Name: oscillator design with a parallel rlc circuit
Uploaded: 2024-04-11T12:48:44.000Z
Duration: 1 min 17 s
Channel: JoVE

Les circuits RLC parallèles sous-amortis peuvent maintenir des oscillations à une fréquence de résonance, ce qui les rend adaptés à une utilisation dans les oscillateurs.
Un ingénieur électricien est chargé de concevoir un circuit d’oscillateur modèle avec une fréquence naturelle amortie de 4 kilohertz et un facteur d’amortissement de 4 radians par seconde.
Avec une résistance réglée de 200 ohms, les valeurs précises de capacité et d’inductance peuvent être déterminées.
Étant donné que le facteur d’amortissement du circuit est l’inverse de deux fois le produit de la résistance et de la capacité, la valeur de capacité requise pour la conception du circuit est obtenue.
L’expression mathématique corrélant la fréquence de résonance, le facteur d’amortissement et la fréquence propre amortie est utilisée pour obtenir la fréquence de résonance.
La fréquence de résonance est inversement proportionnelle à la racine carrée du produit de l’inductance et de la capacité.
Les valeurs connues sont substituées dans cette équation pour obtenir l’inductance requise.
La fréquence propre amortie est inférieure à la fréquence de résonance, et la valeur d’inductance est inférieure à quatre fois le carré de la résistance multipliée par la capacité. Ces deux conditions confirment l’oscillation sous-amortie.

Aucun conflit d’intérêts n’a été déclaré.

exemple de conception: circuit rlc parallèle

Envisagez de concevoir un circuit oscillateur, un composant crucial dans divers appareils et systèmes électroniques. L'objectif est de créer un circuit oscillateur avec des caractéristiques spécifiques : une fréquence propre amortie de 4 kHz et un facteur d'amortissement de 4 radians par seconde. Pour ce faire, un circuit RLC parallèle est utilisé, connu pour sa capacité à entretenir des oscillations à une fréquence de résonance. Dans ce cas, le facteur d’amortissement est essentiel pour atteindre les performances souhaitées. En commençant par une résistance fixe de 200 Ω, les valeurs nécessaires de capacité et d'inductance sont déterminées pour répondre aux spécifications. Premièrement, il est reconnu que le facteur d’amortissement est l’inverse du double du produit de la résistance et de la capacité. Cette information permet d'identifier la valeur de capacité requise pour le circuit. <img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;"> Ensuite, l’attention est portée sur l’expression mathématique qui relie la fréquence de résonance, le facteur d’amortissement et la fréquence propre amortie. En manipulant cette équation, des informations sur la fréquence de résonance peuvent être extraites. <img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;"> La fréquence de résonance, cruciale pour la conception des oscillateurs, est inversement proportionnelle à la racine carrée du produit de l'inductance et de la capacité. Fort de ces connaissances et des valeurs connues, l'inductance nécessaire pour répondre aux critères de conception est calculée. <img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;"> Ces calculs confirment que la fréquence propre amortie est bien inférieure à la fréquence de résonance, et que la valeur de l'inductance tombe en dessous de quatre fois le carré de la résistance multiplié par la capacité. Ces conditions confirment que le circuit oscillateur a été conçu pour présenter les oscillations sous-amorties requises, démontrant ainsi la maîtrise d'une conception de circuit précise.

Exemple de conception: circuit RLC parallèle

Les circuits RLC parallèles sous-amortis peuvent maintenir des oscillations à une fréquence de résonance, ce qui les rend adaptés à une utilisation dans les oscillateurs.
Un ingénieur électricien est...

design-example-underdamped-parallel-rlc-circuit

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

First and Second-Order Circuits

Circuits du premier et du second ordre

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

Design Example: Underdamped Parallel RLC Circuit

oscillator design with a parallel rlc circuit

A parallel RLC circuit can be designed to work as an oscillator with underdamped behavior. This example targets a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. A fixed resistance of 200 Ω is used as the starting point for the design.

The first step is to find the capacitance. The damping factor is the reciprocal of twice the product of resistance and capacitance. Using that relationship, the needed capacitance value can be calculated from the given resistance and damping factor.

Next, the resonant frequency is found from the link between resonant frequency, damping factor, and damped natural frequency. Resonant frequency is important in oscillator design because it is the frequency a parallel RLC circuit tends to sustain. It is also tied to inductance and capacitance through the square root of their product.

With the capacitance known, the inductance is then computed from the resonant frequency equation. The results show that the damped natural frequency is lower than the resonant frequency. They also show that the inductance is below four times the square of the resistance multiplied by capacitance, which supports underdamped oscillations in the circuit.

