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

Certains filtres passifs intègrent des inductances coûteuses conçues pour ne pas dépasser le gain unitaire. Ces filtres peuvent présenter une efficacité d’atténuation réduite à des fréquences inférieures à la plage audio.
Les filtres actifs se composent d’amplificateurs opérationnels, de résistances et de condensateurs.
Utilisés dans les unités de traitement audio, de télécommunications et d’alimentation, ces filtres sont classés en filtres passe-bas de premier ordre, passe-haut de premier ordre, passe-bande et rejet de bande.
Considérez les fonctions de transfert et les réponses en fréquence des filtres actifs passe-bas et passe-haut.
Contrairement aux filtres passifs, le gain basse fréquence fini dans les filtres actifs passe-bas et le gain haute fréquence dans les filtres actifs passe-haut dépendent du rapport rétroaction/résistance d’entrée.
Les filtres passe-bas atténuent les fréquences au-dessus de la fréquence d’angle, tandis que les filtres passe-haut suppriment celles en dessous de la fréquence d’angle.
La combinaison de filtres passe-bas et passe-haut permet d’obtenir un filtre passe-bande, tandis qu’un filtre de rejet de bande combine les deux types avec un amplificateur de sommation.
Les filtres passe-bande transmettent les fréquences entre les fréquences d’angle et rejettent celles à l’extérieur ; les filtres de rejet de bande bloquent les fréquences à l’intérieur de la plage et autorisent les fréquences externes.

réponse en fréquence

Les filtres actifs sont des circuits électroniques qui utilisent des amplificateurs opérationnels (amplis opérationnels), des résistances et des condensateurs pour filtrer les composantes de fréquence indésirables d'un signal. Un filtre actif passe-bas de premier ordre est conçu pour laisser passer les signaux dont la fréquence est inférieure à une certaine fréquence de coupure et atténuer les fréquences supérieures à cette fréquence de coupure. La fonction de transfert pour un filtre actif passe-bas du premier ordre est:
<img alt="Equation 1" src="/files/ftp_upload/15149/15149_Equation_1.svg" style="height: 40px;">
 Où Af est le gain aux basses fréquences, également appelé gain continu, s est la fréquence complexe et ωc est la fréquence de coupure ou de coupure. Un filtre actif passe-haut de premier ordre permet aux signaux supérieurs à une certaine fréquence de coupure de passer tout en atténuant les signaux inférieurs à cette fréquence. Sa fonction de transfert peut s’exprimer comme suit:
<img alt="Equation 2" src="/files/ftp_upload/15149/15149_Equation_2.svg" style="height: 36px;">
Où Af représente le gain aux hautes fréquences et ω_c est la fréquence de coupure en dessous de laquelle la sortie est considérablement réduite. Un filtre passe-bande combine les propriétés des filtres passe-bas et passe-haut. Il ne laisse passer qu’une certaine plage de fréquences tout en atténuant les fréquences en dehors de cette plage. La fonction de transfert d'un filtre passe-bande a la forme:
<img alt="Equation 3" src="/files/ftp_upload/15149/15149_Equation_3.svg" style="height: 42px;">
Ici ω0 est la fréquence centrale et Q est le facteur de qualité. Un filtre à réjection de bande, également appelé filtre coupe-bande, fait le contraire en laissant passer la plupart des fréquences, à l'exception d'une plage spécifique qu'il atténue. La fonction de transfert standard pour un filtre à réjection de bande est:
<img alt="Equation 4" src="/files/ftp_upload/15149/15149_Equation_4.svg" style="height: 50px;">
Dans les filtres actifs, le gain dans la bande passante peut être réglé indépendamment de la fréquence de coupure, le gain est déterminé par le rapport de la résistance de rétroaction à la résistance d'entrée, et les paramètres de conception, tels que les valeurs de résistance et de condensateur, sont choisis pour définir le fréquences de coupure et pour façonner la réponse en fréquence globale du filtre pour répondre à des exigences spécifiques.

Réponse en fréquence

Certains filtres passifs intègrent des inductances coûteuses conçues pour ne pas dépasser le gain unitaire. Ces filtres peuvent présenter une efficacité d’atténuation réduite à ...

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

Frequency Response

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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...

gain

Circuit Gain and Phase Shift

Circuit gain and phase shift describe how a linear circuit changes a sinusoidal input voltage or current. These properties matter in circuits with reactive elements, because the response depends on the input frequency. As the frequency changes, the gain and phase shift also change. Gain compares the size of the output sinusoid to the size of the input sinusoid. If Vin is the input and Vout is the output, the gain K is the ratio of the output amplitude to the input amplitude. A gain greater...

bode plots

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...

series resonance

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...

parallel resonance

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

Touch-Tone Filter Design Example

Touch-tone telephony uses dual-tone multi-frequency (DTMF) signaling and a filter design example to show how keypad tones are separated. It replaced the old rotary dial with a matrix-style keypad arranged in four rows and three columns. Each of the 12 buttons produces a unique signal pair. Every key press creates two sinusoidal tones at the same time. One tone comes from a low-frequency group between 697 and 941 Hz. The other comes from a high-frequency group between 1209 and 1477 Hz. This...

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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