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

특정 수동 필터에는 단위 이득을 초과하지 않도록 설계된 고가의 인덕터가 통합되어 있습니다. 이러한 필터는 오디오 범위 미만의 주파수에서 감소된 감쇠 효율을 나타낼 수 있습니다.
능동 필터는 연산 증폭기, 저항기 및 커패시터로 구성됩니다.
오디오 처리, 통신 및 전원 공급 장치에 사용되는 이 필터는 1차 저역 통과, 1차 고역 통과, 대역 통과 및 대역 제거 필터로 분류됩니다.
저역 통과 필터와 고역 통과 능동 필터의 전달 함수와 주파수 응답을 생각해 보십시오.
패시브 필터와 달리, 저역 통과 능동 필터의 유한 저주파 이득과 고역 통과 능동 필터의 고주파 이득은 피드백 대 입력 저항 비율에 따라 달라진다.
저역 통과 필터는 코너 주파수보다 높은 주파수를 감쇠시키는 반면, 고역 통과 필터는 코너 주파수 미만의 주파수를 억제합니다.
저역 통과 필터와 고역 통과 필터의 조합은 대역 통과 필터를 생성하고, 대역 제거 필터는 두 유형을 합산 증폭기와 결합합니다.
대역 통과 필터는 모서리 주파수 사이에서 주파수를 전송하고 바깥쪽 주파수를 거부하며, 대역 제거 필터는 범위 내의 주파수를 차단하고 외부 주파수를 허용합니다.

주파수 응답

능동 필터는 연산 증폭기(op-amp), 저항기 및 커패시터를 사용하여 신호에서 원치 않는 주파수 성분을 필터링하는 전자 회로입니다. 1차 저역 통과 능동 필터는 특정 차단 주파수보다 낮은 주파수의 신호를 통과시키고 해당 차단 주파수보다 높은 주파수를 감쇠하도록 설계되었습니다. 1차 저역 통과 능동 필터의 전달 함수는 다음과 같습니다.
<img alt="Equation 1" src="/files/ftp_upload/15149/15149_Equation_1.svg" style="height: 40px;">

 여기서 A_f는 dc 이득이라고도 알려진 낮은 주파수에서의 이득이고, s는 복소 주파수, ω_c는 코너 또는 차단 주파수입니다. 1차 고역 통과 능동 필터를 사용하면 특정 차단 주파수 위의 신호는 통과시키는 동시에 이 주파수 아래의 신호는 감쇠됩니다. 전달 함수는 다음과 같이 표현될 수 있습니다.
<img alt="Equation 2" src="/files/ftp_upload/15149/15149_Equation_2.svg" style="height: 36px;">
여기서 A_f는 고주파수에서의 이득을 나타내고 ω_c는 출력이 크게 감소하는 차단 주파수입니다. 대역통과 필터는 저역통과 필터와 고역통과 필터의 특성을 결합한 것입니다. 이 범위 밖의 주파수는 감쇠하면서 특정 범위의 주파수만 통과하도록 허용합니다. 대역통과 필터의 전달 함수는 다음과 같은 형식을 갖습니다.
<img alt="Equation 3" src="/files/ftp_upload/15149/15149_Equation_3.svg" style="height: 42px;">
여기서 ω_0는 중심 주파수이고 Q는 품질 인자입니다. 노치 필터라고도 하는 대역 제거 필터는 감쇠하는 특정 범위를 제외하고 대부분의 주파수를 통과시키는 방식으로 반대의 역할을 합니다. 대역 거부 필터의 표준 전달 함수는 다음과 같습니다.
<img alt="Equation 4" src="/files/ftp_upload/15149/15149_Equation_4.svg" style="height: 50px;">
능동 필터에서 통과대역 내의 이득은 차단 주파수와 독립적으로 설정될 수 있으며, 이득은 피드백 저항과 입력 저항의 비율에 의해 결정되며, 저항 및 커패시터 값과 같은 설계 매개변수를 선택하여 설정합니다. 특정 요구 사항을 충족하기 위해 차단 주파수를 설정하고 필터의 전체 주파수 응답을 형성합니다.

특정 수동 필터에는 단위 이득을 초과하지 않도록 설계된 고가의 인덕터가 통합되어 있습니다. 이러한 필터는 에서 감소된 감쇠 효율을 나타낼 수 있습니다.

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Frequency Response

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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...

frequency response of a circuit

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...

frequency response of op amp circuits

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

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

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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