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

Underdamped parallel RLC circuits can sustain oscillations at a resonant frequency, making them suitable for use in oscillators.
An electrical engineer is tasked with designing a model oscillator circuit with a damped natural frequency of 4 kilohertz and a damping factor of 4 radians per second.
With a set resistance of 200 ohms, the precise values for capacitance and inductance can be determined.
Since the damping factor for the circuit is the reciprocal of twice the product of the resistance and capacitance, the required capacitance value for the circuit design is obtained.
The mathematical expression correlating the resonant frequency, damping factor, and damped natural frequency is used to obtain the resonant frequency.
The resonant frequency is inversely proportional to the square root of the product of inductance and capacitance.
The known values are substituted into this equation to obtain the required inductance.
The damped natural frequency is lower than the resonant frequency, and the inductance value is less than four times the square of resistance multiplied by capacitance. Both these conditions confirm underdamped oscillation.

design example: underdamped parallel rlc circuit

Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed resistance of 200 &#937;, the necessary values for capacitance and inductance are determined to meet the specifications. First, it is recognized that the damping factor is the reciprocal of twice the product of resistance and capacitance. This insight allows the pinpointing of the required capacitance value for the circuit.
<img alt='Capacitance formula \(C = \frac{1}{2&#945;R}\), electrical engineering concept."""
' src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;" data-altupdatedat="1762173717000" data-alt="Equation1" />
Next, attention is turned to the mathematical expression that connects the resonant frequency, damping factor, and damped natural frequency. By manipulating this equation, resonant frequency information can be extracted.
<img alt="Damped oscillator formula: &#969;&#8320;&#178; = &#969;d&#178; + &#945;&#178; (equation, mechanical resonances, physics study)" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;" data-altupdatedat="1762173717000" data-alt="Equation2" />
The resonant frequency, crucial for oscillator design, is inversely proportional to the square root of the product of inductance and capacitance. Armed with this knowledge and the known values, the necessary inductance to meet the design criteria is computed.
<img alt="Capacitance equation diagram, L=1/&#969;&#178;C, illustrating inductance-capacitance relationship." src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;" data-altupdatedat="1762173717000" data-alt="Equation3" />
These calculations confirm that the damped natural frequency is indeed lower than the resonant frequency, and the inductance value falls below four times the square of the resistance multiplied by capacitance. These conditions affirm that the oscillator circuit has been designed to exhibit the required underdamped oscillations, showcasing proficiency in precise circuit design.

Design Example: Underdamped Parallel RLC Circuit

Underdamped parallel RLC circuits can sustain oscillations at a resonant frequency, making them suitable for use in oscillators.
An electrical engineer is ...

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Electrical Engineering

Unit 1

First and Second-Order Circuits

KEY TERMS AND CONCEPTS

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

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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.

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electrical engineering

Oscillator Design with a Parallel RLC Circuit

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