The definition of Q, along with some helpful advice
When one thinks of Q one thinks of that upper class British technocrat explaining how the latest weaponry gadget works, to a disinterested James Bond. Who, himself, is more interested in contemplating how to uncover his next female spy. If you want more of that, I am afraid you will have to go elsewhere. We are not here to discuss what might impede fact or fictional relationships, but rather to discuss the real and imaginary relationships of impedances. Q: initially stood for ‘Quality Factor’. This was due to the fact that it was first used to describe the energy storage properties of a circuit in relation to its energy dissipation properties.
Now it is just Q, a dimensionless number. In fact one must be careful not to refer to it as ‘quality factor’ especially around management types. One could just imagine Dilbert proudly telling ‘Pointy-Hair’ that he has just designed an amplifier circuit that has a very low quality factor and promptly getting fired! The next day, as if on a crusade, ‘Pointy-Hair’ starts putting up motivational posters all around the engineering building: ‘Increase the quality factor of your circuit by 100%’. It would become part of management review and a strategic goal… Stranger things have happened.
But where Q really comes into its own is in terms of bandwidth. If bandwidth is f2-f1 then:
Where f0 is the center frequency.
It is now obvious why we may want to design a circuit with a low Q. As we can see from the first equation (or elementary filter design rules) it will mean greater loss. However, for most circuits we want low Q.
(N.B. If we are talking about an element such as an inductor or capacitor we always want a high Q, as a low Q element would be indicative of parasitic resistance.)
Another useful way of looking at Q is on a Smith Chart.
The blue lines indicate a constant Q. If you want to have a circuit with a Q below a certain value, then you must ensure that the transformation does not go outside the Q circle.