# Relationship between damping ratio and quality factor

### Damping ratio (related to Quality factor) - calculator - fx​Solver There are many ways to describe damping, e.g., damping ratio, quality factor, spa - There are many ways to show or derive the damping ratio relationships. While the Q factor of an element relates to the losses, this links directly in to the Q is defined as the ratio of the energy stored in the resonator to the energy The Quality Factor, Q determines the qualitative behaviour of simple damped. include the tangent of the phase lag, tan *, damping ratio,, specific damping capacity, V, loss factor, T1, inverse quality factor, Q-. 1., and log decrement, 6.

### Q factor - Wikipedia

This case is called underdamped. Between the overdamped and underdamped cases, there exists a certain level of damping at which the system will just fail to overshoot and will not make a single oscillation. This case is called critical damping. The key difference between critical damping and overdamping is that, in critical damping, the system returns to equilibrium in the minimum amount of time.

Definition The effect of varying damping ratio on a second-order system. It is particularly important in the study of control theory. It is also important in the harmonic oscillator.

The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient: Derivation Using the natural frequency of a harmonic oscillator and the definition of the damping ratio above, we can rewrite this as: This equation can be solved with the approach. Using it in the ODE gives a condition on the frequency of the damped oscillations, Undamped: Is the case where corresponds to the undamped simple harmonic oscillator, and in that case the solution looks likeas expected. If s is a complex number, then the solution is a decaying exponential combined with an oscillatory portion that looks like.

This case occurs forand is referred to as underdamped. If s is a real number, then the solution is simply a decaying exponential with no oscillation. This case occurs forand is referred to as overdamped. A high-quality bell rings with a single pure tone for a very long time after being struck.

### Quality Factor | Q Factor Formula | Electronics Notes

A purely oscillatory system, such as a bell that rings forever, has an infinite quality factor. More generally, the output of a second-order low-pass filter with a very high quality factor responds to a step input by quickly rising above, oscillating around, and eventually converging to a steady-state value.

Like an overdamped system, the output does not oscillate, and does not overshoot its steady-state output i. Like an underdamped response, the output of such a system responds quickly to a unit step input. Critical damping results in the fastest response approach to the final value possible without overshoot. Real system specifications usually allow some overshoot for a faster initial response or require a slower initial response to provide a safety margin against overshoot. In negative feedback systems, the dominant closed-loop response is often well-modeled by a second-order system. The phase margin of the open-loop system sets the quality factor Q of the closed-loop system; as the phase margin decreases, the approximate second-order closed-loop system is made more oscillatory i. Quality factors of common systems[ edit ] A unity gain Sallen—Key filter topology with equivalent capacitors and equivalent resistors is critically damped i. 