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Design Example: Underdamped Parallel RLC Circuit

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...

Characteristics of Series Resonant Circuit

Characteristics of Series Resonant Circuit

Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:

Parallel Resonance

Parallel Resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:

Expected Frequencies in Goodness-of-Fit Tests

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).

Series Resonance

Series Resonance

The RLC circuit impedance is defined as the ratio of the supply voltage to the circuit current. Resonance in such a circuit occurs when the imaginary part of this impedance equals zero. This specific condition means that the inductive reactance is exactly equal to the capacitive reactance. The frequency at which this happens is known as the resonant frequency. Mathematically, the resonant frequency is inversely proportional to the square root of the product of the inductance (L) and capacitance...

RLC Circuit as a Damped Oscillator

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...

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Recombination Dynamics in Thin-film Photovoltaic Materials via Time-resolved Microwave Conductivity

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Expected quality factor of a simple tuned oscillator.

¹Universiti Tunku Abdul Rahman, Electronic Engineering, Kampar, Perak, Malaysia. tankh@utar.edu.my

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

|May 31, 2011

Summary

This study reveals a new method for characterizing oscillators, focusing on the expected quality factor (Q) and noise in piezoelectric resonators. It offers insights into injection locking and frequency pulling phenomena in self-sustained oscillators.

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Area of Science:

Electrical Engineering
Physics
Electronics

Background:

Self-sustained oscillators with positive feedback exhibit high gain and are susceptible to noise.
Thermal noise causes linear phase/frequency deviations, amplified near the oscillator frequency.
Frequency pulling can lead to hysteresis and synchronous locking due to truncated limiting curves in real oscillators.

Purpose of the Study:

To introduce a novel approach for designing and characterizing simple tuned oscillators.
To explore the relationship between the expected quality factor and the truncated limiting curve in injection-locked oscillators.
To develop new analytical methods for oscillator characterization, including noise analysis.

Main Methods:

Revision of the transducer loss method for oscillator characterization.
Development of a transparent method for normalizing two-port networks under white noise conditions.
Proposal for characterizing noise in quartz crystal oscillators via equivalent noise-resistance.

Main Results:

A new method for oscillator characterization based on the expected quality factor is presented.
The two-port network model is shown to be approximable on a one-port basis.
Closed-form estimation of the expected Q-factor magnitude for piezoelectric resonator oscillators is calculated.

Conclusions:

The study provides innovative analytical methods for oscillator design and characterization.
New insights into noise phenomena and injection locking in oscillators are offered.
The proposed methods facilitate a more accurate estimation of the Q-factor in piezoelectric resonator oscillators.