Lecture

Frequency Response and Bode Diagrams

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In course

EE-111: Circuits and systems

Ce cours présente une introduction à la théorie et aux méthodes d'analyse et de résolution des circuits électriques. ...

Description

This lecture covers the concept of transfer functions and frequency response in circuits, including the representation of transfer functions, voltage gains, and examples of low pass, high pass, and bandpass filters. It also explains the use of logarithms and decibels in describing linear systems, the behavior of complex functions, and the construction of Bode diagrams to represent amplitude and phase responses. The lecture concludes with a detailed analysis of different types of poles and zeros in transfer functions, along with their corresponding amplitude and phase diagrams.

Instructor

Farhad Rachidi-Haeri

Farhad Rachidi (IEEE Fellow, EMP Fellow, Electromagnetics Academy Fellow) was born in Geneva in 1962. He received the M.S. degree in electrical engineering and the Ph.D. degree from the Swiss Federal Institute of Technology, Lausanne, in 1986 and 1991 respectively. He worked at the Power Systems Laboratory of the same institute until 1996 and had several short stays at the University of Florida and the NASA Kennedy Space Center. In 1997, he joined the Lightning Research Laboratory of the University of Toronto in Canada and from April 1998 until September 1999, he was with Montena EMC in Switzerland. He is currently a titular professor and the head of the EMC Laboratory at the Swiss Federal Institute of Technology, Lausanne, Switzerland. His research interests concern electromagnetic compatibility, lightning electromagnetics and electromagnetic field interactions with transmission lines. Dr. Rachidi is currently a member of the Advisory Board of the IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY and the President of the Swiss National Committee of the International Union of Radio Science. He has received numerous awards including the 2005 IEEE EMC Technical Achievement Award, the 2005 CIGRE Technical Committee Award, the 2006 Blondel Medal from the French Association of Electrical Engineering, Electronics, Information Technology and Communication (SEE), the 2016 Berger Award from the International Conference on Lightning Protection, the 2016 Best Paper Award of the IEEE Transactions on EMC, and the 2017 Motohisa Kanda Award for the most cited paper of the IEEE Transactions on EMC (2012-2016). In 2014, he was conferred the title of Honorary Professor of the Xi’an Jiaotong University in China. He served as the Vice-Chair of the European COST Action on the Physics of Lightning Flash and its Effects from 2005 to 2009, the Chairman of the 2008 European Electromagnetics International Symposium, the President of the International Conference on Lightning Protection from 2008 to 2014, the Editor-in-Chief of the Open Atmospheric Science Journal (2010-2012) and the Editor-in-Chief of the IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY from 2013 to 2015. He is a Fellow of the IEEE and of the SUMMA Foundation, and a member of the Swiss Academy of Sciences. He is the author or coauthor of over 200 scientific papers published in peer-reviewed journals and over 400 papers presented at international conferences.

Official source

Ontological neighbourhood

Information engineering

Control theory and engineering: Control theory

Mathematics

Analysis: Complex analysis

Related concepts (32)

Frequency response

In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems, where they simplify mathematical analysis by converting governing differential equations into algebraic equations.

Complex logarithm

In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which are strongly related: A complex logarithm of a nonzero complex number , defined to be any complex number for which . Such a number is denoted by . If is given in polar form as , where and are real numbers with , then is one logarithm of , and all the complex logarithms of are exactly the numbers of the form for integers .

Step response

The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time. The concept can be extended to the abstract mathematical notion of a dynamical system using an evolution parameter.

Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.

Impulse response

In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (δ(t)). More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system).

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