Re: How to optimize parameters for making a coil with high-Q?

Arthur C. wrote:
I want to make a simple coil (inductor) with a Q value as high as possible.
Now, I would like to know if there are simple guidelines on how to choose
the parameters to obtain this. Parameters are:

- thickness of the wire
- number of rounds
- length of the coil
- area of cross-section

I assume you are talking about an air core coil. Things get even more involved when you include a high permeable core material, but higher Q is often possible in a smaller volume with a core.

Also, I assume you are talking about a lumped inductor, where the length of the wire is very short compared to the signal wavelength (this implies that the current is instantaneously the same in every part of the wire). Otherwise, the effective inductance involves waves reflecting back and forth along the wire.

I understand that a realistic description of a coil involves (at least) a
parallel parasitic capacitance C and a series resistance R.
The resulting Q value would then be Q = (1/R) sqrt (L/C). Is this indeed the
relevant expression for Q?

Only if you are using the inductor as a self resonant system, since that is the formula for the Q of a resonance. If you use the inductor well below its self resonant frequency, the effect of the stray capacitance is to just reduce the total inductance a bit, and the formula for Q is more closely, Q=w*L/R, where w (omega or frequency in radians per second) is 2*pi*frequency in hertz.

If the coil is operated at a frequency of the order 1 MHz, can we assume for
R just the 'DC' series resistance of the wire, or does it change with
frequency?

Unfortunately, it is not so simple. Any time the magnitude or direction of magnetic flux penetrating a conductive material changes, a current is induced to circulate around that changing flux. The magnetic field produced by that circulating (eddy) current bucks the field that is causing the flux to change, slowing the change. The effect in wire is that the current first changes along the surface, and those changes sink into the conductor over time. This "skin effect" causes the current to use less than the full cross section of the wire, raising the effective AC resistance above the DC resistance (which produces no changing flux).
http://en.wikipedia.org/wiki/Skin_effect
At 1 MHz, the effective conductor depth is only 66 um, so wire that is progressively more than twice that distance in diameter has progressively higher AC resistance than its DC resistance.

This wire table:
http://www.pupman.com/listarchives/1998/April/msg00222.html
shows dimensions of AWG sizes. AWG 35 wire has a diameter of 0.143 mm, or 132 um, so any wire larger than about that size wastes progressively more of its cross section as far as its resistance at 1 MHz. This is why high Q RF coils are often made with Litz wire, a woven bundle of fine, insulated strands.

And, how can C be calculated?

Not simply. Either you find an empirical formula for the winding style you are using (i.e. uniformly spaced, straight, single layer solenoid) that someone else has produced, or you use a finite element analysis program that models the surface of the winding to approximate the effective capacitance. Or you make a series of variations and measure their properties at several frequencies and calculate the lumped capacitance resistance and inductance that best fits those measurements.

For inductance L I have found some useful information, but for the others
not yet...


Any suggestions? Thanks for your time,

Google will find you lots of good references, probably starting with:
http://en.wikipedia.org/wiki/Inductor

The subtlety of inductors has kept me entertained for years and years, so don't feel too bad, if you don't answer every question in an afternoon.

--
Regards,

John Popelish
.