corrosion, were modeled using multiphysics COMSOL software. Degradation was modeled for a temperature range 500°C to 700°C. Coupling of the damage mechanisms was not considered. These models predict significant inelastic deformation at most temperatures due to creep, and qualitatively predict chromium depletion both along the liquid/solid interface and along the grain boundaries. An algorithmic approach for compensation of these degradation effects during fluid flow measurements will be developed in the future work. To validate sensor physics, we have performed proof-of-principle test of flow sensing in water. For this test, we have developed a cylindrical resonator for K-band, which was machined from brass. The cavity was excited through WR-42 waveguide through a subwavelength hole on the side of the wall of the cylinder. To increase the spectral signal visibility, we developed a signal processing method for baseline subtraction. A flow loop for proof-of-principle test of transducer performance in water was assembled. A commercial flow meter was installed in the loop for reference measurements. Cylindrical cavity was excited in the TE 011 mode with resonant frequency f ≈ 17.8GHz. Frequency shift of cavity spectral response was obtained by gradually increasing water flow rate from 0 to 60gpm. Corresponding monotonic increase of resonant frequency shift by several MHz was observed. Approximate figure of merit of sensitivity to flow rate is 100KHz/GPM. In addition, we have identified an existing liquid sodium experimental setup for demonstration of flow sensing in environment similar to that of an advanced reactor. The setup consists of a cylindrical vessel and center feed line, where transducer inserted through the lid will measure velocity of the impinging liquid jet. As a calibration experiment, we have assembled a water vessel with center feed with the same dimensions as those of the liquid sodium setup. We have also developed and insertion probe consisting of a 50cm brass waveguide enclosed in protective SS316 tube. Using the water loop, we have demonstrated feasibility of sensing the impinging liquid jet in the vessel.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Progress Towards Developing Neutron Tolerant Magnetostrictive and Piezoelectric Transducers

Current generation light water reactors (LWRs), sodium cooled fast reactors (SFRs), small modular reactors (SMRs), and next generation nuclear plants (NGNPs) produce harsh environments in and near the reactor core that can severely tax material performance and limit component operational life. To address this issue, several Department of Energy Office of Nuclear Energy (DOE-NE) research programs are evaluating the long duration irradiation performance of fuel and structural materials used in existing and new reactors. In order to maximize the amount of information obtained from Material Testing Reactor (MTR) irradiations, DOE is also funding development of enhanced instrumentation that will be able to obtain in-situ, real-time data on key material characteristics and properties, with unprecedented accuracy and resolution. Such data are required to validate new multi-scale, multi-physics modeling tools under development as part of a science-based, engineering driven approach to reactor development. It is not feasible to obtain high resolution/microscale data with the current state of instrumentation technology. However, ultrasound-based sensors offer the ability to obtain such data if it is demonstrated that these sensors and their associated transducers are resistant to high neutron flux, high gamma radiation, and high temperature. To address this need, the Advanced Test Reactor National Scientific User Facility (ATR-NSUF) is funding an irradiation, led by PSU, at the Massachusetts Institute of Technology Research Reactor to test the survivability of ultrasound transducers. As part of this effort, PSU and collaborators have designed, fabricated, and provided piezoelectric and magnetostrictive transducers that are optimized to perform in harsh, high flux, environments. Four piezoelectric transducers were fabricated with either aluminum nitride, zinc oxide, or bismuth titanate as the active element that were coupled to either Kovar or aluminum waveguides and two magnetostrictive transducers were fabricated with Remendur or Galfenol as the active elements. Pulse-echo ultrasonic measurements of these transducers are made in-situ. This paper will present an overview of the test design including selection criteria for candidate materials and optimization of test assembly parameters, data obtained from both out-of-pile and in-pile testing at elevated temperatures, and an assessment based on initial data of the expected performance of ultrasonic devices in irradiation conditions

Reinhardt1, Brian↗

Transducer Resolution Effect on Pressure Fluctuations Beneath Hypersonic Turbulent Boundary Layers

The size of a pressure transducer is known to affect the accuracy of measurements of wall-pressure fluctuations beneath a turbulent boundary layer because of spatial averaging over the sensing area of the transducer. In this paper, the effect of finite transducer size is investigated by applying spatial averaging or wavenumber filters to a database of hypersonic wall pressure generated from a direct numerical simulation (DNS) that simulates the turbulent portion of the boundary layer over a sharp 7° half-angle cone at nominally Mach 8. Here, a good comparison between the DNS and the experiment in the Sandia Hypersonic Wind Tunnel at Mach 8 is achieved after spatial averaging is applied to the DNS data over an area similar to the sensing area of the transducer. The study shows that a finite sensor size similar to that of the PCB132 transducer can cause significant attenuation in the root-mean-square and power spectral density (PSD) of wall-pressure fluctuations, and the attenuation effect is identical between cone and flat plate configurations at the same friction Reynolds number. The Corcos theory is found to successfully compensate for the attenuated high-frequency components of the wall-pressure PSD.

