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

欠阻尼的并联 RLC 电路能够在谐振频率下维持振荡，因此适用于振荡器中。
一名电气工程师需要设计一个模型振荡电路，其阻尼自然频率为 4 千赫兹，阻尼系数为 4 弧度每秒。
在电阻固定为 200 欧姆的情况下，可以确定电容和电感的精确值。
由于该电路的阻尼因子为电阻与电容乘积的两倍的倒数，因此可得到电路设计所需的电容值。
利用关联共振频率、阻尼因子和阻尼固有频率的数学表达式来确定共振频率。
共振频率与电感和电容乘积的平方根成反比。
将已知值代入该方程，以求得所需的电感。
阻尼固有频率低于共振频率，且电感值小于电阻平方乘以电容的四倍。这两个条件均证实了欠阻尼振荡的存在。

设计示例：并联 rlc 电路

假设需要设计一个振荡器电路，它是由各种电子设备和系统中的关键组件所组成。其目标是创建一个具有特定性质的振荡器电路：4 kHz阻尼的固有频率和4弧度每秒的阻尼因数。为了能够实现这一目标，便采用了并联 RLC 电路，该电路以其谐振频率下维持振荡的能力而闻名。在这种情况下，阻尼系数对于实现所需的性能是至关重要的。 从200 Ω 的固定电阻开始，确定必要的电容和电感值以满足其规格的要求。首先，我们认识到阻尼因数是电阻和电容乘积两倍的倒数。这种认识可以精确的确定电路中所需的电容值。 <img alt="Equation1" src="/files/ftp_upload/15175/15175_PT_Equation_1.svg" style="text-align: center; height: 28px;"> 接下来，我们将注意力转向连接谐振频率、阻尼因数和阻尼固有频率的数学表达式。通过对该方程进行运算，可以得出谐振的频率信息。 <img alt="Equation2" src="/files/ftp_upload/15175/15175_PT_Equation_2.svg" style="text-align: center; height: 18px;"> 对于设计振荡器中至关重要的谐振频率，它与电感和电容乘积的平方根成反比。有了这些知识和已知值，就可以计算出满足其设计标准所需的电感值。 <img alt="Equation3" src="/files/ftp_upload/15175/15175_PT_Equation_3.svg" style="text-align: center; height: 34px;"> 这些计算证实了阻尼中的固有频率确实低于谐振频率，并且电感值低于电阻乘以电容平方的四倍。这些条件表明了振荡器电路中的设计能够表现出所需的低阻尼振荡，同时还展示了设计一个精确电路的精湛技术。

设计示例：并联 RLC 电路

欠阻尼并联RLC电路可在谐振频率下维持振荡，因此适用于振荡器中。  
一位电气工程师是……

design-example-underdamped-parallel-rlc-circuit

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

First and Second-Order Circuits

一阶与二阶电路

KEY TERMS AND CONCEPTS

关键术语与概念

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

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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...

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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