Name: parallel rlc tuning at resonance
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 23 s
Channel: JoVE

考虑一个由电阻、电容和电感并联组成的调幅收音机调谐电路，它们共同构成电路的输入导纳。
在共振时，导纳的虚部为零，导致共振频率与电感和电容乘积的平方根成反比。
在谐振频率下，电感器和电容器的并联组合表现为开路。因此，电阻器流过的电流最小，能量在电感器的磁场和电容器的电场之间振荡。
频率响应表明，电流幅值最初减小，在共振频率处达到最小值，随后随着频率的增加而增大。
在半功率频率下，电流是最小电流的1.4142倍。
带宽是通过计算较高和较低半功率频率之间的差值来确定的。
品质因数表示共振曲线的尖锐程度，可以用电抗来表示。
较高的品质因数会使半功率频率在谐振频率两侧对称分布，并具有更窄的带宽。

频率响应

并联 RLC 电路是一种将电阻器（R）、电感器（L）和电容器（C）连接到相同节点的电路，因此它们之间会共享相同的电压。并联 RLC 电路可以通过导纳（Y）来对其进行分析，导纳反映了电流流动的难易程度。导纳的计算公式如下：
<img alt="Equation 1" src="/files/ftp_upload/15145/15145_Equation_1.svg" style="text-align: center; height: 30px;">
当净电抗为零时，并联 RLC 电路中就会产生谐振，这意味着电容和电感效应会相互抵消。当满足以下条件时，便可以实现这一条件：
<img alt="Equation 2" src="/files/ftp_upload/15145/15145_Equation_2.svg" style="text-align: center; height: 30px;">
对谐振频率进行求解能够得出：
<img alt="Equation 3" src="/files/ftp_upload/15145/15145_Equation_3.svg" style="text-align: center; height: 34px;">
在该谐振频率下，电路将会表现出纯电阻特性，并且通过电阻器的电流将会达到最大值。由于电流已经达到最大，因此电路中耗散的功率在谐振时同样是最大的。在半功率点频率中，电流大约为最大电流的 0.707，这是最大功率耗散的一半。并联 RLC 电路的带宽是这些半功率频率之间的差值，可以使用以下公式来进行计算：
<img alt="Equation 4" src="/files/ftp_upload/15145/15145_Equation_4.svg" style="text-align: center; height: 30px;">
品质因数（Q）是一个无量纲参数，能够将谐振频率与带宽进行比较，同时还可以表示谐振峰的选择性或尖锐度。在 Q≥10 的高质量电路中，半功率频率可以使用以下公式来近似表示：
<img alt="Equation 5" src="/files/ftp_upload/15145/15145_Equation_5.svg" style="text-align: center; height: 30px;">
<img alt="Equation 6" src="/files/ftp_upload/15145/15145_Equation_6.svg" style="text-align: center; height: 30px;">
Q 因数越大，表示电路的选择性越强，同时在谐振频率附近的窄频率范围内能够产生强烈的谐振。这一特性在无线电通信中是非常重要的，因为这能够过滤不需要的频率，并且还会最大限度地减少干扰。并联谐振电路在滤波应用中也同样是非常重要的，它能够用作带阻滤波器或陷波滤波器，并阻止特定频率范围，以此来允许其他频率通过。这使得它们在信号处理的过程中能够消除不需要的频率或噪音。

考虑一个AM收音机调谐器，它由一个电阻、电容和电感的并联连接组成，这三者共同决定了电路的……

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

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 resonance, the circuit behaves as a purely resistive circuit, and the current through the resistor reaches its maximum.

Power dissipation is also greatest at resonance because the current is highest. The half-power point frequencies are the points where the current is about 0.707 of the maximum current. At those frequencies, the power dissipation is half of its maximum value. The bandwidth of the parallel RLC circuit is the difference between the two half-power frequencies.

The quality factor, or Q, compares the resonant frequency with the bandwidth. It shows how sharp or selective the resonance peak is. For high-quality circuits where Q is 10 or greater, the half-power frequencies can be approximated with a simpler method. A higher Q means the circuit responds strongly to a narrow range of frequencies around resonance.

This selective behavior is useful in radio communications. It can help filter unwanted frequencies and reduce interference. Parallel resonance circuits are also used as band-stop or notch filters. In these filters, a specific frequency range is blocked while other frequencies pass through, which is useful for removing unwanted signals or noise.

Parallel RLC Tuning at Resonance

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parallel resonance

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key terms and concepts

Explore how a parallel RLC circuit behaves at resonance, including admittance, bandwidth, Q factor, and its use in radio tuning and notch filtering.

Parallel RLC Tuning at Resonance | 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

Parallel RLC Tuning at Resonance

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