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# Design of helical resonator

## Design of helical resonator

(OP)
I am designing an rf coil/helical resonator that wraps around a quartz tube used to create a plasma from gas flowing through the tube. I am copying an old coil design which has the following parameters: 1.5" diameter, 5.775" height, and 28 turns made from 0.08" diameter silver wire. The signal fed to the coil is 45MHz and 12.5W. The coil I am designing is for the same type of application, but needs to be about 6" diameter and 7" height. My question is how does this change in size affect the frequency, power, number of turns, diameter of wire, and length of the coil? Thanks in advance for the help.

### RE: Design of helical resonator

The formula for the inductance of a coil is:

L (uH) = ( (d^2)*(n^2))/(18*d + 40*l)  where d is the diameter, n is the number of turns, and l is the length

Your old coil had an inductance of about 6.84 uH. For your new coil to have a similar inductance, you need around 8.5 turns. No guarantees on my math.

The inductor is probably part of a resonant L/C circuit at 45 MHz. Since the parasitic capacitance of the new inductor will be slightly different, you may need to spread or compress the new coil slightly to achieve the same resonant frequency.

Wire size mainly affects the Q of the inductor. The same diameter wire for the new inductor will probably be fine. Silver plated wire resist corrosion, and silver oxide conducts which is why is is frequently used.

### RE: Design of helical resonator

What the Comcokid said and one more thing.

At 45 MHz, the skin effect comes into play in a relatively large way.  Silver plating will increase the Q of the inductor because of the lower resistance of the silver (or silver oxide).

For example: at 60 HZ, the skin depth in copper is 8.57mm.
At 10 KHz it is .66mm and at 10 MHz it is 21um.

I remain,

The Old Soldering Gunslinger

### RE: Design of helical resonator

I am not so sure that you guys are giving him good advice.  He is building an induction heater to energize his gas.  In microwave terms, that is like strapping a resistor across the coil.  Why should he worry about the Q of the coil, he is deliberately loading the coil so it has a very low "loaded" Q.  I think a coil made out of something like plain old 1/4" diameter copper tubing  or some solid 10# wire would be fine.

### RE: Design of helical resonator

(OP)
Thank you to all for your responses.

My new 'first draft' design has the following parameters: coil diameter is 6.25", height 7.055", 8.5 turns, 0.08" diameter silver wire, which means the length of the wire will be approximately 168". Two things I did not mention in my first post: the wavelength of the coil needs to be half a wavelength, which would put my new design at 35MHz, and secondly, the coil will have a shield around it, so it acts as a coaxial resonator. The shield in my new design would be 12.02" in diameter and 13.055" in length. The plasma that is being generated is for coating purposes. Both ends of the coil are grounded, and the rf signal is fed into one of the turns. Does anyone know if changing the frequency from 45MHz to 35MHz is going to effect the plasma generation. If so, how and why? Also, I read that the old coil had to be fed by a 12ft bnc cable for 45MHz. Does anyone know why it was important that it be 12ft at that frequency? Thanks for your help.

### RE: Design of helical resonator

Geami,
The cable length may just be for convenience. But if they said the exactly 12 feet must be used, then it may be a VSWR matching technique. Two mismatches can be cancelled at one frequency by changing the length of a cable connecting them, just a guess though.
kchiggins

### RE: Design of helical resonator

Hi Geami,

I think that there is some kind of missunderstanding:
1.) your "coil" is no coil anymore since as you said, it is a lambda-half resonator, therefore you can`t estimate the inductance with the simple formula above.
2.) dimensioning a helical resonator (or to be more precise a coaxial transmission line with helical inner conductor) as a half wavelength resonator you have to determine the so called compression "kompression factor" helical transmission line and therefore the electrical length at your desired frequency. There are aprox. formulas around (look for helical transmission line).
3.) Knowing that 180degree electrical length is lambda half your can estimate the length of the helix.
4.) matching the coil to the load can be done either inductive, capacitive or galvanic - the ladder is what you described. So use a network analyser or a reflection bridge to match your resonator to the source. Just play a little bit with the position of the coupling - it should be not too sensitive!
5.) tune your resonator by slinghtly bending and cuting the helix
6.) done!

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