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

מעגלי RLC מקבילים לא משופעים יכולים לקיים תנודות בתדר תהודה, מה שהופך אותם למתאימים לשימוש במתנדים.
על מהנדס חשמל מוטלת המשימה לתכנן מעגל מתנד מודל עם תדר טבעי לח של 4 קילוהרץ ומקדם דעיכה של 4 רדיאנים לשנייה.
עם התנגדות קבועה של 200 אוהם, ניתן לקבוע את הערכים המדויקים עבור קיבול והשראות.
מכיוון שגורם הדעיכה של המעגל הוא הדדי של מכפלה כפולה של ההתנגדות והקיבוליות מתקבל ערך הקיבול הנדרש לתכנון המעגל.
הביטוי המתמטי המקשר בין תדר התהודה, גורם הדעיכה והתדר הטבעי הדעוך משמש לקבלת תדר התהודה.
תדר התהודה עומד ביחס הפוך לשורש הריבועי של מכפלת השראות וקיבול.
הערכים הידועים מוחלפים במשוואה זו כדי לקבל את ההשראות הנדרשת.
התדר הטבעי המוחלש נמוך מתדר התהודה, וערך ההשראות קטן מפי ארבעה מריבוע ההתנגדות כפול הקיבול. שני תנאים אלה מאשרים תנודה תת-רטובה.

לא הוכרז על ניגוד עניינים.

דוגמה לעיצוב: מעגל rlc מקביל

<div style="direction:rtl">חשבו על תכנון מעגל מתנד, מרכיב חיוני במכשירים ומערכות אלקטרוניות שונות. המטרה היא ליצור מעגל מתנד עם מאפיינים ספציפיים: תדר טבעי מופחת של 4 קילו-הרץ ומקדם דעיכה של 4 רדיאנים לשנייה. כדי להשיג זאת, נעשה שימוש במעגל RLC מקביל, הידוע ביכולתו לקיים תנודות בתדר תהודה. במקרה זה, גורם השיכוך הוא מכריע בהשגת הביצועים הרצויים. החל מהתנגדות קבועה של 200 Ω, הערכים הדרושים עבור הקיבול וההשראות נקבעים כדי לעמוד במפרט. ראשית, ידוע שגורם השיכוך הוא ההדדיות של מכפלה כפולה של התנגדות וקיבול. תובנה זו מאפשרת להצביע על ערך הקיבול הנדרש עבור המעגל. <img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;"> לאחר מכן, תשומת הלב מופנית לביטוי המתמטי המחבר בין תדר התהודה, גורם השיכוך והתדר הטבעי המעוכב. על ידי מניפולציה של המשוואה הזו, ניתן לחלץ מידע על תדר תהודה. <img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;"> תדר התהודה, החיוני לתכנון מתנד, עומד ביחס הפוך לשורש הריבועי של תוצר השראות והקיבול. חמוש בידע זה ובערכים הידועים, מחושבת השראות הדרושה כדי לעמוד בקריטריוני התכנון. <img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;"> חישובים אלו מאשרים שהתדר הטבעי המבולק אכן נמוך מתדר התהודה, וערך השראות יורד מתחת לארבע פעמים ריבוע ההתנגדות כפול הקיבול. תנאים אלה מאשרים כי מעגל המתנד תוכנן להציג את התנודות המתבקשות, המציגות מיומנות בתכנון מעגל מדויק.</div>

דוגמה לעיצוב: מעגל RLC מקביל

מעגלי RLC מקבילים לא משופעים יכולים לקיים תנודות בתדר תהודה, מה שהופך אותם למתאימים לשימוש במתנדים.
מהנדס חשמל הוא ...

design-example-underdamped-parallel-rlc-circuit

Education

JoVE Core

Electrical Engineering

הנדסה חשמלית

Unit 1

יחידה 1

First and Second-Order Circuits

מעגלים מסדר ראשון ושני

KEY TERMS AND CONCEPTS

מונחי מפתח ומושגים

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...

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RC Circuit Charging After a DC Step

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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...

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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...

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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

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