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Quality Factor

Updated: Nov 28, 2020

In both #physics and some #engineering applications, we often use a word quality factor. Q factor is a dimensionless parameter that describes the oscillator or a resonator. Q factor is specified as the ratio of the peak energy stored in the #resonator in a cycle of oscillation to the energy lost per radian of the cycle.


If the quality factor is at a higher rate it shows a lower rate of energy loss so then the number of oscillations becomes slow. For example, when we suspend a pendulum in sir it has a high Q factor and in oil, it has less Q when comparative to air. So the resonators which having quality factors have low damping. So they vibrate often longer.

Q Factor

Q factor describes the resonance behaviour of the resonator. Resonators that have higher Q factor sinusoidally driven with greater amplitudes but in this state the frequencies are smaller in range. Through this process, we define a term bandwidth. Bandwidth is the range of frequencies in which the oscillator resonates. In a radio receiver if we use a high Q tuned circuit it will require more selectivity. But it eases the job by filtering out signals from other stations that lie on the nearer spectrum.


In a high oscillator, we have a smaller range of more stable frequencies. The quality factor of oscillators eventually varies from one system to another. It depends on the construction of the system.

The systems for which damping is essential to have Q near ​1⁄2. Like clocks, lasers, and other resonating systems that require strong resonance or high frequency will have high Q factors. Around 1000, quality factors are present in a tuning fork. Some high Q lasers and high-quality factors atomic clocks which have superconducting RF cavities can range up to 10¹¹ and higher.


Often Physicists and engineers use some alternative quantities to describe an oscillator. Like damping ratio, relative bandwidth, line width, etc. The concept of Quality factor is proposed by K.S.Johnson of a western electric company. When he was evaluating the quality coils. He proposed the term Q factor.


Quality Factor And damping


The quality factor depends upon the behaviour of simple damped oscillators.

  • The oscillator becomes overdamped when the system has a low-quality factor. Such a system doesn't oscillate by any means, however, when moving away from its balance consistent state yield it comes back to it by exponential decay, moving toward the consistent state esteem asymptotically. It has a motivation reaction that is the whole of two decaying exponential capacities with various paces of decay. As the quality factor diminishes the more slow decay mode gets more grounded comparative with the quicker mode and overwhelms the system's reaction bringing about a more slow system. A second-request low-pass filter with an extremely bad quality factor has an about first-request step reaction; the system's yield reacts to a stage contribution by gradually ascending toward an asymptote.


  • The Oscillator becomes underdamped when the system has a high-quality factor. This system is a combination of oscillation at a specified frequency which decays the amplitude signal. In underdamped oscillator, the systems which have low-quality factor may oscillate only fewer times. The relative amount of damping decreases concerning an increase in the quality factor. A pure oscillatory system, for example, a bell that rings everlastingly, has a boundless quality factor. All the more, for the most part, the yield of a second-request low-pass filter with a top-notch factor reacts to a stage contribution by rapidly transcending, wavering around, and in the long run meeting to consistent state esteem.


  • The oscillator becomes critically damped when the system has an intermediate quality factor. The output of this system does not oscillate or does not overshoot like an underdamped system. Critical #damping brings the faster reaction which is conceivable without overshoot. Real system details typically permit some overshoot for a quicker introductory reaction or require a more slow starting reaction to give a security edge against overshoot.

Effects of Quality factor


The quality factor is a very important element while dealing with RF tuning circuit. Usually, we require a high amount of quality factor which is very beneficial. But in this, we have some considerations also.


  • Bandwidth: The bandwidth of the tuning #circuit will decrease if we have a high amount of quality factor. So the tuning circuit will be stronger because energy is storing in a circuit.

  • Wide bandwidth: In numerous RF applications, there is a necessity for wide transmission capacity activity. A few types of tweak require a wide data transfer capacity, and different applications require fixed filters to give wideband coverage. While high dismissal of undesirable signs might be required, there is a contending prerequisite for wide transfer speeds. In like manner, in numerous applications, the quality of Q expected should be resolved to give the general performance that is required gathering prerequisites for wide data transmission and dismissal of unwanted signals.

  • General spurious signals: Spurious signals are often removed by tuning circuit. For the higher requirement of the quality factor, we need sharper filters. So by this, we can remove spurious signals from this.

  • Ringing: The quality factor of the resonator circuit increases by these losses decrease. This results that any oscillation which setup will be a long way to die. In other words, we can say it as ringing.


Quality factor formulae


The basic Q or quality factor formula is based upon the energy losses within the #inductor, circuit, or other forms of the component.

  • The mathematical expression of the quality factor concerning the above definition is Q=Estored/Elostper cycle.

  • When we considered the bandwidth of RF then the formula becomes Q=F0/F3dB

Conclusion:


The #qualityfactor or 'Q' is used in the application of the performance of a resonator circuit. The values for the Q factor are often used in defining the performance of an inductor, a capacitor, or a tuned circuit.


See Also:

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  2. Voltage and current

  3. 5G Communications

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