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"Q"

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What is Q?

"Q" is a most important property of both capacitors and inductors although it is actually dimensionless. The "Q" of capacitors is generally so high as to be ignored however it is the "Q" of inductors we mainly concern ourselves with. All inductors exhibit some extra resistance to ac or rf, "Q" is the reactance of the inductor divided by this ac or rf resistance plus the dc resistance of the windings.

The formula for "Q" is Q = (2 * pi * f * L) / R

This factor "Q" largely determines the sharpness of resonant circuits. The actual resistance of wire to ac or rf is often far greater than the dc resitance. At lower rf frequencies up to about 1 Mhz this is due to the "skin effect" where the actual rf travels on the outside perimeter of the wire.

At lower frequencies say at 500 Khz, the "Q" is materially improved by using Litz wire to reduce rf resistance. Litz wire is "bunched" wire strands of almost minute wire size. One extreme example I know of is 220 strands of #44 wire (each strand 2 mils or .002" dia) wound on a T130-2 toroid to produce an extremely high "Q" of over 500 at 250 Khz. That's unloaded Q or Qu.

Now #44 wire has a cross sectional area of 3.1416 mils squared. With 220 strands the total cross sectional area is 691 mils squared or about 30 mils dia. The nearest equivalent wire size for a similar cross sectional area is #20 wire. Had the toroid been wound with the same number of turns of the #20 wire the inductance would probably have been about the same but the "Q" would certainly been far, far less. Why? Skin effect!

Skin effect and Q

Consider this for the purposes of understanding "skin effect". The perimeter of a circle is pi * dia. So for #20 wire which is 32 mils but the above equivalent was 30 mils (these are all thousandths of an inch). That produces a total perimeter for the rf to travel on of pi * dia = 94 mils. On the other hand we said #44 has a dia. of just 2 mils and that's just 6.2832 mils of perimeter but, multiplied 220 times it's 1382 mils instead of 94 mils. A 14 fold improvement. That's why they use Litz wire to vastly improve "Q". Beyond 2 Mhz the effect becomes much less noticeable to almost negligible.

The net result of skin effect is a net decrease in the cross sectional area of the conductor and a consequent  increase in the rf resistance. Consult the references I have suggested you read for a more detailed and informed discussion on this very important topic.

In particular I would recommend RF Circuit Design - Chris Bowick - Sams.

Why is Q so important?

When and if you ever get to our popular tutorials on LC filters, you will learn that the bandwidth of filters is determined principally by loaded Q. A limitation on the design Q is the available inductor Q or unloaded Qu. Usually the design Q can not exceed about one-fifth of the available inductor Q otherwise circuit losses become totally prohibitive.

If you have a typical inductor Q of say 100 then the loaded Q is going to be 20. The filter bandwidth will be the centre frequency, Fo divided by 20. At 7.0 Mhz that's 350 Khz wide. At lower frequencies such as 455 Khz it would be 22 Khz! although there we could use active filtering for LC filters or more likely amplifier tuned circuit filtering. Also see IF Amplifier Filters, that's how IF transformers were often designed in the days before crystal filters and ceramic filters.

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Related topics on "Q"

capacitance

current

impedance

inductance

LC filters

reactance

resonance

voltage

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