Name: how transfer functions shape circuit response
Uploaded: 2024-07-08T13:20:01.000Z
Duration: 1 min 25 s
Channel: JoVE

다양한 신호 주파수에 따른 동작을 특성화하는 회로의 주파수 응답은 전송 또는 네트워크 기능을 사용하여 분석할 수 있습니다.
이 수학 함수는 출력과 입력의 비율을 정의합니다. 전압 이득(Voltage Gain), 전류 이득(Current Gain), 전달 임피던스(Transfer Impedance) 및 전달 어드미턴스(Transfer Admittance)의 4가지 유형으로 분류됩니다.
회로의 동작은 복소 변수 's'를 사용하여 라플라스 영역에서 분석됩니다.
일반적으로 회로의 전달 함수는 0과 극점으로 나타낼 수 있습니다.
여기서 0은 분자 다항식의 근이고 극점은 분모 다항식의 근입니다. 전달 함수 값은 극점에서 무한대가 되고 0에서 0이 됩니다.
두 개의 커패시터와 증폭기에서 트위터로 고주파 신호를 선택하는 인덕터가 있는 오디오 크로스오버 회로를 생각해 보십시오.
인덕터, 저항기 및 커패시터의 조합은 회로 임피던스를 제공합니다.
옴의 법칙을 적용하면 노드 전압은 입력 전압에 비례합니다.
마찬가지로 출력 전압은 노드 전압에 비례합니다.
마지막으로, 출력 대 입력 전압 비율로 표시되는 전달 함수를 얻습니다.

회로의 네트워크 기능

전기 회로의 주파수 응답 분석은 입력 신호의 주파수 변화에 따른 회로 동작에 대한 중요한 통찰력을 제공합니다. 수학적 도구인 전달 함수는 이러한 동작을 이해하는 데 중요한 역할을 합니다. 이는 페이저 출력과 입력 사이의 관계를 정의하며 전압 이득, 전류 이득, 전달 임피던스 및 전달 어드미턴스의 네 가지 유형으로 제공됩니다. 전달 함수의 중요한 구성요소는 극점과 영점입니다.
<img alt="Equation 1" src="/files/ftp_upload/15137/15137_Equation_1.svg" style="height: 32px;">
여기서 0은 분자 다항식의 근이고 극점은 분모 다항식의 근입니다.
예시적인 예로, 트위터의 고주파 신호를 증폭기에서 분리하는 오디오 크로스오버 회로를 생각해 보세요. 신호 주파수에 관한 이 회로의 분석은 's'를 복소 변수로 사용하여 라플라스 도메인에서 발생합니다.
옴의 법칙을 활용하면 입력 전압은 노드 전압과 관련됩니다. 이후 출력 전압은 입력 전압으로 표현됩니다. 이 분석은 출력 대 입력 전압 비율을 나타내는 전달 함수를 도출합니다.
<img alt="Equation 2" src="/files/ftp_upload/15137/15137_Equation_2.svg" style="height: 32px;">
주파수 응답 분석은 특히 통신 및 제어 시스템 분야에서 광범위한 응용 분야를 자랑합니다. 라디오 및 텔레비전 기술과 같은 다양한 응용 분야에 사용되는 전기 필터는 이 분석을 사용하여 원하는 신호는 통과시키고 원하지 않는 신호는 억제합니다. 전달 함수와 주파수 응답에 대한 포괄적인 이해는 회로 설계 및 엔지니어링에 있어 중추적인 역할을 합니다.
기본 도구인 전달 함수는 엔지니어링 및 전자 분야의 다양한 주파수에 걸쳐 회로 동작 평가를 단순화합니다.

다양한 신호 주파수로 동작을 특성화하는 회로의 주파수 응답은 전송 또는 네트워크를 사용하여 분석할 수 있습니다.

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Frequency Response

주파수 응답

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 are the roots of the numerator polynomial, and poles are the roots of the denominator polynomial.

An audio crossover circuit gives a clear example of this idea. It separates high-frequency signals for a tweeter from an amplifier. To analyze this circuit, engineers work in the Laplace domain and use s as a complex variable. Ohm's Law is then used to connect the input voltage to the node voltage, and the output voltage is written in terms of the input voltage.

This process produces the transfer function as the output-to-input voltage ratio. Frequency response analysis is widely used in communication and control systems. Electric filters in radio and television also depend on it to let desired signals pass and reduce unwanted ones. A strong grasp of transfer functions helps with circuit design and with understanding how circuits act at different frequencies.

How Transfer Functions Shape Circuit Response

how-transfer-functions-shape-circuit-response

network function of a circuit

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 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 transfer functions describe circuit behavior across frequency, including poles, zeros, and an audio crossover example used in filters and electronics.

How Transfer Functions Shape Circuit 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

How Transfer Functions Shape Circuit Response

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