42 ENGINEERING↗

The effect of a transducer’s spatial averaging on an elastodynamic guided wave’s wavenumber spectrum

Elastodynamic guided waves propagate in an elastic solid which makes it difficult, if not impractical, to place a receiving transducer in the direct path of the propagating wave (as one would for an acoustic wave in a fluid medium). Thus, to account for this, receiving transducers are often placed on the surface of the solid waveguide such that the transducer surface is parallel to the wave propagation direction. This transducer orientation introduces spatial averaging, which causes the received signal to have an altered signal amplitude and mode bias. We investigate both of these effects and present a simple model from which we derive a scaling-ratio expression that describes the effects of spatial averaging. Furthermore, we then test its performance using finite-element simulations that incorporate “real-world” assumptions (e.g., transient waves, piezoelectric effects, etc.). The results from the simulations demonstrate that the scaling-ratio can characterize the effects resulting from spatial averaging. The scaling-ratio expression will be particularly useful when designing experiments involving high frequency (small wavelength) guided waves. Lastly, the proposed scaling-ratio expression could be applied to other sensing methods, like Laser Doppler Vibrometry (LDV) or piezoelectric waveguides with inter-digitated transducers, because of its generality. However, the authors are careful to note that the scaling-ratio expression is not intended as a replacement of multi-physics analysis or good experimental design, and the effects of spatial averaging should be avoided whenever possible.

2DFFT↗

General Testing Setup for Hyperelastic Transducers-DEEC-Tec & Marine Renewable Energy: Preprint

Distributed embedded energy conversion technologies (DEEC-Tec), an emerging domain for ocean wave energy conversion technology, is showing promise for a range of applications. Research is being conducted at the National Renewable Energy Laboratory that leverages this domain to investigate the potential of ocean wave energy converters (WECs) constructed from hyperelastic forms of distributable and embeddable energy transducers. These transducers are available in forms such as disks, rectangles, or hexagons and can be combined in various ways to form energy-producing metamaterials and flexible WECs. DEEC-Tec, therefore, could open doors that enhance ocean wave energy conversion in ways not previously thought possible by allowing for many WEC topologies and morphologies. However, the same diversity and adaptability pose challenges for the development of these DEEC-Tec-oriented hyperelastic transducers. A commercial tensile testing setup was not found that was adaptable enough to accommodate the varied transducers while providing precise force control, range of motion, and noncontact data collection. Because of this lack, a comprehensive test rig was designed in house to be used with a 3D laser scanning device-providing contactless measurements while also allowing for different geometries and various uniaxial loadings. This paper and presentation will discuss these unique challenges and the processes for overcoming them to provide a robust and general testing setup for hyperelastic transducers, of any form, for the DEEC-Tec marine renewable energy domain.

DEEC-Tec↗

Quantum capacities of transducers

Abstract High-performance quantum transducers, which faithfully convert quantum information between disparate physical carriers, are essential in quantum science and technology. Different figures of merit, including efficiency, bandwidth, and added noise, are typically used to characterize the transducers’ ability to transfer quantum information. Here we utilize quantum capacity, the highest achievable qubit communication rate through a channel, to define a single metric that unifies various criteria of a desirable transducer. Using the continuous-time quantum capacities of bosonic pure-loss channels as benchmarks, we investigate the optimal designs of generic quantum transduction schemes implemented by transmitting external signals through a coupled bosonic chain. With physical constraints on the maximal coupling rate $${g}_{\max }$$ g max , the highest continuous-time quantum capacity $${Q}^{\max }\approx 31.4{g}_{\max }$$ Q max ≈ 31.4 g max is achieved by transducers with a maximally flat conversion frequency response, analogous to Butterworth electric filters. We further investigate the effect of thermal noise on the performance of transducers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Transducer Installation Effects on Pressure Measurements in PGC Devices

Pressure gain devices such as rotating detonation engines present an extremely harsh environment, generally precluding the use of any intrusive probe measurement. The most widely used diagnostic is the measurement of high frequency pressure which can be used to determine the pressure amplitude, number of waves and their direction and the wave structure. The preferred approach for making pressure measurements is to install the sensing element flush with the combustion chamber wall, but is almost always inhibited by the extremely high heat fluxes that can damage the sensor. Alternately, recessed cavity or infinite probe installation is seldom used for high frequency pressure measurements. While amplitude attenuation and phase distortion of the pressure signal can be introduced by these installation types, its characterization in the presence of high amplitude steep fronted pressure waves encountered in PGC devices has not been previously performed. In the current work a highly modular calibration test-bed is designed to enable characterization of pressure transducers based on their installation in the presence of steep fronted high amplitude pressure waves. Two transducer types, piezoelectric PCB® 113B26 and water-cooled piezoresistive Kulite®WCT-312M were used and installed in the flush, recessed cavity and infinite tube probe configuration. The recessed cavity probe showed 5-26% amplitude attenuation and almost negligible time lag compared to the flush transducer, the infinite tube pressure (ITP) transducer showed a significantly higher delay and as much as 50% reduction in measured pressure amplitude. Secondary wave features from reflections within the test article, that were captured by the flush and recessed cavity transducer were damped by the infinite probe measurement.

