Name: reading frequency response with bode plots
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 24 s
Channel: JoVE

Les électrodes tissulaires des électrocardiogrammes (E-C-G) établissent une voie conductrice pour les courants électriques entre les tissus et les électrodes de mesure, permettant l’observation de l’activité cardiaque.
La dynamique de l’interface électrode-tissu a un modèle de circuit englobant la résistance de l’électrode, la capacité à l’interface électrode-tissu et la résistance tissulaire. La différence de potentiel représente la différence de tension entre l’électrode et le tissu.
Ici, l’impédance d’entrée est égale à la résistance du tissu. L’impédance de sortie est l’addition de la résistance tissulaire à la combinaison parallèle de résistance et de capacité à l’interface électrode-tissu.
Le rapport entre le phaseur de sortie et le phaseur d’entrée, calculé à l’aide des valeurs de résistance et de capacité connues, est la fonction de transfert.
Cela peut être approximé sur trois gammes de fréquences distinctes.
Le diagramme de magnitude de Bode sur un graphique semi-logarithmique représente le gain logarithmique calculé en décibels en fonction de la fréquence en radians par seconde.
Les asymptotes basse et haute fréquence sont des lignes horizontales à gain constant. Dans la gamme de fréquences intermédiaires, le graphique de magnitude asymptotique est linéaire avec une pente de 20 décibels par décennie.

réponse en fréquence

Bode Plots Construction

Le tracé de Bode est un outil essentiel dans l'analyse des systèmes de contrôle, car il cartographie la réponse en fréquence d'un système via un tracé d'amplitude et un tracé de phase, tous deux par rapport à un axe de fréquence logarithmique. Pour construire un tracé de Bode, considérons la fonction de transfert H(ω) :

<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_1.svg" style="height: 32px;">

Elle a un gain constant, des zéros et des pôles. Après normalisation, la fonction de transfert s’écrit :

<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_2.svg" style="height: 32px;">

Chaque terme de cette fonction normalisée affecte distinctement le tracé de Bode. Le terme 10jω a un gain constant de 10 et un zéro à l'origine jω. Chaque terme de pôle simple (1+jω/ωi) introduit un point d'arrêt ou une fréquence de coin ωiω_iωi. La pente positive du zéro est évidente depuis l'origine, tandis que les pentes négatives des pôles commencent à leurs fréquences de coin, ω=2 et ω=10 respectivement.

<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_3.svg" style="height: 36px;">

<img alt="Equation 1" src="/files/ftp_upload/15102/15102_Equation_4.svg" style="height: 28px;">

Une fois la contribution individuelle de chaque terme identifiée, le tracé de Bode global peut être construit. Cela implique de superposer les pentes et les changements de phase de chaque facteur. Aux basses fréquences, le tracé d'amplitude commence à 20 dB (since 20log10(10) =20) et maintient une réponse plate jusqu'à la première fréquence de coin. Le tracé de phase commence à 90° en raison du zéro à l'origine et commence sa descente avant la première fréquence de coin.

La pente du tracé d'amplitude changera à chaque fréquence de coin, diminuant de 20 dB/décennie à ω=2 et de nouveau à ω=10. En conséquence, le tracé de phase se courbera vers le bas, approchant -90° à une fréquence bien supérieure à ω=10.

Enfin, le tracé asymptotique de Bode, constitué de ces lignes droites, peut être ajusté pour se rapprocher plus fidèlement de la réponse en fréquence réelle. Cela implique l'ajout d'une courbe lisse coupant le tracé asymptotique à chaque fréquence de coin, ce qui entraîne généralement un léger dépassement près des fréquences de coin, appelé "pic".

Réponse en fréquence

Les électrodes tissulaires dans les électrocardiogrammes (E-C-G) établissent une voie conductrice pour les courants électriques entre les tissus et les électrodes de mesure, ...

Education

JoVE Core

Electrical Engineering

Unit 1

Frequency Response

KEY TERMS AND CONCEPTS

reading frequency response with bode plots

Bode plots show the frequency response of a system with a magnitude plot and a phase plot. Both plots use a logarithmic frequency axis. In control system analysis, this makes it easier to see how a transfer function changes with frequency.

