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

Started by June 20, 2008
```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 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?
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?
And, how can C be calculated?
For inductance L I have found some useful information, but for the others
not yet...

Any suggestions? Thanks for your time,

Arthur C.

```
```"Arthur Cretin "

>I want to make a simple coil (inductor) with a Q value as high as possible.

** Air cored or not   ??

You are one colossal ASS for not saying so straight off.

.....  Phil

```
```"Phil Allison" <philallison@tpg.com.au> wrote in message
news:6c1mu0F3e5ktsU1@mid.individual.net...
>
> "Arthur Cretin "
>
> >I want to make a simple coil (inductor) with a Q value as high as
possible.
>
>
> ** Air cored or not   ??
>
> You are one colossal ASS for not saying so straight off.

Thanks for the compliment. Return to sender, and take a wild guess. Or, if
you only have comments no more useful than this, I suggest you let your
frustration out somewhere else...

Arthur

>
>
>
> .....  Phil
>
>

```
```"Arthur C." <nospam@nospam.sorry.com> wrote in message
news:485b86ff\$0\$14348\$e4fe514c@news.xs4all.nl...
> 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 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?
> 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?
> And, how can C be calculated?
> For inductance L I have found some useful information, but for the others
> not yet...
>
>
> Any suggestions? Thanks for your time,
>
> Arthur C.

To maximize Q, the wire should be a short as possible.

In general air core coils will have a higher Q than those with magnetic
materials. But the core material depends on the frequency range consistent
with the short statement. High inductance is not feasible in air core coils.

Wire should be litz wire made up of multiple strands of thin wire insulated
from each other. Especially true at 1MHz

High power, high frequency coils can be solid wire or tubing. 30MHz up.

To minimize winding capacitance, wire should be lace wound, layered back and
forth to minimize the proximity of one turn to the next. Necessary for High
Q at 1 MHz

The models of an inductor is the inductance in series with the resistance
and shunted by the stray capacitance. Below self resonance, the Q = Xl/R.
But, the R is the AC resistance of the wire at frequency, not the DC
resistance. At one MHz this value is much higher than the DC resistance
because of skin effect. That's the reason for Litz wire.

Lace winding is best done on a coil winding machine. It's probably a good
idea to go buy the inductor you need.

```
```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
```
```"Arthur C." <nospam@nospam.sorry.com> wrote in message
news:485b86ff\$0\$14348\$e4fe514c@news.xs4all.nl...
> 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 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?
> 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?
> And, how can C be calculated?
> For inductance L I have found some useful information, but for the others
> not yet...
>
>
> Any suggestions? Thanks for your time,
>
> Arthur C.
>
Look at his "LC experiments" series at http://www.crystal-radio.eu/
It's a  tour-de-force on achieving  ridiculously high Q values.

```
```
> Arthur C. wrote:
>> I want to make a simple coil (inductor) with a Q value as high as
>>  >>possible.

Can you tell us what the use of the inductor is?

Is there a maximum length and diameter your limited to?

What is the inductance your looking for?

> 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.
>
Well said John.
Mike

```
```"john jardine" <john.jardine@idnet.co.uk> wrote in message
news:IYP6k.180962\$pm2.115964@en-nntp-04.dc1.easynews.com...
> Look at his "LC experiments" series at http://www.crystal-radio.eu/
> It's a  tour-de-force on achieving  ridiculously high Q values.

Wow, that's impressive!

```
``` "Arthur Cretin "
>>
>> >I want to make a simple coil (inductor) with a Q value as high as
> possible.
>>
>>
>> ** Air cored or not   ??
>>
>> You are one colossal ASS for not saying so straight off.
>
> Thanks for the compliment. Return to sender, and take a wild guess.

**  Go get fucked you asinine,   TROLLING  POS  !!

...  Phil

```
```"Bob Eld"

> To maximize Q, the wire should be a short as possible.
>

** Huh  ??

> In general air core coils will have a higher Q than those with magnetic
> materials.

** Double huh   ??

Magnetic cores increase L while leaving R and stray C the same

......  Phil

```