Amplitude | EPFL Graph Search

The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a periodic function is sometimes called the amplitude. Definitions Peak amplitude & semi-amplitude For symmetric periodic waves, like sine waves, square waves or triangle waves peak amplitude and semi amplitude are the same. Peak amplitude In audio system measurements, telecommunications and others where the measurand is a signal that swings above and below a reference value but is not sinusoidal, peak amplitude is often used. If the reference is zero, this is the maximum absolute value of the signal; if the reference is a mean value (DC component), the peak amplitude i

Analytical Methods for the Study and Design of Integrated Switched Oscillators and Antennas for Mesoband Radiation

Jose Felix Vega Stavro

This thesis was carried out within the framework of a scientific cooperation project entitled “Application of High Power Electromagnetics to Human Safety” developed by the EPFL, the National University of Colombia and Los Andes University, Colombia. The project was funded by the Swiss Agency for Development and Cooperation (SDC) through the EPFL Centre Coopéation & Développement (CODEV). The Scientific Cooperation aimed at the study and development of techniques for the generation of high power electromagnetic signals for the disruption or preemptive activation of Improvised Explosive Devices (IEDs) during humanitarian clearance activities. The results and conclusions of the thesis will be applied to the construction of a resonant radiator, which can be used for securing humanitarian demining operations in Colombia. The thesis is devoted to the analysis of a specific type of resonant radiators known as Switched Oscillators (SWO). An SWO is a radiator constituted by a high voltage charging circuit that drives a quarter-wave transmission line resonator connected to an antenna. An SWO can produce high-amplitude, short duration, electromagnetic fields, with a moderate bandwidth, when compared to the main resonance frequency. The outcome of the thesis can be also be used in electromagnetic compatibility applications, for the production of resonant, high power electromagnetic fields, with the aim of testing the immunity of electronic systems against Intentional Electromagnetic Interference (IEMI) attacks. The thesis is divided in three parts. The first part deals with the electrostatic design of an SWO. A method for producing an optimized design of the electrodes forming the spark gap of the SWO is presented. The method is based on the generation of a curvilinear coordinate space on which the electrodes are conformal to one of the coordinate axis of the space. Laplace equation is solved in the interelectrodic space, obtaining an analytical solution for the electrostatic distribution. Furthermore, using appropriate mathematical manipulations, we derive an analytical expression for the impedance of the transmission line formed by the proposed electrodes. The second part of the thesis is devoted to the analysis of SWOs in the frequency domain. An original analysis approach, based on the chain-parameter technique, is proposed in which the SWO and the connected antenna are described using a two-port network using which a transfer function between the input voltage and the radiated field is established. A closed form expression of the resonance frequency of the SWO is also obtained. The developed technique makes it possible to study the response of an SWO when connected to an arbitrary antenna with a frequency-dependent input impedance. The final part of the thesis presents the construction and test of an SWO prototype. The prototype design is based on the theoretical developments presented in the first two parts of the thesis. The realized SWO is experimentally characterized using different antennas. It is characterized by an input voltage of 30 kV and a resonance frequency of 433 MHz. Radiated electric fields using monopole antennas were in the order of 10 kV/m at a distance of 1.5 m. The prototype is used for testing the validity of the electrodynamic model for the analysis of SWOs connected to frequency dependent antennas. Different monopole antennas connected to the SWO are considered and the radiated fields are measured and compared with theoretical calculations. It is shown that the developed theoretical model is able to reproduce with a good accuracy the behavior of the SWO connected to a frequency dependent antenna.

EPFL2013

Visualisation of magnetic domain structures and magnetisation processes in Goss-oriented, high permeability steels using neutron grating interferometry

