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

La scala di ampiezza e frequenza semplifica la progettazione dei filtri calibrando le risposte dei filtri e i parametri del circuito per adattarli agli intervalli utilizzabili.
Il magnitude scaling comporta l'amplificazione di tutte le impedenze in una rete di un fattore, mantenendo risposte in frequenza coerenti.
I valori di impedenza e frequenza scalati vengono quindi espressi utilizzando il fattore di scala.
Questo processo non altera la frequenza di risonanza del circuito, il fattore di qualità, la larghezza di banda o le funzioni di trasferimento.
La scala di frequenza sposta la risposta in frequenza di una rete verso l'alto o verso il basso sull'asse delle frequenze, lasciando invariata l'impedenza. Si ottiene moltiplicando la frequenza per un fattore di scala.
La scala di frequenza influenza le impedenze degli elementi reattivi dipendenti dalla frequenza, ma il resistore rimane inalterato.
Il fattore di scala altera la frequenza di risonanza e la larghezza di banda, ma il fattore di qualità rimane lo stesso.
Un'espressione generale per la scala di impedenza e frequenza si adatta alla scala simultanea di grandezza e frequenza.
Per i casi in cui la scala di magnitudine non viene applicata, il fattore di scala di grandezza è impostato su uno. Analogamente, senza il ridimensionamento della frequenza, il fattore di scala della frequenza è impostato su uno.

risposta in frequenza

Nella progettazione e nell'analisi di filtri, circuiti risonanti o nell’analisi dei circuiti in generale, può essere conveniente lavorare con valori di elementi standard come 1 ohm, 1 henry o 1 farad prima di ridimensionare questi valori a cifre più realistiche. Questo approccio è ampiamente utilizzato, non impiegando valori di elementi realistici, in numerosi esempi e problemi; semplifica la padronanza dell'analisi del circuito attraverso convenienti valori dei componenti. La complessità dei calcoli viene quindi ridotta, con la consapevolezza che le tecniche di scaling possono successivamente adattare questi valori a livelli più pratici.

Il ridimensionamento di un circuito può essere eseguito in due modi: ridimensionamento dell'ampiezza (o impedenza) e ridimensionamento della frequenza. Questi metodi regolano i componenti del circuito in modo che funzionino entro intervalli pratici. Il ridimensionamento della grandezza modifica la dimensione dei componenti senza influenzare il modo in cui il circuito risponde alle diverse frequenze. D'altro canto, il ridimensionamento della frequenza sposta la risposta del circuito a frequenze più alte o più basse sullo spettro.


Ridimensionamento della grandezza:

Il ridimensionamento della grandezza comporta la regolazione delle dimensioni dei componenti del circuito (come resistori, induttori e condensatori) di un certo fattore, ma senza modificare il modo in cui il circuito risponde alle diverse frequenze. Le impedenze del circuito sono in termini di resistori (R), induttori (L) e condensatori (C) in un circuito. Quando si applica la scalatura della magnitudo Km, questi componenti vengono trasformati come segue:

<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;">

 Scala della frequenza:

Il ridimensionamento della frequenza, sposta la risposta in frequenza di un circuito lungo l'asse della frequenza, verso l'alto o verso il basso, senza alterare i livelli di impedenza. Ciò si ottiene moltiplicando la frequenza per un fattore di scala, indicato con Kf. I nuovi valori dell'induttanza e della capacità sono determinati da:

<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;">

Se un circuito viene ridimensionato contemporaneamente per entrambi i parametri, grandezza e frequenza, allora:

<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;">

Se i fattori di scala della magnitudo e della frequenza sono uguali, non si verifica né lo scaling della magnitudo né della frequenza.

Risposta in Frequenza

La scala di ampiezza e frequenza semplifica la progettazione dei filtri calibrando le risposte dei filtri e i parametri del circuito per adattarli agli intervalli utilizzabili.
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Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

Frequency Response

Risposta in frequenza

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

Scaling

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-ii

Bode Plot Slope and Phase Changes

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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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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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