Name: inductive circuit frequency response
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 20 s
Channel: JoVE

시간 영역의 유도 회로를 고려하십시오. 등가 주파수 영역 회로는 저항과 인덕턴스를 임피던스로 대체하여 얻습니다.
회로는 가변 주파수의 입력에 연결되고 출력은 인덕턴스를 가로질러 사용됩니다.
 출력-입력 전압 구간은 전달 기능을 결정합니다.
 전달 함수의 표현은 그로부터 파생된 크기와 위상을 제공합니다.
저항에 대한 인덕턴스의 비율은 인덕티브 회로의 시간 상수와 같습니다.
크기와 위상은 시간 상수로 작성할 수 있습니다.
주파수가 0에 가까워지면 전달 함수가 0에 가까워지고 위상 변이는 2에 대해 pi를 근사합니다.
주파수가 시간 상수의 역과 같을 때 진폭은 최대값의 약 0.707배에 도달하고 위상 편이는 4에 대한 파이입니다.
마찬가지로, 더 높은 주파수에서 전달 함수는 단위에 가까워지고 위상 변이는 0이 되는 경향이 있습니다.
몇 가지 추가 점 중 이러한 점은 진폭 또는 크기 및 위상 응답 그래프를 통해 주파수 응답을 나타냅니다.

회로의 주파수 응답

유도 회로는 특히 시간 영역에서 주파수 영역으로 전환하는 동안 전기 공학에서 흥미로운 과제를 제시합니다. 이 변환에는 유도자를 온저항으로 변환하고 페이저 표현을 활용하는 작업이 포함됩니다.
전달 함수는 이러한 회로가 다양한 주파수에 어떻게 반응하는지 특성화하여 해당 동작에 대한 깊은 이해를 촉진하는 데 중추적인 역할을 합니다. 필수 매개변수는 회로의 유도계수 대 저항 비율을 나타내는 시상수입니다.
전달 함수의 크기는 시간 상수의 역수를 전달 함수 방정식에 통합하여 도출됩니다. 또한 이 접근 방식을 사용하면 위상 변이를 계산하여 출력 정현파와 입력 정현파 간의 위상 각도 차이를 밝힐 수 있습니다.
<img alt="Equation 1" src="/files/ftp_upload/15138/15138_Equation_1.svg" style="height: 32px;">
<img alt="Equation 2" src="/files/ftp_upload/15138/15138_Equation_2.svg" style="height: 32px;">
진폭과 위상 응답을 그래프로 나타내면 회로의 주파수 특성을 시각적으로 표현하여 성능의 기본 측면을 효과적으로 전달할 수 있습니다. 주파수 스펙트럼을 조사하면 독특한 경향이 나타납니다. 전달 함수는 대략적인 π/2 위상 변이와 함께 더 낮은 주파수에서 0에 접근합니다. 반대로 전달 함수는 더 높은 주파수에서 1로 수렴하는 반면 위상 변이는 0에 가까워집니다.
가장 중요한 것은 시간 상수의 역수를 나타내는 반전력 주파수를 식별하는 것입니다. 이 특정 주파수에서는 전달 함수의 크기와 위상을 정확하게 평가할 수 있어 회로의 응답 특성을 포괄적으로 이해할 수 있습니다.

시간 영역의 유도 회로를 고려하십시오. 등가 주파수 영역 회로는 저항과 인덕턴스를 다음으로 대체하여 얻습니다.

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Frequency Response

주파수 응답

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 ratio of inductance to resistance in the circuit. The magnitude of the transfer function is found by using the inverse of the time constant in the transfer function equation.

This approach also gives the phase shift between the output and input sinusoids. The phase angle shows how far one signal leads or lags the other. Graphs of amplitude response and phase response help show the circuit’s frequency behavior in a clear way.

The response changes across the frequency spectrum. At low frequencies, the transfer function approaches zero, and the phase shift is about π/2. At high frequencies, the transfer function approaches unity, and the phase shift moves toward zero.

The half-power frequency is an important point in this behavior. It is the inverse of the time constant. At this frequency, the magnitude and phase of the transfer function can be determined accurately, giving a complete view of the circuit’s response.

Inductive Circuit 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 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 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

Explore how inductive circuits change with frequency, using impedance, phasors, transfer functions, phase shift, and the half-power frequency.

Inductive Circuit 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

Inductive Circuit Frequency Response

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