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

크기와 위상각으로 표현되는 복잡한 네트워크 함수를 가진 저역 통과 필터를 사용하는 심전도 단위를 생각해 보십시오.
데시벨 로그 이득은 네트워크 함수 크기의 밑이 되는 10 로그에 20을 곱하여 계산됩니다.
Bode plot은 로그 이득을 데시벨 단위로 표시하고 위상 각도를 주파수 전체에서 도 단위로 표시하는 반로그 그래프입니다.
더 낮은 주파수에서는 로그 이득과 위상각이 0에 가깝습니다.
그 결과 Bode plot에 저주파 점근선으로 알려진 수평선이 생성됩니다.
더 높은 주파수에서 이득 및 위상 각도에 대한 계산은 주파수에 대한 의존성을 반영합니다.
그들은 음의 기울기를 가진 직선으로 묘사되며 고주파 점근선으로 알려져 있습니다.
저주파 및 고주파 점근선은 코너 주파수라고도 하는 코너에서 교차합니다.
이 주파수에서 점근 크기는 정확한 값에서 거의 -3데시벨 벗어나고 위상각은 약 -45도입니다.
점근 보드 플롯은 실제 보드 플롯에 대한 좋은 근사치입니다.

보드 플롯

보드 플롯은 x축의 주파수에 로그 스케일을 사용하고 y축의 데시벨 단위 게인을 사용하는 그래픽 도구입니다. 이 로그 방법을 사용하면 광범위한 주파수를 간결하게 표시할 수 있으므로 광범위한 주파수 스펙트럼에 걸쳐 회로 동작에 대한 구성요소 효과를 분석할 수 있습니다.
네트워크 함수는 복잡한 네트워크 함수에서 파생된 크기와 위상각을 사용하여 시스템의 출력과 입력의 비율을 나타냅니다. 데시벨 로그 게인은 네트워크 함수 크기의 밑이 10인 로그에 20을 곱하여 결정됩니다. 보드 플롯의 게인은 로그 방식으로 표현됩니다. 로그 게인의 단위는 데시벨이며, 이득(dB)이라고도 합니다. 데시벨(dB)은 게인을 정량화하며, 1dB는 벨의 1/10을 의미하며 알렉산더 그레이엄 벨을 기리는 의미입니다.
반로그 그래프인 보드 플롯은 주파수 범위에 대한 데시벨 단위의 로그 이득과 도 단위의 위상 각도를 표시합니다. 이러한 플롯을 통해 시스템의 주파수 응답을 쉽게 이해할 수 있습니다.
더 낮은 주파수에서는 로그 이득과 위상 각도가 모두 0에 접근하여 저주파 점근선으로 알려진 보드 플롯에 수평선을 형성합니다. 이 선은 해당 주파수에서 신호에 대한 필터의 영향이 최소화되었음을 나타냅니다. 주파수가 증가함에 따라 이득 및 위상각 계산은 주파수 의존성을 반영합니다. 보드 플롯에서 이러한 종속성은 고주파 점근선이라고 하는 음의 기울기를 갖는 직선으로 나타납니다. 이 선은 필터가 고주파수 신호를 어떻게 감쇠하는지 보여줍니다. 저주파 및 고주파 점근선은 코너 주파수에서 교차합니다. 여기서 점근 크기는 정확한 값에서 약 -3데시벨 정도 벗어나 필터 응답에 상당한 변화가 있음을 나타냅니다. 또한 코너 주파수의 위상각은 약 -45도입니다.
점근적 보드 플롯은 실제 보드 플롯의 합리적인 근사치를 제공하므로 합리적인 정확도를 유지하면서 단순화된 분석이 가능합니다.

크기와 위상각으로 표현되는 복잡한 네트워크 함수를 가진 저역 통과 필터를 사용하는 심전도 단위를 생각해 보십시오.
그만큼 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Frequency Response

주파수 응답

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 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

Reading Frequency Response on Bode Plots

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