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

Untergedämpfte parallele RLC-Schaltungen können Schwingungen mit einer Resonanzfrequenz aufrechterhalten, wodurch sie für den Einsatz in Oszillatoren geeignet sind.
Ein Elektroingenieur hat die Aufgabe, eine Modell-Oszillatorschaltung mit einer gedämpften Eigenfrequenz von 4 Kilohertz und einem Dämpfungsfaktor von 4 Bogenmaß pro Sekunde zu entwerfen.
Mit einem eingestellten Widerstand von 200 Ohm können die genauen Werte für Kapazität und Induktivität bestimmt werden.
Da der Dämpfungsfaktor für die Schaltung der Kehrwert des Doppelten des Produkts aus Widerstand und Kapazität ist, erhält man den für den Schaltungsentwurf erforderlichen Kapazitätswert.
Der mathematische Ausdruck, der die Resonanzfrequenz, den Dämpfungsfaktor und die gedämpfte Eigenfrequenz korreliert, wird verwendet, um die Resonanzfrequenz zu erhalten.
Die Resonanzfrequenz ist umgekehrt proportional zur Quadratwurzel des Produkts aus Induktivität und Kapazität.
Die bekannten Werte werden in diese Gleichung eingesetzt, um die erforderliche Induktivität zu erhalten.
Die gedämpfte Eigenfrequenz ist niedriger als die Resonanzfrequenz, und der Induktivitätswert ist weniger als das Vierfache des Quadrats des Widerstands multipliziert mit der Kapazität. Beide Bedingungen bestätigen eine unterdämpfte Schwingung.

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entwurfsbeispiel: parallele rlc-schaltung

Erwägen Sie den Entwurf einer Oszillatorschaltung, einer entscheidenden Komponente in verschiedenen elektronischen Geräten und Systemen. Ziel ist es, eine Oszillatorschaltung mit spezifischen Eigenschaften zu schaffen: einer gedämpften Eigenfrequenz von 4 kHz und einem Dämpfungsfaktor von 4 Radiant pro Sekunde. Um dies zu erreichen, wird eine parallele RLC-Schaltung eingesetzt, die für ihre Fähigkeit bekannt ist, Schwingungen auf einer Resonanzfrequenz aufrechtzuerhalten. In diesem Fall ist der Dämpfungsfaktor entscheidend für das Erreichen der gewünschten Leistung. Ausgehend von einem festen Widerstand von 200 Ω werden die notwendigen Werte für Kapazität und Induktivität ermittelt, um die Spezifikationen zu erfüllen. Zunächst wird erkannt, dass der Dämpfungsfaktor der Kehrwert des doppelten Produkts aus Widerstand und Kapazität ist. Diese Erkenntnisse ermöglichen die Bestimmung des erforderlichen Kapazitätswerts für die Schaltung. <img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;"> Als nächstes wird die Aufmerksamkeit auf den mathematischen Ausdruck gerichtet, der die Resonanzfrequenz, den Dämpfungsfaktor und die gedämpfte Eigenfrequenz miteinander verbindet. Durch Manipulation dieser Gleichung können Resonanzfrequenzinformationen extrahiert werden. <img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;"> Die für das Oszillatordesign entscheidende Resonanzfrequenz ist umgekehrt proportional zur Quadratwurzel des Produkts aus Induktivität und Kapazität. Basierend auf diesem Wissen und den bekannten Werten wird die erforderliche Induktivität berechnet, um die Designkriterien zu erfüllen. <img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;"> Diese Berechnungen bestätigen, dass die gedämpfte Eigenfrequenz tatsächlich niedriger als die Resonanzfrequenz ist und der Induktivitätswert unter das Vierfache des Quadrats des Widerstands multipliziert mit der Kapazität fällt. Diese Bedingungen bestätigen, dass die Oszillatorschaltung so konzipiert wurde, dass sie die erforderlichen unterdämpften Schwingungen aufweist, was ein Beweis für die Kompetenz im präzisen Schaltungsdesign ist.

Entwurfsbeispiel: Parallele RLC-Schaltung

Untergedämpfte parallele RLC-Schaltungen können Schwingungen mit einer Resonanzfrequenz aufrechterhalten, wodurch sie für den Einsatz in Oszillatoren geeignet sind.
Ein Elektroingenieur ist ...

design-example-underdamped-parallel-rlc-circuit

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

First and Second-Order Circuits

Schaltungen erster und zweiter Ordnung

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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

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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...

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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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