Name: circuit gain and phase shift
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 15 s
Channel: JoVE

İletişim sistemlerinde kazanç, sinyal amplifikasyonunun veya zayıflamasının derecesini ölçer.
Güç kazancı, çıkış gücünün giriş gücüne oranının ortak logaritmasını belirtir ve bel cinsinden ifade edilir.
Pratik ölçümler için yaygın olarak bir desibel kullanılır. Bir belin onda birine eşdeğer bir alt birimdir.
Giriş ve çıkış voltajları ve dirençleri olan bir ağ düşünün. Çıkış gücü bu ağdaki giriş gücüne eşitse, kazanç sıfır desibeldir.
Çıkış gücü, giriş gücünün iki katı olduğunda, kazanç üç desibeldir. Tersine, çıkış gücü giriş gücünün yarısına düşerse, kazanç eksi üç desibeldir.
Alternatif olarak, güç voltaj ve direnç kullanılarak temsil edilebilir.
Logaritma kuralları, voltaj ve direnç oranları cinsinden güç kazancı için bir ifade elde etmek için uygulanır.
Giriş direnci yük direncine eşit olduğunda, kazanç çıkış ve giriş voltajı oranıyla orantılı hale gelir.
Benzer şekilde, kazanç, akım ve direnç oranları cinsinden temsil edilebilir.

frekans tepkisi

Kazanç ve faz kayması, bir devrenin sinüzoidal giriş voltajı veya akımı üzerindeki etkisini tanımlayan doğrusal devrelerin özellikleridir. Reaktif elemanlar içeren devrenin davranışı, giriş sinüzoidinin frekansına bağlı olacaktır. Sonuç olarak kazanç ve faz kaymasının tamamının frekans fonksiyonu olacağı gözlenmiştir.

Kazanım:

V_iç'in bir devreye giriş olduğunu ve V_dış'ın bir devrenin çıkış sinyali olduğunu varsayalım.

<img alt="Equation 1" src="/files/ftp_upload/15139/15139_Equation_1.svg" style="height: 20px;">

<img alt="Equation 2" src="/files/ftp_upload/15139/15139_Equation_2.svg" style="height: 16px;">

Giriş ve çıkış sinyalleri A ve B genliğine ve sırasıyla 0° ve θ° faz açısına sahiptir.

Devrenin kazancı, giriş ve çıkış sinüzoidlerinin boyutları arasındaki ilişkiyi verir. Özellikle kazanç (K), çıkış sinüzoidinin genliğinin giriş sinüzoidinin genliğine oranıdır.

<img alt="Equation 3" src="/files/ftp_upload/15139/15139_Equation_3.svg" style="height: 28px;">

K kazancı birden büyük olduğunda, bu artış anlamına gelirken, birden küçük bir kazanç zayıflamayı gösterir. Kazanç logaritmik bir ölçek kullanılarak tanımlanır. Desibel (dB) cinsinden ifade edildiğinde kazanç, aynı ölçekte çok büyük ve çok küçük sayıları temsil etmek için uygun bir yol sağlar. Desibel cinsinden kazanç aşağıdaki formül kullanılarak hesaplanır:

<img alt="Equation 4" src="/files/ftp_upload/15139/15139_Equation_4.svg" style="height: 15px;">

Burada:

dB desibel cinsinden kazançtır,

K kazançtır,

log, 10 tabanındaki logaritmadır.

Faz değişimi:

Faz kayması, giriş sinyalinin fazına kıyasla çıkış sinyalinin fazının geciktirildiği veya ilerletildiği miktarı ifade eder. Çıkış ve giriş sinüzoidleri arasındaki açısal farktır. Giriş ve çıkış sinyali sırasıyla 0° ve θ° faz açısına sahiptir, bu durumda faz kayması (θ_kayma) şu şekilde verilir:

<img alt="Equation 5" src="/files/ftp_upload/15139/15139_Equation_5.svg" style="height: 18px;">

Pozitif bir θ_kaymat, çıkış sinyalinin giriş sinyalinin gerisinde kaldığını gösterirken, negatif çıkış sinyalinin giriş sinyaline göre önde olduğu anlamına gelir.

Frekans Tepkisi

İletişim sistemlerinde kazanç, sinyal amplifikasyonunun veya zayıflamasının derecesini ölçer.
Güç kazancı, oranının ortak logaritmasını gösterir ...

Education

JoVE Core

Electrical Engineering

Elektrik Mühendisliği

Unit 1

Ünite 1

Frequency Response

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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 than one means the circuit amplifies the signal, while a gain less than one means the circuit attenuates it.

Gain is often written on a logarithmic scale. When gain is expressed in decibels, or dB, it gives a practical way to show very large and very small values on the same scale. The dB value is found from the gain K using a base-10 logarithm.

Phase shift describes how much the output waveform is delayed or advanced compared with the input waveform. It is the angular difference between the input and output sinusoids. If the input has a phase angle of 0° and the output has a phase angle of θ°, then the phase shift is θ shift.

A positive phase shift means the output lags behind the input. A negative phase shift means the output leads the input. Together, gain and phase shift show both the size change and the timing change caused by a linear circuit.

Circuit Gain and Phase Shift

network function of a circuit

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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

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gain

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

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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

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scaling

Circuit Component Scaling for Filters

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design example

Touch-Tone Filter Design Example

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key terms and concepts

Learn how linear circuits change sinusoidal signals through gain and phase shift, including amplitude ratio, decibels, and lag or lead.

Circuit Gain and Phase Shift | JoVE K12

JoVE Core Elektrik Mühendisliği, devre analizi teknikleriyle birlikte elektrik devrelerinin temel kavramlarını kapsayan, anlaşılması kolay animasyonlu videolar sunar. Operasyonel amplifikatörler ve devre dönüşümü kavramlarını kullanarak birinci dereceden ve ikinci dereceden devreleri içerir. Pratik tasarım örneklerinin ve gerçek dünya uygulamalarının bilim insanlarınca hazırlanan videolar aracılığıyla dahil edilmesi, karmaşık kavramları erişilebilir hale getirerek önemli bir eğitim değeri katmaktadır.

electrical engineering

Circuit Gain and Phase Shift

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