20 FOSSIL-FUELED POWER PLANTS↗

Selection of Shear Horizontal Wave Transducers for Robotic Nondestructive Inspection in Harsh Environments

Harsh environments and confined spaces require that nondestructive inspections be conducted with robotic systems. Ultrasonic guided waves are well suited for robotic systems because they can provide efficient volumetric coverage when inspecting for various types of damage, including cracks and corrosion. Shear horizontal guided waves are especially well suited for robotic inspection because they are sensitive to cracks oriented perpendicular or parallel to the wave propagation direction and can be generated with electromagnetic acoustic transducers (EMATs) and magnetostrictive transducers (MSTs). Both types of transducers are investigated for crack detection in a stainless steel plate. The MSTs require the robot to apply a compressive normal force that creates frictional force coupling. However, the coupling is observed to be very dependent upon surface roughness and surface debris. The EMATs are coupled through the Lorentz force and are thus noncontact, although they depend on the lift off between transducer and substrate. After comparing advantages and disadvantages of each transducer for robotic inspection the EMATs are selected for application to canisters that store used nuclear fuel.

Choi, Sungho↗

Irradiation Testing of Ultrasonic Transducers

Ultrasonic technologies offer the potential for high accuracy and resolution in-pile measurement of numerous parameters, including geometry changes, temperature, crack initiation and growth, gas pressure and composition, and microstructural changes. Many Department of Energy-Office of Nuclear Energy (DOE-NE) programs are exploring the use of ultrasonic technologies to provide enhanced sensors for in-pile instrumentation during irradiation testing. For example, the ability of single, small diameter ultrasonic thermometers (UTs) to provide a temperature profile in candidate metallic and oxide fuel would provide much needed data for validating new fuel performance models. Other efforts include an ultrasonic technique to detect morphology changes (such as crack initiation and growth) and acoustic techniques to evaluate fission gas composition and pressure. These efforts are limited by the lack of existing knowledge of ultrasonic transducer material survivability under irradiation conditions. To address this need, the Pennsylvania State University (PSU) was awarded an Advanced Test Reactor National Scientific User Facility (ATR NSUF) project to evaluate promising magnetostrictive and piezoelectric transducer performance in the Massachusetts Institute of Technology Research Reactor (MITR) up to a fast fluence of at least 1021 n/cm2 (E> 0.1 MeV). This test will be an instrumented lead test; and real-time transducer performance data will be collected along with temperature and neutron and gamma flux data. By characterizing magnetostrictive and piezoelectric transducer survivability during irradiation, test results will enable the development of novel radiation tolerant ultrasonic sensors for use in Material and Test Reactors (MTRs). The current work bridges the gap between proven out-of-pile ultrasonic techniques and in-pile deployment of ultrasonic sensors by acquiring the data necessary to demonstrate the performance of ultrasonic transducers

Daw, J.↗

A high-precision miniaturized rotating coil transducer for magnetic measurements

A miniaturized Printed Circuit Board (PCB) sensing coil, jointly developed by CERN and Fermilab for measuring the field of small-gap (less than 10 mm) accelerator magnets, is illustrated. A sensing coil array, with a scheme for compensating the main field when measuring the harmonic error components, hosted on a synthetic sapphire-based transducer, is presented. Key innovating features are (i) very-small size, both for the sensing coil array (thickness of 1.380 mm) and for the transducer (overall diameter of 7.350 mm), (ii) metrological performance, namely accuracy (more than five times better than state of the art), and 1-sigma repeatability (ten times better on harmonics with amplitude less than 100 ppm), and (iii) manufacturing technology of both the coil array (13 double layers aligned within 10 μm), and the sapphire support (concentricity, the most important uncertainty source for rotating coils, 3 μm of uncertainty, namely one order of magnitude better than fiberglass support). After stating the measurement problem, the design of the transducer and a case study of a two-layer PCB sensor array are also illustrated. Then, the prototyping and quality control of both the sensor and the transducer are discussed. Furthermore, the calibration and the results obtained with a prototype setup at Fermilab are presented. Finally, in the appendix, the theory of the rotating coil, the sensor geometry, and the harmonic compensation are briefly reviewed for the reader easiness.

06.20.fb/calibration↗