# Q Factor and its Relevance in Electrical Circuits

By Jairam Sankar

33078

## 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)

where:

Q = Q Factor

= Damping Ratio

where:

x = Position (m)

t = Time (s)

= Damping Ratio

### Damping Ratio

where:

= Damping Ratio

c = Damping Coefficient

k = Spring Constant (N/m)

m = Mass (kg)

### Different Damped systems based on Q Factor

1. A system withlow quality factor (Q < 12) 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.
2. A system withhigh quality factor (Q > 12) 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 = 12) may oscillate only once or a few times before dying out.
3. A system with anintermediate quality factor (Q = 12) 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