Name: series resonance and rlc filter behavior
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 24 s
Channel: JoVE

ضع في اعتبارك وحدة إرسال لاسلكية تتضمن مرشح تمرير نطاق رنين سلسلة RLC.
تشير استجابة تردد هذه الدائرة إلى أن حجم التيار يزداد في البداية ، ويبلغ ذروته عند تردد الرنين ، وينخفض مع زيادة التردد.
تبديد الطاقة ، المقابل للقيمة القصوى الحالية ، هو الأعلى عند الرنين.
عند ترددات نصف الطاقة ، يكون التيار 0.707 ضعف الحد الأقصى للتيار ، والطاقة المشتتة هي نصف الحد الأقصى.
تردد الرنين هو المتوسط الهندسي لهذه الترددات نصف الطاقة.
عرض النطاق الترددي ، المعرف بأنه نطاق التردد بين ترددات نصف الطاقة ، يساوي نسبة المقاومة إلى الحث.
يربط عامل الجودة ، الذي يمثل حدة منحنى الرنين ، الحد الأقصى للطاقة المخزنة في الدائرة بالطاقة المشتتة لكل دورة تذبذب.
عند الرنين ، تتأرجح الطاقة التفاعلية بين العناصر التفاعلية ، مما ينتج عنه تعبير عن عامل الجودة من حيث المفاعلات.
يمكن التعبير عن هذا العامل كنسبة تردد الرنين إلى عرض النطاق الترددي.
وينطوي عامل الجودة الأعلى على نطاق ترددي أضيق، مما يزيد من الانتقائية.

الاستجابة الترددية

Characteristics of Series Resonant Circuit

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يحدث الرنين التسلسلي في دائرة تحتوي على عناصر حثية (L)، سعوية (C)، ومقاومة (R) متصلة تسلسليًا. عند تردد الرنين، تكون المفاعلات التحريضية والسعوية متساوية في الحجم ولكنها متعارضة في الإشارة، مما يؤدي إلى إلغاء بعضها البعض بشكل فعال. يؤدي هذا إلى تقليل ممانعة الدائرة، ويتم تحديدها بشكل أساسي بواسطة المقاومة R. يتم تعريف تردد الرنين لدائرة RLC على النحو التالي:


<img alt="Equation 1" src="/files/ftp_upload/15144/15144_Equation_1.svg" style="height: 34px;">

يتناسب تبديد الطاقة في المقاومة مع مربع التيار. وهذا يدل على أن تبديد الطاقة يصل أيضًا إلى الحد الأقصى عندما يصل التيار إلى الحد الأقصى في حالة الرنين. يتم إعطاء هذه القوة القصوى بواسطة:


<img alt="Equation 2" src="/files/ftp_upload/15144/15144_Equation_2.svg" style="height: 24px;">

حيث I_max هو أقصى تيار عند الرنين.


يتم تعريف عرض النطاق الترددي للدائرة على أنه نطاق التردد الذي تتبدد فيه الطاقة إلى نصف قيمتها القصوى. ويحدث ذلك عند ترددات نصف القدرة، حيث ينخفض التيار إلى حوالي 70.7% من مستواه الأقصى. يتم حساب عرض النطاق الترددي على أنه الفرق بين ترددات نصف الطاقة الأعلى والأدنى.


عند الرنين، لا تتبدد القدرة التفاعلية، بل تتأرجح بين ملف الحث والمكثف، بينما تتبدد قدرة المقاومة في المقاومة. ويتعلق عامل الجودة بالحد الأقصى من الطاقة المخزنة في الدائرة مقابل الطاقة المتبددة في كل دورة. ومن الناحية التطبيقية، يمكن لجهاز إرسال راديوي ذو عامل Q أعلى لمرشح RLC الخاص به أن يعزل الإشارة المرغوبة بشكل أفضل عن ضوضاء التردد القريبة. والمقايضة هي عرض النطاق الترددي: حيث يؤدي ارتفاع Q إلى تقليل عرض النطاق الترددي، مما قد يحد من إمكانية تطبيق المرشح في الأنظمة التي تتطلب نطاق تردد أكثر شمولاً.


تمثل دائرة الرنين من سلسلة RLC الهندسة الدقيقة في الإرسال الراديوي من خلال العمل كمرشح فعال لتمرير النطاق. تم تصميم هذه الدائرة بدقة للسماح ببلوغ ذروة التيار عند تردد الرنين، مما يتيح إرسال واستقبال التردد الانتقائي.


</div>

ضع في اعتبارك وحدة إرسال لاسلكية تتضمن مرشح تمرير نطاق رنين سلسلة RLC.
تشير استجابة تردد هذه الدائرة إلى أن ...

characteristics-of-series-resonant-circuit

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

Frequency Response

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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 value. Because power loss in the resistor depends on the square of the current, the power dissipated in the resistor is also highest at resonance.

Bandwidth describes the range of frequencies over which the power falls to half of its maximum value. These are the half-power frequencies, where the current drops to about 70.7% of its peak value. The bandwidth is found by subtracting the lower half-power frequency from the higher one.

At resonance, reactive power does not turn into heat. Instead, it moves back and forth between the inductor and the capacitor. The resistor is where real power is dissipated. The quality factor, or Q factor, compares the maximum energy stored in the circuit with the energy lost each cycle.

This behavior is useful in radio transmitters and similar systems. A higher-Q RLC filter can separate a desired signal from nearby frequency noise more effectively. The trade-off is a narrower bandwidth, which can limit use in systems that need a wider frequency range. In this way, a series resonant circuit works as a band-pass filter that favors one frequency range over others.

Series Resonance and RLC Filter Behavior

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...

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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

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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

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...

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Op Amp Gain and Bode Plot Basics

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key terms and concepts

Learn how series resonance in an RLC circuit creates maximum current, minimum impedance, bandwidth limits, and filter behavior used in radio systems.

Series Resonance and RLC Filter Behavior | 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

Series Resonance and RLC Filter Behavior

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