Table of Contents
Introduction
The idea of Q, Quality Factor, was first conceived by an engineer named K. S. Johnson from the Engineering Department of Western Electric Company in the United States. He had been assessing the performance and quality of various coils. During his investigations, he developed the concept of Q. Surprisingly, he ended up choosing the letter Q because all other letters of the alphabet had been taken, rather than because of the term quality factor, though in hindsight, the alphabet Q for quality factor could not have been any better. The concept of quality factor is applicable in many areas of physics and engineering. Q is described in electronic circuits as the ratio of the energy stored in the resonator to the energy supplied by a to it per cycle in order to maintain signal amplitude constant at a frequency where the stored energy is constant with time. Although the Q factor of an element is related to losses, it is directly related to the bandwidth of a resonator in relation to its centre frequency.
Overview
The quality factor, or Q factor, is indeed a dimensionless parameter in physics and engineering that describes how underdamped an oscillator or resonator is. It really is defined as the ratio of the resonator’s initial energy to the energy lost in one radian of the oscillation cycle. When subjected to an oscillating driving force, the Q factor is defined as the ratio of a resonator’s centre frequency to its bandwidth. The numerical results from these two definitions are similar, but not identical. Greater Q implies a lower rate of energy loss and slower decay of oscillations. A pendulum suspended from one high-quality bearing and oscillating in the air has a high Q, whereas one immersed in oil has a low. Resonators having high-quality factors have limited damping, allowing them to ring or vibrate for a longer period of time.
Resonance: Quality factor
A Q factor is just a parameter that describes an underdamped harmonic oscillator’s resonance behaviour (resonator). Higher Q factor sinusoidally driven resonators resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the bandwidth will be the range of frequencies for which the oscillator resonates. Thereby, a high-Q tuned circuit in a radio receiver would be more difficult to tune, but it would be more selective; it would do a better job of filtering out signals from other stations on the same frequency band. High-Q oscillators have a narrower frequency range and are more stable.
The q – factor of oscillators differ depending on their construction from system to system. Q is close to 1/2 in systems where damping is important (for example, dampers that keep a door from slamming shut). High-quality factors are required for clocks, lasers, and other resonating systems that require either strong resonance or high-frequency stability. Tuning forks have quality factors as in thousands. Atomic clocks, superconducting RF cavities used in accelerators, and some high-Q lasers have quality factors of 1011 or higher.
Numerous different quantities are used by physicists and engineers to describe how damped an oscillator is. The damping ratio, relative bandwidth, linewidth, and bandwidth measured in octaves are all important examples.
In electronic circuits, Q is described as the ratio of the energy stored in the resonator to the energy supplied by a to it per cycle in order to maintain signal amplitude constant at a frequency where the stored energy is constant with time. This is also a measure of an inductor’s efficiency and can be defined as the ratio of its inductive reactance to its resistance at a specific frequency.
Effects of Q factor
There are numerous reasons why the Q factor is important when dealing with RF tuned circuits. A high level of Q is usually advantageous, but in some applications, a defined level of Q may be required.
A few of the Q-related considerations in RF tuned circuits are summarised below:
- Bandwidth: As the Q factor or quality factor increases, so does the bandwidth of the tuned circuit filter. Whenever losses decrease, the tuned circuit sharpens as energy is better stored in the circuit. It does seem that as Q increases, so does the 3 dB bandwidth and the overall response of the tuned circuit. Throughout many cases, a high Q factor is required to achieve the desired level of selectivity.
- Wide bandwidth: Wide bandwidth procedure is required in many RF applications. A few modulation schemes necessitate a wide bandwidth, whereas other applications necessitate fixed filters to provide wideband coverage. Whereas high rejection of unwanted signals may be required, wide bandwidths are also required. As a result, in many applications, the level of Q required to provide the overall performance required to meet requirements for wide bandwidth and adequate rejection of unwanted signals must be determined.
- Oscillator phase noise: Phase noise is generated by an oscillator. This consists of random phase shifts in the signal. One such expresses as noise that radiates from the main carrier. As one could expect, such a noise is undesirable and must be reduced. An oscillator layout could be tailored to reduce this in a variety of ways, the most important of which is to increase the Q, or quality factor, of the oscillator tuned circuit.
- General spurious signals: To remove spurious signals, tuned circuits and filters are frequently used. The higher the level of Q and the sharper the filter, the better the circuit will be able to remove spurious signals.
- Ringing: As such Q of a resonant circuit rises, so do the losses. It thus means that any oscillations created within the circuit will last longer. That is, the circuit will “ring” more frequently. Because less energy is lost in the tuned circuit, this is ideal for use within an oscillator circuit because it is easier to set up and maintain an oscillation.
Q factor formulas
The fundamental Q or quality factor formula is based on the energy losses within the inductor, circuit, or another type of component.
The Q factor can be mathematically expressed using the Q factor formula below, based on the definition of a quality factor given above:
While looking at an RF resonant circuit’s bandwidth, this translates to the Q factor formula:
Each individual component in any RF or other circuit can contribute to the Q or quality factor of the circuit network as a whole. Components such as inductors and capacitors are frequently referred to as having a specific Q factor or quality factor.
Quality factor and damping
The damping is an important aspect of the Q factor in many circuits. The Quality Factor, Q, governs the qualitative behaviour of simple damped oscillators and influences other circuits such as filter response, etc.
When it comes to damping and Q factor, there are three main regimes to consider:
- Under-damped (Q > 1/2): The under system has a Q factor that is greater than half. When a step impulse is applied to a system with a Q factor of less than half, the oscillation may occur once or twice before it disappears. As the quality factor increases, the damping decreases and the oscillations last longer. In some kind of a theoretical system with an infinite Q factor, the oscillation would be maintained indefinitely without the need for any additional stimulus. Some signal is fed back into oscillators to provide additional stimulus, but a high Q factor produces a much cleaner result. The signal contains lower levels of phase noise.
- Over-damped (Q <1/2): The Q factor of an over-damped system is less than 1/2. The losses in this type of system are high, and the system has no overshoot. Instead, after a step impulse is applied, the system will exponentially decay, asymptotically approaching the steady-state value. As the Q factor (or quality factor) decreases, the system responds more slowly.
- Critically damped (Q = 1/2): A critically damped system seems to have a Q factor of 0.5, and the output, like an over-damped system, does not oscillate and does not overshoot its steady-state output. This same system will approach the steady-state asymptote as quickly as possible, with no overshoot.
FAQ’s
Q. What do you mean by the Q factor?
Ans: The Q factor, as well known as the quality factor, is a dimensionless parameter that characterises the bandwidth and centre frequency of an underdamped resonator.
Q. What is the Q factor of the coil?
Ans: For a given frequency, the Q factor of a coil is defined as the ratio of its inductance L to its resistance R.
Q. What is the filter quality factor?
Ans: Such a Q Factor indicates how “Selective” or “Un-selective” the bandpass filter is toward a given frequency range. The smaller the value of the Q factor, the wider the filter’s bandwidth, and the higher the Q factor, the narrower and more “selective” the filter.
