**Q factor and Damping Ratio**

The *damping ratio* is a parameter, usually denoted by ζ (zeta), that characterizes the frequency response of a second order ordinary differential equation. 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. The various expressions for damping ratio is given below:

**Damping Factor in an RLC Circuit**

where:

= Damping Factor

R = Resistance (Ω)

C = Capacitance (Fa)

L = Inductance (H)

**Q Factor**

where:

Q = Q Factor

= Damping Ratio

**Equation for Damped Harmonic Oscillator**

where:

x = Position (m)

t = Time (s)

= Damping Ratio

= Angular Frequency (rad/s)

**Damping Ratio**

where:

= Damping Ratio

c = Damping Coefficient

k = Spring Constant (N/m)

m = Mass (kg)

__Different Damped systems based on Q Factor__

__Different Damped systems based on Q Factor__

- A system with
**low quality factor**(*Q*<^{1}⁄_{2}) is said to be**overdamped**. Such a system doesn’t oscillate at all, but when displaced from its equilibrium steady-state output it returns to it by exponential decay, approaching the steady state value asymptotically. - A system with
**high quality factor**(*Q*>^{1}⁄_{2}) is said to be**underdamped**. Underdamped systems combine oscillation at a specific frequency with a decay of the amplitude of the signal. Underdamped systems with a low quality factor (a little above*Q*=^{1}⁄_{2}) may oscillate only once or a few times before dying out. - A system with an
**intermediate quality factor**(*Q*=^{1}⁄_{2}) is said to be**critically damped**. Like an overdamped system, the output does not oscillate, and does not overshoot its steady-state output

When choosing defining the Q factor for a system, it is common to opt for the highest level. In this way the optimum performance is normally achieved. However there are instances where lower levels of Q may be advantageous.

*I am currently pursuing my final year Btech in ECE at RSET, Cochin*

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The definitions are incorrectly defined here.

The correct ones are:

Damping factor ( represented by alpha or Xi) = R/2L

Damping ratio ( represented by zeta) = Damping Factor/ Resonant Frequency.

The formula that you have mentioned under Damping Factor is actually for Damping Ratio.

Kindly do the needful.

What are the units of electrical damped oscillator the quality R/2L ?