Benedikt Karl-Josef Gerhard Betz

Industrial transformers cores are built from stacked sheets of an iron silicon alloy, called laminations. The magnetic domain structures of these highly anisotropic electrical steels with a sharp (110)[001]-texture, the so-called Gosstexture, determines the magnetic properties of transformers. Commonly used investigation techniques for these laminations are inductive B-H-measurements. This technique reveals global magnetic properties such as hysteresis, remanence, saturation and losses. Locally resolved information about the underlying domain structure cannot be obtained. In this thesis, the neutron grating interferometer (nGI) is used to investigate the domain structures in Goss-oriented (GO) electrical steels at the Swiss Spallation Neutron Source using the cold neutron imaging facility ICON. In contrast to the attenuation based transmission image, the dark-field image (DFI) is related to multiple refraction of unpolarised neutrons at magnetic domain walls. Thereby the use of the DFI allows for the visualisation of bulk magnetic domain structures in two and three dimensions with a spatial resolution of down to 70 um in a field of view of 64mm x 64mm. The DFI is used for the visualisation of the locally resolved response of the bulk magnetic domain structures under the influence of externally applied magnetic fields. In the first part, the domain formation and growth along the initial magnetisation curve (0-6000 A/m) up to saturation in static DC magnetic fields was studied. For decreasing field values, the visualisation of the recurrence of the hysteretic domain structure down to the remanent (0 A/m) state is given. A correlation of the grain orientation and the corresponding basic and supplementary domain structure is given. In the second part, the DFI is used to investigate the response of magnetic domain walls to dynamic AC magnetic excitations. The visualisation of the domain wall motion under influence of alternating magnetic fields is performed. In detail, scans combining varying levels of an offset DC (0-30 A/m), oscillation amplitude A (0-1500 A/m), and oscillation frequency f (0-200 Hz) are conducted. By increasing the amplitude while maintaining constant values of DC and f, the transition from a frozen domain wall structure to a mobile one is recorded. Vice versa, increasing f while keeping A and DC constant led to the reverse transition from a mobile domain wall structure into a frozen one. It is shown that varying both, A and f shifts the position of transition region. Higher frequencies require higher oscillation amplitudes to overcome the freezing. The DFI allows for the analysis of the laminations coatings impact to the magnetic structures. To visualise the stress effect of the coating to the underlying domain formation an uncoated lamination is investigated with stepwise increasing applied external tensile stresses up to 20MPa. The domain configurations of the intermediate stress states are imaged and the original domain structure of the coated state is reproduced. To verify the results, complementary experiments using Kerr microscopy, Faraday imaging, small-angle neutron scattering and Laue X-ray diffraction were performed. The here presented findings allow for new insights into macromagnetism and enable new approaches in the field of descriptive models for bulk macromagnetism. Furthermore the results have the potential to further improve the properties of GO-steels used in industrial transformer applications.

EPFL2016

Magnonic crystals with reconfigurable magnetic defects for spin-based microwave electronics

Korbinian Baumgärtl

Collective spin excitations can propagate in magnetically ordered materials in the form of waves. These so-called spin waves (SWs) or magnons are promising for low-power beyond-CMOS information processing, which does not rely anymore on the lossy movement of electric charges. SWs in the few GHz frequency regime possess nanoscale wavelengths about five orders of magnitude smaller than electromagnetic waves of the same frequency. This property makes SWs ideally suited for application in microwave technology, essential for on-chip processing of wireless telecommunication signals. In this thesis, three crucial challenges relevant for the technological application of SWs are addressed: First, to functionalize SWs and exploit their small wavelengths, it is necessary to control them at the nanoscale. Here, periodically nanostructured materials, denoted magnonic crystals, are promising, as they allow to tailor the band structure of SWs. We report on SWs propagating in a prototypical one-dimensional magnonic crystal consisting of dipolarly coupled magnetic nanostripes. The remanent magnetization of individual stripes was designed to be bistable along the long axis. By magnetizing an individual stripe in opposite direction to the others, we created a magnetic defect. We measured by means of all-electrical spin wave spectroscopy and Brillouin light scattering microscopy phase and amplitude of SWs trespassing the defect. We found that SW phases and amplitudes were modified at the nanoscale, and phase shifts could be tuned by an applied bias magnetic field. Using micromagnetic simulations, we identified specific bias fields for which phase shifts of Pi are achieved without suppressing SW amplitudes. This result is highly relevant for the implementation of logic gates based on interference of phase-controlled SWs. We further measured propagation of short-waved SWs in an antiferromagnetically ordered one-dimensional magnonic crystal, where every second stripe was magnetized in opposite direction. We found a band gap closing at the Brillouin zone boundary when no magnetic bias field was applied. Our observations are promising for reprogrammable microwave filters capable of adjusting stop- and passband. Second, we address how long-waved electromagnetic waves can be coupled efficiently to nanoscale SWs. We demonstrate by space- and time-resolved scanning X-ray transmission measurements, that excited nanogratings allow to transfer their reciprocal lattice vector and multiple of it to an underlying magnetic thin film, in which nanoscale propagating SWs are launched. Additionally, we discovered a second method for short-waved SW generation based on magnetic microwave guides. This approach is easy to fabricate and relies on the adaption of the SW wavelength to a changing effective magnetic field. Efficient coupling of electromagnetic waves to nanoscale SWs promises an unprecedented miniaturization of microwave components. Third, we found that the magnetization direction of bistable nanomagnets can be switched by propagating SWs in an underlying magnetic thin film when a threshold amplitude is reached. This discovery is promising for the realization of a non-volatile magnonic memory, which stores SW amplitudes. A possible application are SW logic gates, which encode the outcome of a logic operation in the output SW amplitude. Magnonic memory would allow for storing these amplitudes directly, without requiring lossy conversion into the electrical domain.

EPFL2021