Name: reading frequency response on bode plots
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 26 s
Channel: JoVE

例えば、その大きさと位相角で表される複雑なネットワーク関数を持つローパスフィルタを利用する心電図ユニットを考えてみましょう。
デシベル対数ゲインは、ネットワーク関数の大きさの10を底とする対数に20を掛けて計算されます。
ボード線図は、対数ゲインをデシベル単位で表示し、周波数間での位相角を度単位で表示する半対数グラフです。
周波数が低いと、対数ゲインと位相角はゼロに近づきます。
これにより、ボード線図上には、低周波漸近線と呼ばれる水平線が表示されます。
周波数が高い場合、ゲインと位相角の計算は周波数への依存性を反映します。
これらは負の傾きを持つ直線として描かれ、高周波漸近線として知られています。
低周波と高周波の漸近線は、コーナー周波数とも呼ばれるコーナーで交差します。
この周波数では、漸近の大きさは正確な値から約-3デシベルずれ、位相角は約-45度です。
漸近ボード線図は、実際のボード線図に近似しています。

ボード線図

ボード線図は、x 軸に周波数の対数スケール、y 軸にゲインのデシベルを使用するグラフィカル ツールです。この対数方式により、幅広い周波数をコンパクトに表示できるため、幅広い周波数スペクトルにわたって回路の動作に対するコンポーネントの影響を分析できます。

ネットワーク関数は、システムの出力と入力の比率を表し、振幅と位相角は複雑なネットワーク関数から得られます。デシベル対数ゲインは、ネットワーク関数の振幅の 10 を底とする対数に 20 を掛けて決定されます。ボード線図のゲインは対数で表されます。対数ゲインの単位はデシベルで、dB 単位のゲインとも呼ばれます。デシベル (dB) はゲインを定量化します。1 dB はベルの 10 分の 1 で、アレクサンダー・グラハム・ベルに敬意を表しています。
片対数グラフであるボード線図は、さまざまな周波数範囲にわたって対数ゲインをデシベルで、位相角を度で示します。これらの線図により、システムの周波数応答を理解しやすくなります。
低周波数では、対数ゲインと位相角の両方がゼロに近づき、ボード線図上で低周波数漸近線と呼ばれる水平線が形成されます。これらの線は、これらの周波数での信号に対するフィルターの影響が最小限であることを示します。周波数が増加すると、ゲインと位相角の計算は周波数依存性を反映します。ボード線図では、これらの依存性は、高周波漸近線と呼ばれる負の傾斜を持つ直線として表示されます。これらの線は、フィルターが高周波信号をどのように減衰させるのかを示しています。低周波数漸近線と高周波漸近線はコーナー周波数で交差します。ここで、漸近振幅は正確な値から約 -3 デシベルずれており、フィルターの応答に大きな変化が見られます。さらに、コーナー周波数での位相角は約 -45 度です。
漸近ボード線図は実際のボード線図の適切な近似値を提供し、妥当な精度を維持しながら簡略化された分析を可能にします。

例えば、その大きさと位相角で表される複雑なネットワーク関数を持つローパスフィルタを利用する心電図ユニットを考えてみましょう。
ザ。。。

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

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 the base-ten logarithm of that magnitude by 20. The gain is measured in decibels, or dB. A decibel is one-tenth of a bel, and the unit honors Alexander Graham Bell.

Because Bode plots are semilogarithmic graphs, they show gain in dB and phase angle in degrees over frequency. This makes the frequency response of a system easier to study. At low frequencies, both gain and phase angle approach zero. These flat regions are called low-frequency asymptotes, and they show that the filter has little effect on the signal there.

As frequency rises, the gain and phase angle change with frequency. On the plot, this appears as straight lines with negative slopes called high-frequency asymptotes. These lines show that the filter attenuates higher-frequency signals. The low- and high-frequency asymptotes meet at the corner frequency. At that point, the asymptotic magnitude is about -3 decibels from the exact value, and the phase angle is about -45 degrees. Asymptotic Bode plots give a reasonable approximation of the actual plot and make analysis simpler while keeping useful accuracy.

Reading Frequency Response on Bode Plots

analyzing-filter-response-with-bode-plots

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

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 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...

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 Bode plots use decibels, phase angle, and asymptotes to show frequency response, including corner frequency and filter behavior.

Reading Frequency Response on Bode Plots | 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

Reading Frequency Response on Bode Plots

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