Name: active filter design and frequency response
Uploaded: 2025-05-22T09:06:15.000Z
Duration: 1 min 25 s
Channel: JoVE

Certos filtros passivos incorporam indutores caros projetados para não exceder o ganho de unidade. Esses filtros podem apresentar eficácia de atenuação reduzida em frequências abaixo da faixa de áudio.
Os filtros ativos consistem em amplificadores, resistores e capacitores operacionais.
Empregados em unidades de processamento de áudio, telecomunicações e fonte de alimentação, esses filtros são categorizados como filtros passa-baixa de primeira ordem, passa-alta de primeira ordem, passa-banda e rejeição de banda.
Considere as funções de transferência e as respostas de frequência dos filtros ativos passa-baixa e passa-alta.
Ao contrário dos filtros passivos, o ganho finito de baixa frequência em filtros ativos passa-baixa e o ganho de alta frequência em filtros ativos passa-alta dependem da relação entre feedback e resistor de entrada.
Os filtros passa-baixa atenuam as frequências acima da frequência de canto, enquanto os filtros passa-alta suprimem as abaixo da frequência de canto.
A combinação de filtros passa-baixa e passa-alta resulta em um filtro passa-banda, enquanto um filtro de rejeição de banda combina os dois tipos com um amplificador de soma.
Os filtros passa-banda transmitem frequências entre as frequências de canto e rejeitam as externas; os filtros de rejeição de banda bloqueiam as frequências dentro da faixa e permitem frequências externas.

resposta de frequência

Filtros ativos são circuitos eletrônicos que usam amplificadores operacionais (amplificadores operacionais), resistores e capacitores para filtrar componentes de frequência indesejados de um sinal. Um filtro ativo passa-baixa de primeira ordem é projetado para passar sinais com uma frequência inferior a uma determinada frequência de corte e atenuar frequências superiores a essa frequência de corte. A função de transferência para um filtro ativo passa-baixa de primeira ordem é:
<img alt="Equation 1" src="/files/ftp_upload/15149/15149_Equation_1.svg" style="height: 40px;">
 Onde A_f é o ganho em baixas frequências, também conhecido como ganho CC, s é a frequência complexa e ω_c é a frequência de canto ou de corte. Um filtro ativo passa-alta de primeira ordem permite a passagem de sinais acima de uma determinada frequência de corte enquanto atenua sinais abaixo dessa frequência. Sua função de transferência pode ser expressa como:
<img alt="Equation 2" src="/files/ftp_upload/15149/15149_Equation_2.svg" style="height: 36px;">
Onde A_f representa o ganho em altas frequências e ω_c é a frequência de corte abaixo da qual a saída é significativamente reduzida. Um filtro passa-banda combina propriedades de filtros passa-baixa e passa-alta. Ele permite a passagem de apenas uma determinada faixa de frequências, enquanto atenua frequências fora dessa faixa. A função de transferência de um filtro passa-faixa tem a forma:
<img alt="Equation 3" src="/files/ftp_upload/15149/15149_Equation_3.svg" style="height: 42px;">
Aqui ω_0 é a frequência central e Q é o fator de qualidade. Um filtro de rejeição de banda, também conhecido como filtro notch, faz o oposto, permitindo a passagem da maioria das frequências, exceto em uma faixa específica que ele atenua. A função de transferência padrão para um filtro de rejeição de banda é:
<img alt="Equation 4" src="/files/ftp_upload/15149/15149_Equation_4.svg" style="height: 50px;">
Em filtros ativos, o ganho dentro da banda passante pode ser definido independentemente da frequência de corte, o ganho é determinado pela relação entre o resistor de feedback e o resistor de entrada, e os parâmetros de projeto, como valores de resistor e capacitor, são escolhidos para definir o frequências de corte e moldar a resposta de frequência geral do filtro para atender a requisitos específicos.

Resposta de Frequência

Certos filtros passivos incorporam indutores caros projetados para não exceder o ganho de unidade. Esses filtros podem apresentar eficácia de atenuação reduzida em ...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Frequency Response

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

Active Filters

active filter design and frequency response

Active filters use op-amps, resistors, and capacitors to shape a signal's frequency response. They remove unwanted frequency components while keeping the parts of the signal that are needed. The design depends on the choice of resistor and capacitor values, which set the cutoff points and help define the overall response.

A first-order low-pass active filter passes signals below a cutoff frequency and reduces signals above it. Its transfer function includes the low-frequency gain, also called the dc gain, along with the complex frequency s and the corner or cutoff frequency ωc. A first-order high-pass active filter does the opposite. It lets signals above a cutoff frequency pass and reduces signals below that frequency.

Active filters can also be built as band-pass filters. These filters combine low-pass and high-pass behavior and allow only a certain range of frequencies to pass. Their transfer function includes the center frequency ω0 and the quality factor Q. A band-reject filter, also called a notch filter, works in the opposite way. It passes most frequencies but attenuates a specific range.

In active filters, the gain in the passband can be set independently of the cutoff frequency. The gain is determined by the ratio of the feedback resistor to the input resistor. By choosing resistor and capacitor values carefully, engineers can set the cutoff frequencies and shape the frequency response to meet specific needs.

Active Filter Design and Frequency Response

active-filter-design-and-frequency-response

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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gain

Circuit Gain and Phase Shift

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Reading Frequency Response on Bode Plots

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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

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...

series resonance

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

Series resonance in an RLC circuit happens when the inductor, capacitor, and resistor are connected in series. At the resonant frequency, the inductive reactance and capacitive reactance are equal in size but opposite in sign, so they cancel each other. As a result, the circuit impedance becomes very small and is mainly set by the resistance. The resonant frequency of a series RLC circuit can be calculated from its inductance and capacitance. At this frequency, the current reaches its maximum...

parallel resonance

Parallel RLC Tuning at Resonance

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Op Amp Gain and Bode Plot Basics

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passive filters

Audio Frequency Control with Passive Filters

Passive filters shape the frequency spectrum of electrical signals. They use only passive parts such as resistors, inductors, and capacitors. Because they do not need an external power source, they can let selected frequency ranges pass or block others in many applications. Low-pass filters pass signals below the cutoff frequency, ωc, and reduce signals above it. In audio systems, they can send bass frequencies to woofers or subwoofers. For an RC low-pass filter, the transfer function H(s)...

active filters

Active filters use op-amps, resistors, and capacitors to shape a signal's frequency response. They remove unwanted frequency components while keeping the parts of the signal that are needed. The design depends on the choice of resistor and capacitor values, which set the cutoff points and help define the overall response. A first-order low-pass active filter passes signals below a cutoff frequency and reduces signals above it. Its transfer function includes the low-frequency gain, also called...

scaling

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design example

Touch-Tone Filter Design Example

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key terms and concepts

Learn how active filters use op-amps, resistors, and capacitors to shape frequency response with low-pass, high-pass, band-pass, and notch designs.

Active Filter Design and Frequency Response | 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

Active Filter Design and Frequency Response

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