Name: circuit component scaling for filters
Uploaded: 2024-07-08T13:20:03.000Z
Duration: 1 min 26 s
Channel: JoVE

La mise à l’échelle de l’amplitude et de la fréquence simplifie la conception des filtres en calibrant les réponses des filtres et les paramètres du circuit pour s’adapter aux plages utilisables.
La mise à l’échelle de l’amplitude consiste à amplifier toutes les impédances d’un réseau d’un facteur, en maintenant des réponses en fréquence cohérentes.
Les valeurs d’impédance et de fréquence mises à l’échelle sont ensuite exprimées à l’aide du facteur d’échelle.
Ce processus ne modifie pas la fréquence de résonance, le facteur de qualité, la bande passante ou les fonctions de transfert du circuit.
La mise à l’échelle de la fréquence décale la réponse en fréquence d’un réseau vers le haut ou vers le bas de l’axe des fréquences tout en laissant l’impédance inchangée. Cela se fait en multipliant la fréquence par un facteur d’échelle.
La mise à l’échelle des fréquences influence les impédances des éléments réactifs dépendants de la fréquence, mais la résistance n’est pas affectée.
Le facteur d’échelle modifie la fréquence de résonance et la bande passante, mais le facteur de qualité reste le même.
Une expression générale pour l’impédance et la mise à l’échelle de fréquence s’adapte à la mise à l’échelle simultanée de l’amplitude et de la fréquence.
Dans les cas où la mise à l’échelle de magnitude n’est pas appliquée, le facteur de mise à l’échelle de magnitude est défini sur un. De même, sans mise à l’échelle de fréquence, le facteur d’échelle de fréquence est défini sur un.

réponse en fréquence

Scaling

Lors de la conception et de l'analyse de filtres, de circuits résonants ou d'analyses de circuits en général, il peut être pratique de travailler avec des valeurs d'éléments standard telles que 1 ohm, 1 Henry ou 1 farad avant de mettre ces valeurs à l'échelle à des chiffres plus réalistes. Cette approche est largement utilisée car elle n'utilise pas de valeurs d'éléments réalistes dans de nombreux exemples et problèmes ; il simplifie la maîtrise de l'analyse des circuits grâce à des valeurs de composants pratiques. La complexité des calculs est ainsi réduite, étant entendu que les techniques de mise à l'échelle peuvent ensuite ajuster ces valeurs à des niveaux plus pratiques.
La mise à l'échelle d'un circuit peut être effectuée de deux manières : la mise à l'échelle de l'amplitude (ou de l'impédance) et la mise à l'échelle de la fréquence. Ces méthodes ajustent les composants du circuit pour fonctionner dans des plages pratiques. La mise à l'échelle de l'ampleur modifie la taille des composants sans affecter la façon dont le circuit répond aux différentes fréquences. D'un autre côté, la mise à l'échelle des fréquences déplace la réponse du circuit vers des fréquences plus élevées ou plus basses sur le spectre.
Mise à l'échelle de la magnitude:
La mise à l'échelle de l'ampleur implique d'ajuster la taille des composants du circuit (tels que les résistances, les inductances et les condensateurs) selon un certain facteur, mais sans modifier la façon dont le circuit répond aux différentes fréquences. Les impédances du circuit sont exprimées en termes de résistances (R), d'inductances (L) et de condensateurs (C) dans un circuit. Lorsque la mise à l'échelle de magnitude Km est appliquée, ces composantes sont transformées comme suit:
<img alt="Equation 1" src="/files/ftp_upload/15150/15150_Equation_1.svg" style="height: 12px;">
<img alt="Equation 2" src="/files/ftp_upload/15150/15150_Equation_2.svg" style="height: 36px;">
 Mise à l'échelle des fréquences:
La mise à l'échelle de fréquence décale la réponse en fréquence d'un circuit le long de l'axe des fréquences, vers le haut ou vers le bas, sans modifier les niveaux d'impédance. Ceci est obtenu en multipliant la fréquence par un facteur d'échelle, noté Kf. Les nouvelles valeurs de l'inductance et de la capacité sont déterminées par:
<img alt="Equation 3" src="/files/ftp_upload/15150/15150_Equation_3.svg" style="height: 36px;">
<img alt="Equation 4" src="/files/ftp_upload/15150/15150_Equation_4.svg" style="height: 36px;">
Si un circuit est mis à l'échelle à la fois pour les paramètres d'amplitude et de fréquence, alors:
<img alt="Equation 5" src="/files/ftp_upload/15150/15150_Equation_5.svg" style="height: 36px;">
<img alt="Equation 6" src="/files/ftp_upload/15150/15150_Equation_6.svg" style="height: 36px;">
Si les facteurs d'échelle d'amplitude et de fréquence sont égaux, aucune échelle d'amplitude ni de fréquence ne se produit.

Réponse en fréquence

La mise à l’échelle de l’amplitude et de la fréquence simplifie la conception des filtres en calibrant les réponses des filtres et les paramètres du circuit pour s’adapter aux plages utilisables.
Magnitude...

Education

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Electrical Engineering

Génie électrique

Unit 1

Unité 1

Frequency Response

KEY TERMS AND CONCEPTS

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circuit component scaling for filters

Circuit component scaling helps turn simple circuit values into practical ones for filter design and circuit analysis. Engineers often start with standard values like 1 ohm, 1 henry, or 1 farad because they make examples and problems easier to work through. Later, those values can be scaled to more realistic levels.

This method is useful in filters, resonant circuits, and many other circuit analysis problems. It reduces calculation complexity while keeping the circuit behavior easy to study. The idea is to learn the analysis first and then adjust the component values to fit real-world use.

There are two main ways to scale a circuit: magnitude scaling, also called impedance scaling, and frequency scaling. Magnitude scaling changes the size of the components without changing how the circuit responds to different frequencies. Frequency scaling shifts the circuit response higher or lower on the frequency axis without changing the impedance levels.

Magnitude scaling uses a factor called K m to change resistors, inductors, and capacitors. Frequency scaling uses a factor called K f to move the frequency response and to determine new inductance and capacitance values. When both magnitude and frequency scaling are applied together, the circuit can be adjusted in both size and response range. If the magnitude and frequency scaling factors are equal, neither type of scaling occurs.

Circuit Component Scaling for Filters

network function of a circuit

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transfer function and bode plots-i

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transfer function and bode plots-ii

Bode Plot Slope and Phase Changes

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bode plots construction

Reading Frequency Response with Bode Plots

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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 resonance

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scaling

Circuit component scaling helps turn simple circuit values into practical ones for filter design and circuit analysis. Engineers often start with standard values like 1 ohm, 1 henry, or 1 farad because they make examples and problems easier to work through. Later, those values can be scaled to more realistic levels. This method is useful in filters, resonant circuits, and many other circuit analysis problems. It reduces calculation complexity while keeping the circuit behavior easy to study.

design example

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key terms and concepts

Learn how magnitude scaling and frequency scaling adjust resistors, inductors, capacitors, and circuit response for easier filter design and analysis.

Circuit Component Scaling for Filters | 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

Circuit Component Scaling for Filters

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