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
- A system withlow 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 withhigh 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 anintermediate 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
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 ?