To build a Bode plot, start with the transfer function H(ω). After normalization, the function includes constant gain, zeros, and poles. Each term affects the plot in a different way.

A constant gain of 10 gives a starting magnitude of 20 dB, since 20 log10(10) = 20. The term 10jω also creates a zero at the origin, so the magnitude has a positive slope from the start. Each simple pole term, such as 1 + jω/ωi, adds a breakpoint or corner frequency ωi.

The zero at the origin gives the phase plot an initial value of 90°. The phase then begins to fall before the first corner frequency. The poles at ω = 2 and ω = 10 add negative slope changes to the magnitude plot, each reducing the slope by 20 dB per decade at its corner frequency.

The full Bode plot comes from adding the effects of each factor together. At low frequencies, the magnitude stays flat until the first corner frequency. The phase curve bends downward and approaches -90° at a frequency much higher than ω = 10.

The first result is an asymptotic Bode plot made of straight-line segments. A smoother curve can then be added to match the actual frequency response more closely. This adjustment often crosses the asymptotic lines near each corner frequency and can show a small peak, called peaking.

Reading Frequency Response with Bode Plots

reading-frequency-response-with-bode-plots

network function of a circuit

How Transfer Functions Shape Circuit Response

Transfer functions show how a circuit responds as signal frequency changes. They describe the link between input and output in frequency response analysis. This makes them useful for studying how circuits behave in electronics and engineering. A transfer function is a mathematical tool that relates phasor output to phasor input. It can be written as voltage gain, current gain, transfer impedance, or transfer admittance. The poles and zeros are the most important parts of the function. Zeros...

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Inductive Circuit Frequency Response

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Circuit Gain and Phase Shift

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Reading Frequency Response on Bode Plots

Bode plots show how a circuit or system responds across frequency. They use a logarithmic frequency scale on the x-axis and gain in decibels on the y-axis. This format makes it easier to display a wide range of frequencies and to see how circuit parts affect behavior over that range. A network function gives the ratio of output to input for a system. Its complex form provides both magnitude and phase angle. The logarithmic gain on a Bode plot comes from the magnitude, calculated by multiplying...

transfer function and bode plots-i

Transfer Function Gain and Origin Effects

Transfer function gain and poles or zeros at the origin shape a system's Bode plot. The transfer function is often written in standard form after the polynomial coefficients are normalized. In that form, the constant gain, zeros, poles, and quadratic terms all appear clearly. The poles and zeros mark critical frequencies where the output magnitude and phase change noticeably. The constant gain K creates a fixed magnitude and phase term. Its magnitude is 20 log 10 K in decibels, and its phase...

transfer function and bode plots-ii

Bode Plot Slope and Phase Changes

Bode plots show how a transfer function changes with frequency. The standard form includes constant gain, poles and zeros at the origin, simple poles and zeros, and quadratic poles and zeros. Each part shapes the system response in a different way. A simple zero sets the magnitude trend first. The Bode magnitude plot stays flat at low frequencies, near 0 dB, and then rises at 20 dB per decade after the corner or break frequency, ω1. That corner frequency is where the straight-line...

bode plots construction

Bode plots show the frequency response of a system with a magnitude plot and a phase plot. Both plots use a logarithmic frequency axis. In control system analysis, this makes it easier to see how a transfer function changes with frequency. To build a Bode plot, start with the transfer function H(ω). After normalization, the function includes constant gain, zeros, and poles. Each term affects the plot in a different way. A constant gain of 10 gives a starting magnitude of 20 dB, since 20...

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Series Resonance in RLC Circuits

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characteristics of series resonant circuit

characteristics-of-series-resonant-circuit

Series Resonance and RLC Filter Behavior

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Parallel RLC Tuning at Resonance

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Op Amp Gain and Bode Plot Basics

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design example

Touch-Tone Filter Design Example

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key terms and concepts

Learn how Bode plots track magnitude and phase on a log frequency axis, including gain, zeros, poles, corner frequencies, and peaking.

Reading Frequency Response with Bode Plots | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Reading Frequency Response with Bode Plots

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