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Concept# Transfer function

Summary

In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input. They are widely used in electronic engineering tools like circuit simulators and control systems. In some simple cases, this function can be represented as two-dimensional graph of an independent scalar input versus the dependent scalar output, called a transfer curve or characteristic curve. Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory.
The dimensions and units of the transfer function model the output response of the device for a range of possible inputs. For example, the transfer function of a two-port electronic circuit like an amplifier might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar volta

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MICRO-211: Analog circuits and systems

This course introduces the analysis and design of linear analog circuits based on operational amplifiers. A Laplace early approach is chosen to treat important concepts such as time and frequency responses, convolution, and filter design. The course is complemented with exercises and simulations.

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EE-348: Electroacoustics

Ce cours a pour objectif de former les étudiants de section Génie Electrique et Electronique à la conception de systèmes acoustiques, à l'aide d'un formalisme basé sur l'électrotechnique. A la fin du semestre, les étudiants seront capables de dimensionner, entre autres, des filtres acoustiques.

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.

Zhe Chen, Mario Paolone, Zhaoyang Wang

The classical electromagnetic time reversal (EMTR) fault location method in power systems can be time consuming, especially when a high location accuracy is desired. To cope with this issue, the concept of EMTR in mismatched media has recently been introduced, substantially improving the fault location efficiency. In this paper, we present a theoretical study and rigorous demonstration of the mismatched-media-based mirrored minimum energy property. Firstly, we infer a direct-reversed-time transfer function and present a theorem according to which, at the fault switching frequency and its odd harmonics, the mirror-image point of the fault location with respect to the line center corresponds to a local minimum of the squared modulus of the transfer function. Next, it is proved that the mirrored minimum energy property is a corollary of this theorem. Based on these theoretical findings, we propose an algorithm that uses the reversed-time voltage energy as a fault location metric in the frequency domain, instead of the original time-domain approach. We further propose applying a data-driven strategy to maximize the computation efficiency of the algorithm. The applicability and robustness of the frequency-domain fault location metric, together with the computational efficiency of the accelerating algorithm, are numerically and experimentally validated.

2021Related lectures (342)

In recent years, optical gas detectors based on a tunable diode laser absorption spectrometer has become more and more important for monitoring trace gases in atmospheric, medical, and industrial processes. In the medical field, blood gases, essentially pO2 and pCO2, are vital parameters for patient respiratory status monitoring. Typically, hypoxaemia or hypercapnia can be very harmful, especially for neonates, and requires continuous monitoring for rapid clinical intervention. Transcutaneous blood gases, permeating through the skin, can be continuously measured in patients by electrochemical sensors applied to the surface of the skin. These sensors suffer specific instability and must be re-calibrated. For this reason, the present thesis explores a new concept of gas sensors, applying light absorption at the surface of an integrated optics waveguide and using the advantages of a modulated spectroscopy technique for sensitivity and selectivity enhancement. In other words, the present thesis sets a mathematical model and demonstrates experimentally a new concept of evanescent wave gas sensing based on modulation spectroscopy. The field of application considered in this book is restricted to gas detection, however the concept can also be applied to the detection of liquids. In particular, we demonstrate the potential applicability of the concept to transcutaneous blood gas monitoring, and especially carbon dioxide monitoring. The system transfer function modelization of the concept includes carbon dioxide absorption spectrum in the near-infrared region (1.6µm), laser diode modulation spectroscopy assuming optical frequency modulation (FM) as well as intensity modulation (IM) induced by current modulation, and integrated optics sensor-head transmission. The modelization evidences that the silicon nitride technology has the advantage of: high evanescent wave sensitivity (8% for the selected TE mode), low propagation loss, possibility of strong curvatures for miniaturization and availability of fiberto- waveguide mode matching technique (taper). In the modelization, we evidence that the optimal waveguide length equals the inverse of the propagation loss which is mainly limited by the waveguide scattering. Also, we demonstrate that the implementation of a fiber-to-waveguide mode matching taper at both waveguide ends, drastically decreases the resonance limitation of the system resolution. Experimentally, the transfer function of the concept is validated and characterized based on a free-space modulation spectroscopy setup whose performance, in terms of second harmonic resolution, is first measured at 3.55 · 10-6 1/√Hz corresponding to 0.275 mmHg/√Hz CO2 partial pressure. In the chosen region of 200-400MHz of frequency modulation, we confirm that the 1/f-noise is negligible and the dominating amplifier noise can be approximated by the thermal noise. In the case of high insertion loss and short interaction length the interferometric noise (or etalon-effect) becomes the system resolution limitation. By the insertion of a prism coupled planar waveguide instead of the free-space cell, we demonstrate the concept of integrated optics evanescent wave sensing based on modulation spectroscopy. The system characterization is completed by the validation of the evanescent wave sensitivity in gas of about 8% for a laterally confined waveguide. The outlook of a transcutaneous blood gas monitoring instrument is also established. We first extrapolate the expected waveguide characteristics to show that a resolution of 1mmHg CO2 partial pressure can be reached in 4.5 to 12sec response-time. Then, the requirement of a maximal sensing area of 10mm diameter is at the origin of two geometries of sensor-head: a crossing spiral and a non-crossing double spiral. We verify experimentally a propagation loss as low as 0.5dB/cm and observe a stringent tolerance for light injection. The latter requires an integrated device for mode matching and pigtailing. After implementation of a taper at both waveguide ends, we demonstrate the drastic reduction of the total coupling loss. The carbon dioxide measurements reveal a relatively deep pattern on the second harmonic signal that tends to prove that polarization and resonances are coupled together most likely at the waveguide level. Applying nitrogen (N2) as reference gas, the pattern compensation results in the carbon dioxide signature measurement in direct detection only. The next generation, now in process, is a patented pigtailed non-crossing double-spiral sensor-head building the first step towards an industrial prototype. The waveguide miniaturization allows an interaction length longer than 21cm on a 3×3mm area. The improvement towards a high resolution system concerns the propagation loss and the coupling loss on the sensor-head, and concerns the polarization control or scrambling on the modulation spectroscopy setup. We finally conclude, following the demonstration on the planar waveguide and the extrapolation of the measured characteristics, that the concept of evanescent wave gas sensing based on modulation spectroscopy, can compensate the lack of sensitivity of an integrated optics sensor-head and can be applied in gas and liquid sensing. Moreover, based on the sensor-head developments and realistic improvements, we also conclude that the perspective of high resolution sensing system, and in particular for carbon dioxide determination, evidences the potential applicability of the concept to transcutaneous blood gas monitoring. This opens a new optical outlook of continuous and non-invasive blood gas monitoring, applied in medicine for patient respiratory status monitoring.