Definitions of quality factor (Q)

As far as I learned,there are three different definitions about quality factor(Q)
1.Q=energy stored/average power dissipation
2.Q=f(center)/gap of f(-3db)
3.Q=ω/2σ, for a pole loated at σ+jω

My question is that ,since all these three definitions are for the same guy,they must have something in common,what is that?
and why do we use different definitions,is there some different thing among these three definitions?

Thanks very much for your help!

Re: Quality factor

pugongying said:

As far as I learned,there are three different definitions about quality factor(Q)
1.Q=energy stored/average power dissipation
2.Q=f(center)/gap of f(-3db)
3.Q=ω/2σ, for a pole loated at σ+jω

My question is that ,since all these three definitions are for the same guy,they must have something in common,what is that?
and why do we use different definitions,is there some different thing among these three definitions?

Thanks very much for your help!

Click to expand...

4.Q=f(center)/gap of f(7dB) of return loss if f(center) matched for maximum possible return loss.

(one of method to measure unloaded Q in ceramic resonator with only one port)

---

You can find couple of definitions of Q - not only three...

but all of then handle ratio of reactive storage energy compare to dissipation in network itself or/and tapped/coupled energy to other connected network.

for example:

Q = X / R (ratio of reactive impedance compare to real impedance) is implement of point 1 and for inductance with unwanted serie resistance can give Q = (L*2*PI*f)/R

you have loaded Q with respect to coupled other network as load, and unload Q with ratio of reactive part and resistive part in network itself (for example resonator)

Quality factor

xxargs:
Much thanks to your detailed answers
Regards,
pugongying

Quality factor

1 is the definition of the components.
2 is the for filter.
3 is for poles.

Re: Quality factor

Q is defined for the characteristic polynomial of second-order circuits:

1) s^2+2*a*s+wo^2=0

wd=(wo^2-a^2)^0.5

2) Q=wo/(2*a)

3) s^2+(wo/Q)*s+wo^2=0

All other formulas and 'definitions' for Q are based on the above one.

Re: Quality factor

quality factor means less resistive factor and more reactive factor.
as the Q factor is more the system is less lossy .