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

在通信系统中，增益用于量化信号放大或衰减的程度。
功率增益表示输出功率与输入功率之比的常用对数，以贝尔为单位。
在实际测量中，通常使用分贝。它是贝尔的十分之一，为贝尔的子单位。
考虑一个具有输入和输出电压及电阻的网络。如果该网络中的输出功率等于输入功率，则增益为零分贝。
当输出功率达到输入功率的两倍时，增益为3分贝。相反，如果输出功率降至输入功率的一半，则增益为负3分贝。
或者，功率也可以用电压和电阻来表示。
应用对数运算法则，可得到以电压比和电阻比表示的功率增益表达式。
当输入电阻等于负载电阻时，增益与输出电压和输入电压的比值成正比。
类似地，增益可以用电流和电阻的比值来表示。

频率响应

增益和相移是线性电路的特征，能够用来描述电路对正弦输入电压或电流所产生的影响。包含无功元件的电路行为将取决于输入电压为正弦波时的频率。因此，增益和相移都是频率函数。
增益：
假设 V_in 是电路的输入，V_out 是电路的输出信号。
<img alt="Equation 1" src="/files/ftp_upload/15139/15139_Equation_1.svg" style="text-align: center; height: 20px;">
<img alt="Equation 2" src="/files/ftp_upload/15139/15139_Equation_2.svg" style="text-align: center; height: 16px;">
输入和输出信号的幅度分别为 A 和 B，相位角分别为 0° 和 θ°。
电路的增益给出了输入和输出正弦波大小之间的关系。具体来说，增益（K）是输出正弦波幅度与输入正弦波幅度之比。
<img alt="Equation 3" src="/files/ftp_upload/15139/15139_Equation_3.svg" style="text-align: center; height: 28px;">
当增益 K 大于 1 时，表示放大，而增益小于 1 表示衰减。增益使用对数刻度来描述。当以分贝（dB）表示时，增益提供了一种方便的方法，可以在同一刻度上表示非常大和非常小的数字。分贝增益使用以下公式计算：
<img alt="Equation 4" src="/files/ftp_upload/15139/15139_Equation_4.svg" style="text-align: center; height: 15px;">
其中：
dB 是分贝增益，
K 是增益，
log 是以 10 为底的对数。
相移：
相移是指输出信号的相位相对于输入信号的相位延迟或提前的量。它是输出和输入正弦波之间的角度差。输入和输出信号的相位角分别为 0° 和 θ°，则相移 (θ_shift) 为：
<img alt="Equation 5" src="/files/ftp_upload/15139/15139_Equation_5.svg" style="text-align: center; height: 18px;">
正 θ_shift 表示输出信号滞后于输入信号，负 θ_shift 表示输出信号领先于输入信号。

在通信系统中，增益用于量化信号放大或衰减的程度。  
功率增益表示输出功率与输入功率之比的常用对数。

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Frequency Response

KEY TERMS AND CONCEPTS

关键术语与概念

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

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 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

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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 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 Gain and Phase Shift

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