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

저항기, 커패시터 및 인덕터의 병렬 연결로 구성된 AM 라디오 튜너가 회로의 입력 어드미턴스에 총체적으로 기여한다고 가정해 보십시오.
공진에서 어드미턴스의 허수 부분은 0이며, 이로 인해 공진 주파수는 인덕턴스와 커패시턴스 곱의 제곱근에 반비례하여 변합니다.
공진 주파수에서 인덕터와 커패시터의 병렬 조합은 개방 회로로 작동합니다. 결과적으로 저항기는 최소한의 전류를 소비하고 에너지는 인덕터의 자기장과 커패시터의 전기장 사이에서 진동합니다.
주파수 응답은 전류 크기가 초기에 감소하고, 공진 주파수에서 최소값에 도달하고, 주파수가 증가함에 따라 증가함을 나타냅니다.
절반 전력 주파수에서 전류는 최소 전류의 1.4142배입니다.
대역폭은 더 높은 절반 전력 주파수와 더 낮은 절반 전력 주파수 간의 차이를 결정하여 계산됩니다.
공진 곡선의 선명도를 나타내는 품질 계수는 리액턴스로 표현할 수 있습니다.
품질 계수가 높을수록 공진 주파수 주위에 대칭적으로 분포된 절반 전력 주파수와 더 좁은 대역폭을 생성합니다.

주파수 응답

병렬 RLC 회로는 저항기(R), 유도자(L) 및 축전기(C)가 모두 동일한 노드에 연결되어 결과적으로 이들 간에 동일한 전압을 공유하는 배열입니다. 병렬 RLC 회로는 전류가 흐르기 쉬운 정도를 반영하는 어드미턴스(Y)로 분석됩니다. 입학 허가는 다음과 같습니다:
<img alt="Equation 1" src="/files/ftp_upload/15145/15145_Equation_1.svg" style="height: 30px;">
병렬 RLC 회로의 공진은 순 리액턴스가 0일 때 발생합니다. 즉, 용량성 효과와 유도성 효과가 서로 상쇄됩니다. 이 조건은 다음과 같은 경우에 달성됩니다.
<img alt="Equation 2" src="/files/ftp_upload/15145/15145_Equation_2.svg" style="height: 30px;">
공진 주파수를 풀면 다음이 제공됩니다.
<img alt="Equation 3" src="/files/ftp_upload/15145/15145_Equation_3.svg" style="height: 34px;">
이 공진 주파수는 회로가 순전히 저항성 동작을 나타내고 저항기를 통과하는 전류가 최대가 되는 지점입니다. 회로에서 소비되는 전력은 최대 전류 흐름으로 인해 공진 시 최대가 됩니다. 절반 전력점 주파수에서 전류는 최대 전류의 약 0.707이므로 최대 전력 손실이 절반이 됩니다. 병렬 RLC 회로의 대역폭은 이러한 반전력 주파수 간의 차이이며 다음을 사용하여 구합니다.
<img alt="Equation 4" src="/files/ftp_upload/15145/15145_Equation_4.svg" style="height: 30px;">
품질 계수(Q)는 공진 주파수를 대역폭과 비교하는 무차원 매개변수로, 공진 피크의 선택성 또는 선명도를 나타냅니다. Q≥10인 고품질 회로에서는 다음을 사용하여 반전력 주파수를 근사화할 수 있습니다.
<img alt="Equation 5" src="/files/ftp_upload/15145/15145_Equation_5.svg" style="height: 30px;">
<img alt="Equation 6" src="/files/ftp_upload/15145/15145_Equation_6.svg" style="height: 30px;">
 Q 인자가 높을수록 회로의 선택성이 높아 공진 주파수 주변의 좁은 주파수 범위에서 강하게 공진한다는 의미입니다. 이 속성은 원치 않는 주파수를 필터링하고 간섭을 최소화할 수 있어 무선 통신에 특히 유용합니다. 병렬 공진 회로는 특정 주파수 범위를 차단하고 다른 주파수 범위는 통과시키는 대역 차단 또는 노치 필터 역할을 하는 필터링 애플리케이션에 특히 유용합니다. 따라서 원치 않는 주파수나 잡음을 제거하기 위한 신호 처리에 유용합니다.

저항기, 커패시터 및 인덕터의 병렬 연결로 구성된 AM 라디오 튜너를 생각해 보십시오. 이는 집합적으로 회로의 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Frequency Response

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

network function of a circuit

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transfer function and bode plots-ii

Bode Plot Slope and Phase Changes

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Reading Frequency Response with Bode Plots

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Series Resonance in RLC Circuits

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characteristics-of-series-resonant-circuit

Series Resonance and RLC Filter Behavior

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parallel 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...

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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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