Oscillator Design with a Parallel RLC Circuit

oscillator-design-with-a-parallel-rlc-circuit

first-order circuits

First-Order Circuits in Flashing Lamps

First-order circuits use a resistor and one energy storage element, either a capacitor or an inductor. They are common in electronic systems and are described by a first-order differential equation that links the input and output signals. One important example is the RC circuit, which uses a resistor and a capacitor. In a relaxation oscillator such as a neon lamp circuit, the capacitor starts charging when voltage is applied. At first, the lamp behaves like an open circuit. When the capacitor...

rc circuit without source

RC Capacitor Discharge After Power Loss

An RC circuit discharges after the DC source is removed. If the capacitor was fully charged first, its initial voltage, V0, provides the energy that drives the source-free circuit. Kirchhoff’s current law is applied at the top node of the circuit. The current terms for the resistor and capacitor are then substituted, which leads to a first-order differential equation. Rearranging, integrating, and taking the exponential gives the natural response of the circuit. The integration constant in...

rc circuit with source

RC Circuit Charging After a DC Step

An RC circuit with a DC source shows how a capacitor charges after a sudden voltage step. The applied source is treated as a unit step function, and the capacitor voltage is the step response of the circuit. This response describes how the circuit reacts right after the input changes. A capacitor cannot change its voltage instantly. So, immediately after the switch closes at t=0, the capacitor voltage stays at its initial value. Kirchhoff’s current law is then applied at that moment and...

rl circuit without source

RL Circuit Decay After Source Removal

An RL circuit begins to decay after the DC source is removed. At that moment, the circuit becomes source-free. If the inductor has an initial current, I0, it also stores initial energy. That stored energy drives the natural response of the circuit. Kirchhoff’s voltage law is applied around the loop. The inductor voltage and resistor voltage are substituted into the equation. This gives a first-order differential equation for the current. Rearranging the terms produces a logarithmic form, which...

rl circuit with source

RL Step Response Under a DC Source

An RL circuit connected to a DC source has a step response that changes over time. The response has two parts: the transient response and the steady-state response. The transient response is the short-lived reaction that happens right after the source is applied. During the transient phase, the current changes exponentially. If the circuit starts with current in the inductor, that current decays toward zero as time goes on. At this stage, the inductor acts like a short circuit, so the source...

design example: frog muscle response

RL Circuit and Frog Leg Current Response

An RL circuit is used to model the frog leg’s response to electrical stimulation. In this setup, the student studies how current changes in a resistor-inductor circuit can trigger muscle contraction. The circuit provides a way to control and measure the electrical impulses involved in the experiment. When the switch is closed, the frog’s leg shows a brief contraction. At steady state, the inductor acts like a short circuit. That lets current bypass the resistor and produces a mild, short...

second-order circuits

RLC Damping and Resonant Frequency

Second-order circuits use two energy storage elements, such as a capacitor and an inductor, to shape how current and voltage change over time. These circuits include RLC circuits, along with RC and RL circuits that have two capacitors or two inductors. Their behavior is described by second-order differential equations that connect the input signal to the output signal. The input usually comes from a voltage source or a current source. The output is often the voltage across the capacitor, the...

series rlc circuit without source

Natural Response of a Source-Free RLC Circuit

A source-free RLC circuit is a series circuit with a resistor, inductor, and capacitor, but no external energy source. It begins with the energy already stored in the capacitor and inductor. That stored energy drives the circuit at first. The circuit is described by a second-order differential equation. This equation shows how the resistor, inductor, and capacitor interact over time. The resistor removes energy from the circuit, so the solution has an exponential form. When the exponential...

types of responses of series rlc circuits

types-of-responses-of-series-rlc-circuits

Damping in Series RLC Circuit Responses

A source-free series RLC circuit shows three response patterns based on damping. The circuit is described by a second-order differential equation. Its complete solution is made from two distinct solutions. Those solutions depend on the roots, which are written in terms of the damping factor and the resonant frequency. When the damping factor is greater than the resonant frequency, both roots are real and negative. This gives an overdamped response. The circuit output decays slowly over time. <br...

series rlc circuit with source

Forced Response in a Series RLC Circuit

A series RLC circuit with a DC source can model an automobile ignition system. The circuit shows how a battery can produce the high voltage needed for a spark. In this case, the input DC voltage acts like a forcing step function. Applying Kirchhoff's voltage law leads to a second-order differential equation. A second-order differential equation is an equation with a term for the second derivative. The form of this equation is very similar to the one used for a source-free RLC circuit, so the...

parallel rlc circuits

Parallel RLC Step Response in Surge Protectors

Parallel RLC circuits help explain how a surge protector works in a street lamp. The circuit model uses a DC input source that creates a step response when the switch is turned on. This setup shows how the lamp’s components can be protected from sudden voltage spikes. When the switch closes, Kirchhoff’s current law is applied to the parallel RLC circuit. That leads to a second-order differential equation. The solution has two parts: a transient response and a steady-state response. The...

second-order op amp circuits

Second-Order Op Amp Low-Pass Filters

Second-order op-amp low-pass filters remove unwanted high-frequency noise from audio signals. They are used in audio systems to refine sound quality. These filters are often built as voltage followers and have two nodes with storage elements. The circuit analysis follows the same basic method used for second-order RLC circuits. In practice, bulky inductors are usually avoided because of their size and weight. For that reason, the focus here is on RC second-order op-amp circuits, which are...

design example: underdamped parallel rlc circuit

A parallel RLC circuit can be designed to work as an oscillator with underdamped behavior. This example targets a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. A fixed resistance of 200 Ω is used as the starting point for the design. The first step is to find the capacitance. The damping factor is the reciprocal of twice the product of resistance and capacitance. Using that relationship, the needed capacitance value can be calculated from the given resistance...

key terms and concepts

Learn how a parallel RLC circuit is sized for oscillator use by finding capacitance and inductance from a target damped natural frequency and damping factor.

Oscillator Design with a Parallel RLC Circuit | 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

Oscillator Design with a Parallel RLC Circuit

Description

Transcript

Tags