Name: op amp gain and bode plot basics
Uploaded: 2024-07-08T13:20:03.000Z
Duration: 1 min 20 s
Channel: JoVE

バッファアンプに接続されたギターピックアップを考えてみましょう。このバッファアンプは、非反転オペアンプを備えており、ギターの高インピーダンスとアンプの低インピーダンスをブリッジします。
オペアンプのボード振幅プロットは、コーナー周波数より低いゲインを一定に維持し、それを超えると10年あたりマイナス20デシベルの割合で減少します。
回路は等価周波数依存構成に変換され、出力電圧は周波数依存のゲインと入力電圧にリンクされます。
ノード方程式を記述し、その式をオペアンプの入力電圧に代入すると、回路の伝達関数が得られます。これは、理想的な非反転アンプのゲインに依存します。
アンプのゲインの式を使用すると、伝達関数は非反転アンプのDCゲインで表すことができます。
近似は、コーナー周波数と理想的なゲインを使用して表される簡略化された伝達関数につながります。
ゲイン帯域幅積は、DCゲインにコーナー周波数を掛けたものに等しくなります。
これは、ゲインが高くなると帯域幅が減少し、ゲイン-帯域幅積が一定に保たれ、実効周波数範囲が制限されることを示しています。

周波数応答

オペアンプ (op-amp) は、信号調整、フィルタリング、または加算、減算、積分、微分などの数学演算の実行に使用されます。オペアンプの周波数応答は、アンプのゲイン（利得）が周波数によってどのように変化するかを説明する重要な側面です。

周波数応答とゲイン:
オペアンプのゲイン A(ω) は定数ではなく、入力信号周波数の関数です。オペアンプは、直流 (DC) ゲイン A_0 として知られる低周波数で一定のゲインを維持できます。ゲインは、次の式で表すことができます:
<img alt="Equation 1" src="/files/ftp_upload/15147/15147_Equation_1.svg" style="height: 36px;">

ω は入力信号周波数、ω_1 はゲインが DC ゲイン A_0 を下回り始めるコーナーまたは折点周波数です。
ボード線図は、オペアンプのゲインと周波数の対数グラフを表します。これは、オペアンプのゲインが高周波数でどのように減少するかをグラフで表したものです。
非反転アンプの場合、回路構成では入力電圧がオペアンプの非反転端子に印加され、入力と同位相の増幅出力電圧が得られます。この回路のゲインは、オペアンプの周波数応答と、回路で使用される抵抗 R_1 と R_2 の比率によって左右されます。非反転アンプのネットワーク関数は、次の式で表されます。
<img alt="Equation 2" src="/files/ftp_upload/15147/15147_Equation_2.svg" style="height: 38px;">
ここで、K はアンプの理想的なゲインで、次のように表されます。
<img alt="Equation 3" src="/files/ftp_upload/15147/15147_Equation_3.svg" style="height: 36px;">
オペアンプの周波数応答は、オペアンプがさまざまな周波数で信号をどれだけ効果的に増幅できるかを判断する上で不可欠です。ゲイン対周波数の概念とゲイン帯域幅積は、電子機器のオペアンプ回路の設計と適用で使用されます。

バッファアンプに接続されたギターピックアップを考えてみましょう。このバッファアンプは、非反転オペアンプを備えており、ギターの高インピーダンスと...

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

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 words, the amplifier does not keep the same gain at every frequency.

A Bode plot is a logarithmic graph of the magnitude of gain versus frequency. It gives a clear view of how op-amp gain falls at higher frequencies. Engineers use this graph to study the gain-bandwidth product and to understand how well an op-amp can amplify signals across different frequency ranges.

The noninverting amplifier is a common op-amp circuit discussed with frequency response. In this setup, the input voltage goes to the non-inverting terminal, and the output stays in phase with the input. Its gain depends on the op-amp frequency response and on the ratio of resistances R1 and R2. The network function also shows the ideal gain, K, of the amplifier.

Op Amp Gain and Bode Plot Basics

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

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 op-amp gain changes with frequency, what dc gain and corner frequency mean, and how a Bode plot helps analyze noninverting amplifier circuits.

Op Amp Gain and Bode Plot Basics | 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

Op Amp Gain and Bode Plot Basics

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