Calculating Q of passive network

[uoficowboy]

Hi - is there a general scheme for calculating Q of a network of passives? I've seen a lot of techniques, but none that I really like. I would lik eto do this in a way that will result in a formula (ie so measuring off of a graph is probably out).

So one method for calculating Q is finding the SRF and then finding the half power frequencies on either side of that, and dividing the SRF by the frequency span between the two half power frequencies. This works well (ish) on a graph. But not so well in terms of formulas. Further, I'm not sure what is meant by half power. Does that mean half the power dissipation when presented with the same voltage? so, since P =V^2/R:

the full power point would be at P(srf) = V^2/Zsrf
The half power points would be at 0.5P(srf) = V^2/Zhalf
So the half power point would be where 1/Zsrf = 2/Zhalf (or Zhalf = 2*Zsrf)

Does that make sense? I guess really it should be |Zhalf| = 2*|Zsrf|, otherwise it often would be impossible to solve. Also, this only gives you Q as the SRF. It would be more useful to have a general equation for Q (with one parameter of that equation being frequency), not just a SRF Q.

But Q is also given as 2 * pi * peak energy stored/[energy lost (per cycle)]. Solving that becomes extra nasty, as you have to figure out (unless I'm missing something) the solution to a differential equation. I tried doing this for a simple RLC circuit and was able to get the standard definition of Q, but it was a significant effort.

Wikipedia talks about finding Qs of individual components, and then combining them, here: https://en.wikipedia.org/wiki/Q_factor#Individual_reactive_components. The Q of an individual component is X/R, and then you combine them with 1/(1/QL+1/QC) however I suspect that that is a method of calculation that only works for specific circuits - just circuits with one inductor and one capacitor. Or maybe not? I'm not sure. I do not know how a series R driving a paralleled L and C would be calculated using that formula.

I would love some help with this as I'm pretty confused. I'm not trying to solve a specific problem, by the way, more just trying to understand the proper method of solving it.

Thanks!!

 

[FvM]

Some thoughts in this previous thread https://www.edaboard.com/threads/128004/

 

[uoficowboy]

Some thoughts in this previous thread https://www.edaboard.com/threads/128004/

Hi FvM - unfortunately I did not find an answer useful to me in that thread.

I found this paper: http://ve2azx.net/technical/QEXaudet-Rev1.pdf that gives a formula of (w/(2R)) * (dX/dw + |X|/w) for the Q of an RLC network, but I believe it is only correct for series resonant systems.

Ideally I would like a method of taking a Z and calculating a Q from that. Is that just not possible? Do you have to know the actual components in the network, and not just the impedance?

 

[FvM]

Hi FvM - unfortunately I did not find an answer useful to me in that thread.

I didn't expect that the thread answers your question. It rather problematizes the question. Under which prerequisites can we define a quality factor (or possible multiple Q values). Is there an unique definition of Q factor at all?

In my view, the (quite interesting) paper is referring to a special case of Q-factor calculation, a distributed resonator with distinct modes, e.g. a cable or an antenna. I'm not able to recognize a generalized approach that could be applied to different kinds of passive networks.

In the analysis of filters, a Q value is assigned to each complex pole pair, it represents the angular position of the pole pair.
Seee: https://www.edaboard.com/threads/164378/#post694250

Although the multiple pole Qs can be extracted from the transfer function, they don't show visually in the filter transfer function. Determinig half power points won't arrive at a set of multiple Q values.