Name: circuit component scaling for filters
Uploaded: 2024-07-08T13:20:03.000Z
Duration: 1 min 26 s
Channel: JoVE

Magnitude and Frequency Scaling은 사용 가능한 범위에 맞게 필터 응답과 회로 파라미터를 보정하여 필터 설계를 단순화합니다.
크기 스케일링은 네트워크의 모든 임피던스를 계수로 증폭하여 일관된 주파수 응답을 유지하는 것을 포함합니다.
그런 다음 스케일링된 임피던스 및 주파수 값은 스케일링 팩터를 사용하여 표현됩니다.
이 프로세스는 회로의 공진 주파수, 품질 계수, 대역폭 또는 전달 함수를 변경하지 않습니다.
Frequency scaling은 임피던스를 변경하지 않고 네트워크의 주파수 응답을 주파수 축의 위 또는 아래로 이동합니다. 이는 주파수에 스케일링 팩터를 곱하여 수행됩니다.
주파수 스케일링은 주파수 종속 반응 소자의 임피던스에 영향을 미치지만 저항은 영향을 받지 않습니다.
스케일링 계수는 공진 주파수와 대역폭을 변경하지만 품질 계수는 동일하게 유지됩니다.
임피던스 및 주파수 스케일링에 대한 일반적인 표현은 동시 크기 및 주파수 스케일링을 수용합니다.
크기 배율이 적용되지 않는 경우 크기 배율 계수가 1로 설정됩니다. 마찬가지로, 빈도 스케일링이 없으면 빈도 배율이 1로 설정됩니다.

주파수 응답

Scaling

필터, 공진 회로 또는 대규모 회로 분석을 설계하고 분석할 때 이러한 값을 보다 현실적인 수치로 확장하기 전에 1옴, 1헨리 또는 1패럿과 같은 표준 요소 값을 사용하여 작업하는 것이 편리할 수 있습니다. 이 접근 방식은 수많은 예제와 문제에서 현실적인 요소 값을 사용하지 않음으로써 널리 활용됩니다. 편리한 구성 요소 값을 통해 마스터링 회로 분석을 단순화합니다. 따라서 스케일링 기술을 통해 나중에 이러한 값을 보다 실용적인 수준으로 조정할 수 있다는 점을 이해하면 계산의 복잡성이 줄어듭니다.
회로 스케일링은 크기(또는 온저항) 스케일링과 주파수 스케일링이라는 두 가지 방법으로 수행할 수 있습니다. 이러한 방법은 실제 범위 내에서 작동하도록 회로의 구성 요소를 조정합니다. 크기 스케일링은 회로가 다양한 주파수에 반응하는 방식에 영향을 주지 않고 구성 요소의 크기를 변경합니다. 반면, 주파수 스케일링은 회로의 응답을 스펙트럼의 더 높거나 낮은 주파수로 이동시킵니다.
크기 조정:
크기 스케일링에는 회로 구성요소(예: 저항기, 유도자 및 축전기)의 크기를 특정 요인으로 조정하는 작업이 포함되지만 회로가 다른 주파수에 응답하는 방식은 변경하지 않습니다. 회로의 온저항은 회로의 저항기(R), 유도자(L) 및 축전기(C)로 표시됩니다. 크기 스케일링 K_m이 적용되면 이러한 구성 요소는 다음과 같이 변환됩니다.
<img alt="Equation 1" src="/files/ftp_upload/15150/15150_Equation_1.svg" style="height: 12px;">

<img alt="Equation 2" src="/files/ftp_upload/15150/15150_Equation_2.svg" style="height: 36px;">
 주파수 스케일링:
주파수 스케일링은 온저항 레벨을 변경하지 않고 주파수 축을 따라 회로의 주파수 응답을 위 또는 아래로 이동합니다. 이는 주파수에 K_f로 표시되는 스케일링 계수를 곱하여 달성됩니다. 유도계수와 전기용량의 새로운 값은 다음에 의해 결정됩니다.
<img alt="Equation 3" src="/files/ftp_upload/15150/15150_Equation_3.svg" style="height: 36px;">

<img alt="Equation 4" src="/files/ftp_upload/15150/15150_Equation_4.svg" style="height: 36px;">
회로가 크기와 주파수 매개변수에 대해 동시에 스케일링되면 다음과 같습니다.
<img alt="Equation 5" src="/files/ftp_upload/15150/15150_Equation_5.svg" style="height: 36px;">

<img alt="Equation 6" src="/files/ftp_upload/15150/15150_Equation_6.svg" style="height: 36px;">
크기와 주파수 스케일링 계수가 동일하면 크기나 주파수 스케일링이 발생하지 않습니다.

Magnitude and Frequency Scaling은 사용 가능한 범위에 맞게 필터 응답과 회로 파라미터를 보정하여 필터 설계를 단순화합니다.
크기...

Education

JoVE Core

Electrical Engineering

Unit 1

Frequency Response

KEY TERMS AND CONCEPTS

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. The idea is to learn the analysis first and then adjust the component values to fit real-world use.

There are two main ways to scale a circuit: magnitude scaling, also called impedance scaling, and frequency scaling. Magnitude scaling changes the size of the components without changing how the circuit responds to different frequencies. Frequency scaling shifts the circuit response higher or lower on the frequency axis without changing the impedance levels.

Magnitude scaling uses a factor called K m to change resistors, inductors, and capacitors. Frequency scaling uses a factor called K f to move the frequency response and to determine new inductance and capacitance values. When both magnitude and frequency scaling are applied together, the circuit can be adjusted in both size and response range. If the magnitude and frequency scaling factors are equal, neither type of scaling occurs.

Circuit Component Scaling for Filters

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

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 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 magnitude scaling and frequency scaling adjust resistors, inductors, capacitors, and circuit response for easier filter design and analysis.

Circuit Component Scaling for Filters | 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

Circuit Component Scaling for Filters

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