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

A escala de magnitude e frequência simplifica o projeto do filtro, calibrando as respostas do filtro e os parâmetros do circuito para caber dentro das faixas utilizáveis.
A escala de magnitude envolve a amplificação de todas as impedâncias em uma rede por um fator, mantendo respostas de frequência consistentes.
Os valores de impedância e frequência escalados são então expressos usando o fator de escala.
Este processo não altera a frequência de ressonância do circuito, fator de qualidade, largura de banda ou funções de transferência.
A escala de frequência muda a resposta de frequência de uma rede para cima ou para baixo no eixo de frequência, deixando a impedância inalterada. Isso é feito multiplicando a frequência por um fator de escala.
A escala de frequência influencia as impedâncias dos elementos reativos dependentes da frequência, mas o resistor permanece inalterado.
O fator de escala altera a frequência de ressonância e a largura de banda, mas o fator de qualidade permanece o mesmo.
Uma expressão geral para escala de impedância e frequência acomoda escala simultânea de magnitude e frequência.
Para casos em que a escala de magnitude não é aplicada, o fator de escala de magnitude é definido como um. Da mesma forma, sem escala de frequência, o fator de escala de frequência é definido como um.

resposta de frequência

Ao projetar e analisar filtros, circuitos ressonantes ou análise de circuitos em geral, trabalhar com valores de elementos padrão como 1 ohm, 1 Henry ou 1 farad pode ser conveniente antes de dimensionar esses valores para valores mais realistas. Esta abordagem é amplamente utilizada por não empregar valores de elementos realistas em vários exemplos e problemas; simplifica o domínio da análise de circuitos por meio de valores de componentes convenientes. A complexidade dos cálculos é assim reduzida, entendendo-se que as técnicas de escalonamento podem posteriormente ajustar estes valores para níveis mais práticos.
O escalonamento de um circuito pode ser feito de duas maneiras: escalonamento de magnitude (ou impedância) e escalonamento de frequência. Esses métodos ajustam os componentes do circuito para funcionarem dentro de faixas práticas. A escala de magnitude altera o tamanho dos componentes sem afetar a forma como o circuito responde a diferentes frequências. Por outro lado, a escala de frequência move a resposta do circuito para frequências mais altas ou mais baixas no espectro.
Escala de magnitude:
A escala de magnitude envolve o ajuste dos tamanhos dos componentes do circuito (como resistores, indutores e capacitores) por um determinado fator, mas sem alterar a maneira como o circuito responde a diferentes frequências. As impedâncias do circuito são em termos de resistores (R), indutores (L) e capacitores (C) em um circuito. Quando a escala de magnitude K_m é aplicada, esses componentes são transformados da seguinte forma:
<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;">
 Escala de frequência:
A escala de frequência muda a resposta de frequência de um circuito ao longo do eixo de frequência, para cima ou para baixo, sem alterar os níveis de impedância. Isto é conseguido multiplicando a frequência por um fator de escala, denotado por K_f. Os novos valores da indutância e capacitância são determinados por:
<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 um circuito for dimensionado para ambos os parâmetros - magnitude e frequência ao mesmo tempo, então:
<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 os fatores de escala de magnitude e frequência forem iguais, não ocorre escala de magnitude nem de frequência.

Resposta de Frequência

A escala de magnitude e frequência simplifica o projeto do filtro, calibrando as respostas do filtro e os parâmetros do circuito para caber dentro das faixas utilizáveis.
Magnitude...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Frequency Response

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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

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characteristics of series resonant circuit

characteristics-of-series-resonant-circuit

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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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