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

特定のパッシブフィルタには、ユニティゲインを超えないように設計された高価なインダクタが組み込まれています。これらのフィルターは、オーディオ範囲より低い周波数で減衰効率が低下する可能性があります。
アクティブフィルタは、オペアンプ、抵抗、コンデンサで構成されています。
オーディオ処理、通信、および電源ユニットで使用されるこれらのフィルタは、1次ローパス、1次ハイパス、バンドパス、およびバンドリジェクトフィルタに分類されます。
ローパスおよびハイパスアクティブフィルターの伝達関数と周波数応答について考えます。
パッシブ・フィルタとは異なり、ローパス・アクティブ・フィルタの有限の低周波数ゲインとハイパス・アクティブ・フィルタの高周波ゲインは、フィードバックと入力抵抗の比率に依存します。
ローパスフィルターはコーナー周波数より上の周波数を減衰させ、ハイパスフィルターはコーナー周波数より低い周波数を抑制します。
ローパスフィルタとハイパスフィルタの組み合わせはバンドパスフィルタになり、バンドリジェクトフィルタは両方のタイプをサミングアンプと組み合わせます。
バンドパスフィルタは、コーナー周波数間で周波数を送信し、外部周波数を拒否します。バンドパスフィルタは、範囲内の周波数をブロックし、外部周波数を許可します。

周波数応答

アクティブフィルタは、オペアンプ、抵抗器、コンデンサを使用して信号から不要な周波数成分を除去する電子回路です。1次ローパスアクティブフィルタは、特定のカットオフ周波数より低い周波数の信号を通過させ、そのカットオフ周波数より高い周波数を減衰させるように設計されています。1 次ローパスアクティブ フィルタの伝達関数は次のとおりです。
<img alt="Equation 1" src="/files/ftp_upload/15149/15149_Equation_1.svg" style="height: 40px;">
ここで、A_f は低周波数でのゲイン (DC ゲインとも呼ばれます)、s は複素周波数、ω_c はコーナーまたはカットオフ周波数です。1 次ハイパスアクティブ ィルタは、特定のカットオフ周波数より高い信号を通過させ、この周波数より低い信号を減衰させます。その伝達関数は次のように表すことができます。
<img alt="Equation 2" src="/files/ftp_upload/15149/15149_Equation_2.svg" style="height: 36px;">
ここで、A_f は高周波数でのゲイン、ω_c は出力が大幅に減少するカットオフ周波数です。バンドパスフィルタは、ローパスフィルタとハイパスフィルタの両方の特性を備えています。このフィルタは、特定の範囲の周波数のみを通過させ、この範囲外の周波数を減衰させます。バンドパスフィルタの伝達関数は次の形式になります。
<img alt="Equation 3" src="/files/ftp_upload/15149/15149_Equation_3.svg" style="height: 42px;">
ここで、ω_0 は中心周波数、Q は品質係数です。ノッチフィルタとも呼ばれるバンドリジェクトフィルタは、減衰させる特定の範囲を除き、ほとんどの周波数を通過させることで、その逆を行います。バンドリジェクトフィルタの標準的な伝達関数は次のとおりです。
<img alt="Equation 4" src="/files/ftp_upload/15149/15149_Equation_4.svg" style="height: 50px;">
アクティブフィルタでは、通過帯域内のゲインはカットオフ周波数とは無関係に設定できます。ゲインはフィードバック抵抗と入力抵抗の比率によって決まり、抵抗値やコンデンサ値などの設計パラメータを選択してカットオフ周波数を設定し、フィルタの全体的な周波数応答を特定の要件に合わせて形成します。

特定のパッシブフィルタには、ユニティゲインを超えないように設計された高価なインダクタが組み込まれています。これらのフィルターは、...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Frequency Response

周波数特性

KEY TERMS AND CONCEPTS

主要用語および概念

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Active Filter Design and Frequency Response

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