# Theoretically determining Q for an inductor

I've recently been looking into passive filter design a little more closely than my classes have gone into, so far as actual component selection and design are concerned. The biggest sticking point for me has been understanding how to gauge Q, specifically for hand wound toroidal inductors.

I understand Q is the reactance over the resistance, and is only valid for a specific frequency. The reactance is a fairly simple equation for a toroid, but I can't seem to find any discussion of how to determine R. All sites that I've found talking about inductors and Q factor only mention that it's a complicated value that has to take into account skin depth, eddy currents and hysteresis losses, but there is never any way given to estimate it nor is any method discussed so far as I've seen. All the responses here to similar questions unilaterally say to refer to the datasheet, but with a hand wound inductor, those are in short supply.

Furthermore, how much Q do I need for an inductor in a filter? From what I've seen higher Q leads to more efficiency, but how much Q is enough to provide acceptable losses?

There are two aspects to be considered: Determination of the actual Q value for the inductor and the influence of finite Q on filter performance.

• Q can be determined by finding the quality factor Q for a tank circuit consisting of the corresponding L and a parallel capacitor C. This capacitor must be selected with respect to the desired frequency (identical to the resulting resonant frequency). Assuming a high-Q capacitor (best quality) the resulting Q of the tank circuit is approximately equal to the inductor Q.
• Knowing this Q value it is, in principle, possible to take this Q value (resp. the corresponding loss resistance) into account during design of a filter circuit. However, in this case, no standard formulas can be used. That means, you have to derive the design formulas from the circuit.

However, the decision if the finite Q value must be taken into account (or not) must be made with respect to other uncertainties within the whole circuit (in particular, tolerances of the other parts).

Here's the frequency response of an LCR low pass filter: -

Between a Q of 0.7 and a Q of 1 the filter can be said to be maximally flat up to about 2kHz and this makes a nice audio cross over circuit. So do you really want to maximize the Q of the inductor?

On the other hand, using a high Q inductor can give you the opportunity of making a very high resonant peak in the frequency response and, if you are filtering the output of a musical synthesizer this might produce a nice dramatic effect.

How long is a pice of string? What do you want to do or achieve?

• I'm actually analyzing a ham radio design and low pass filter after the pa stage. I'm trying to understand what the design is optimizing for. Commented Nov 28, 2015 at 20:56