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

Ciertos filtros pasivos incorporan inductores costosos diseñados para no exceder la ganancia unitaria. Estos filtros pueden exhibir una eficacia de atenuación reducida a frecuencias por debajo del rango de audio.
Los filtros activos constan de amplificadores operacionales, resistencias y condensadores.
Empleados en unidades de procesamiento de audio, telecomunicaciones y fuente de alimentación, estos filtros se clasifican como filtros de paso bajo de primer orden, paso alto de primer orden, paso de banda y rechazo de banda.
Tenga en cuenta las funciones de transferencia y las respuestas de frecuencia de los filtros activos de paso bajo y paso alto.
A diferencia de los filtros pasivos, la ganancia finita de baja frecuencia en los filtros activos de paso bajo y la ganancia de alta frecuencia en los filtros activos de paso alto dependen de la relación entre la resistencia de retroalimentación y entrada.
Los filtros de paso bajo atenúan las frecuencias por encima de la frecuencia de esquina, mientras que los filtros de paso alto suprimen las que están por debajo de la frecuencia de esquina.
La combinación de filtros de paso bajo y paso alto da como resultado un filtro de paso de banda, mientras que un filtro de rechazo de banda combina ambos tipos con un amplificador sumador.
Los filtros de paso de banda transmiten frecuencias entre las frecuencias de esquina y rechazan las externas; los filtros de rechazo de banda bloquean las frecuencias dentro del rango y permiten frecuencias externas.

respuesta de frecuencia

Los filtros activos son circuitos electrónicos que utilizan amplificadores operacionales (op-amps), resistencias y condensadores para filtrar componentes de frecuencia no deseados de una señal. Un filtro activo de paso bajo de primer orden está diseñado para pasar señales con una frecuencia inferior a una determinada frecuencia de corte y atenuar frecuencias superiores a esa frecuencia de corte. La función de transferencia para un filtro activo de paso bajo de primer orden es:
<img alt="Equation 1" src="/files/ftp_upload/15149/15149_Equation_1.svg" style="height: 40px;">
 Donde A_f es la ganancia a bajas frecuencias, también conocida como ganancia de CC, s es la frecuencia compleja y ω_c es la frecuencia de corte o de esquina. Un filtro activo de paso alto de primer orden permite que pasen señales por encima de una determinada frecuencia de corte mientras atenúa las señales por debajo de esta frecuencia. Su función de transferencia se puede expresar como:
<img alt="Equation 2" src="/files/ftp_upload/15149/15149_Equation_2.svg" style="height: 36px;">
Donde A_f representa la ganancia a altas frecuencias y ω_c es la frecuencia de corte por debajo de la cual la salida se reduce significativamente. Un filtro de paso de banda tiene propiedades combinadas de filtros de paso bajo y de paso alto. Sólo permite el paso de un cierto rango de frecuencias y atenúa las frecuencias fuera de este rango. La función de transferencia de un filtro de paso de banda tiene la forma:
<img alt="Equation 3" src="/files/ftp_upload/15149/15149_Equation_3.svg" style="height: 42px;">
Aquí ω_0 es la frecuencia central y Q es el factor de calidad. Un filtro de rechazo de banda, también conocido como filtro de muesca, hace lo contrario al permitir el paso de la mayoría de las frecuencias, excepto un rango específico que atenúa. La función de transferencia estándar para un filtro de rechazo de banda es:
<img alt="Equation 4" src="/files/ftp_upload/15149/15149_Equation_4.svg" style="height: 50px;">
En los filtros activos, la ganancia dentro de la banda de paso se puede configurar independientemente de la frecuencia de corte, la ganancia está determinada por la relación entre la resistencia de retroalimentación y la resistencia de entrada, y los parámetros de diseño, como los valores de resistencia y capacitor, se eligen para establecer la frecuencias de corte y para dar forma a la respuesta de frecuencia general del filtro para cumplir con requisitos específicos.

Respuesta de frecuencia

Ciertos filtros pasivos incorporan inductores costosos diseñados para no exceder la ganancia unitaria. Estos filtros pueden exhibir una eficacia de atenuación reducida ...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Frequency Response

Respuesta en frecuencia

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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

Inductive circuit frequency response shows how a circuit with an inductor reacts to different frequencies. The analysis starts in the time domain and then moves into the frequency domain. In that step, the inductor is replaced by an impedance, and the circuit is written with phasors, which are sinusoidal signals shown with magnitude and phase. The transfer function describes how the output changes compared with the input at each frequency. A key parameter is the time constant, which is the...

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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

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...

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Series Resonance in RLC Circuits

Series resonance in an RLC circuit happens when the inductive reactance and capacitive reactance are equal. An RLC circuit contains a resistor, an inductor, and a capacitor. The impedance of the circuit is the ratio of the supply voltage to the circuit current. At resonance, the imaginary part of the impedance becomes zero. The frequency at which this occurs is called the resonant frequency. It depends on the inductance (L) and capacitance (C) of the circuit. Mathematically, the resonant...

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...

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Parallel RLC Tuning at Resonance

A parallel RLC circuit uses a resistor, inductor, and capacitor connected to the same nodes. Because they share the same voltage, the circuit is analyzed with admittance, which describes how easily current can flow. In a parallel RLC circuit, admittance helps show how the circuit responds as the frequency changes. Resonance happens when the net reactance is zero. At that point, the capacitive and inductive effects cancel each other out. The resonant frequency is found from this condition. At...

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Op Amp Gain and Bode Plot Basics

Operational amplifiers are used for signal conditioning, filtering, and mathematical tasks such as addition, subtraction, integration, and differentiation. Their frequency response shows how amplifier gain changes as the input frequency changes. This makes the gain of an op-amp a key idea in circuit design. At low frequencies, an op-amp can hold a constant gain called the dc gain, A0. As frequency rises, the gain starts to drop after the corner frequency, or break frequency, ω1. In other...

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

Circuit Component Scaling for Filters

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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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