Lecture

Three-Port Devices: Lossless, Matched, and Reciprocal

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In course

EE-445: Microwaves, the basics of wireless communications

This course is an introduction to microwaves and microwave passive circuits. A special attention is given to the introduction of the notion of distributed circuits and to the scattering matrix ...

Description

This lecture covers the fundamental properties of three-port devices, explaining why a three-port cannot be lossless, matched, and reciprocal simultaneously. It delves into the conditions for lossless, matched, and reciprocal three-port circuits, as well as the implications of nearly matched ports. The lecture also explores the concept of circulators and Y-junctions, discussing the design and characteristics of these components. Additionally, it examines the behavior of lossy three-port circuits, such as resistive dividers and Wilkinson dividers, highlighting the matching conditions and network equivalences. The lecture concludes with a study of symmetric and asymmetric excitations in three-port devices, analyzing the reflection coefficients and impedance matching at different ports.

Instructor

Anja Skrivervik

Anja Skrivervik obtained her electrical engineering degree from Ecole Polytechnique Fédérale de Lausanne in 1986, and her PhD from the same institution in 1992, for which she received the Latsis award. After a stay at the University of Rennes as an invited Research Fellow and two years in the industry, she returned part time to EPFL as an Assistant Professor in 1996, and is now a Professeur Titulaire at this institution, where she is the head of the Microwave and Antenna Group. Her research activities include electrically small antennas, antennas in biological media, periodic structures, reflect- and tranmitarrays, and numerical techniques for electromagnetics. She is author or co-author of more than 200 peer reviewed scientific publications. Her teaching activities include courses on microwaves and antennas, and she has course at Bachelor, Master and PhD levels. She was director of the EE section form 1996-2000, and is currently the director of the EE doctoral school at EPFL. She is very active in European collaboration and European projects. She was the chairperson of the Swiss URSI until 2012, is a Board member of the European School on Antennas and is frequently requested to review research programs and centers in Europe. She is a member of the board of directors of the European Association on Antennas and Propagation (EurAAP) since 2017.

Official source

Ontological neighbourhood

Physics

Electromagnetism: Electrical networks

Related concepts (32)

RLC circuit

An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent components of this circuit, where the sequence of the components may vary from RLC. The circuit forms a harmonic oscillator for current, and resonates in a manner similar to an LC circuit. Introducing the resistor increases the decay of these oscillations, which is also known as damping.

Scatter matrix

For the notion in quantum mechanics, see scattering matrix. In multivariate statistics and probability theory, the scatter matrix is a statistic that is used to make estimates of the covariance matrix, for instance of the multivariate normal distribution. Given n samples of m-dimensional data, represented as the m-by-n matrix, , the sample mean is where is the j-th column of . The scatter matrix is the m-by-m positive semi-definite matrix where denotes matrix transpose, and multiplication is with regards to the outer product.

Two-port network

In electronics, a two-port network (a kind of four-terminal network or quadripole) is an electrical network (i.e. a circuit) or device with two pairs of terminals to connect to external circuits. Two terminals constitute a port if the currents applied to them satisfy the essential requirement known as the port condition: the current entering one terminal must equal the current emerging from the other terminal on the same port. The ports constitute interfaces where the network connects to other networks, the points where signals are applied or outputs are taken.

Distributed-element circuit

Distributed-element circuits are electrical circuits composed of lengths of transmission lines or other distributed components. These circuits perform the same functions as conventional circuits composed of passive components, such as capacitors, inductors, and transformers. They are used mostly at microwave frequencies, where conventional components are difficult (or impossible) to implement. Conventional circuits consist of individual components manufactured separately then connected together with a conducting medium.

Series and parallel circuits

Two-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology. Whether a two-terminal "object" is an electrical component (e.g. a resistor) or an electrical network (e.g. resistors in series) is a matter of perspective. This article will use "component" to refer to a two-terminal "object" that participate in the series/parallel networks.

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