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### Author Topic: standing wave coil frequency  (Read 29585 times)

#### Montec

• Newbie
• Posts: 34
##### standing wave coil frequency
« on: March 22, 2011, 05:11:11 AM »
Hello all
After reading about "slow wave" traveling wave tubes for high frequency amplification I came up with the following equations.

f = (.9c/Lc)sin(acrtan(P/D))  where

.9c is the speed of light within a insulated copper wire. This will vary because the speed is influenced by changes in the permittivity around the wire. Your hand, etc.

Lc = length of the coil (or a toroid's major radius circumference)

P = Pitch of coil - distance between adjacent coils Controls the "slow wave" speed in the coil.

D = Diameter of coil

Lw/N = P/Sin(a)   where

Lw = length of straight wire used to make coil

N = number of turns on the coil

a = arctan(P/D)

Sin(a) = Lc/Lw

Lc = (lamda)sin(a) where "lamda" is the "free space" wavelength.

Have fun

#### Free Energy | searching for free energy and discussing free energy

##### standing wave coil frequency
« on: March 22, 2011, 05:11:11 AM »

#### Montec

• Newbie
• Posts: 34
##### Re: standing wave coil frequency
« Reply #1 on: March 25, 2011, 10:14:56 PM »
Hello all
As a corollary to the above post I looked into skin effect. The general rule of thumb is that that the skin effect should be more than 1/4 of the wire diameter. This works out for copper to be:

f = 0.06987/d2  where "d" is the diameter of the wire in meters (m)

So for 20 Gage (0.8128mm) wire the maximum frequency is approximately 105KHz and

for 48 Gage (0.0315mm) wire the maximum frequency is approximately 70MHz.

Looks like Litz wire is the way to go when driving a circuit at higher frequencies to avoid higher resistance and heating problems.

#### stevenfrank38

• Newbie
• Posts: 3
##### Re: standing wave coil frequency
« Reply #2 on: April 03, 2011, 11:15:17 PM »
lol
by the way you do a outstanding job
I think This kinds of work is very impotent for refereeing the mind
And you have done it well
I think you should do this kinds of work more and more
thank you very much

#### Free Energy | searching for free energy and discussing free energy

##### Re: standing wave coil frequency
« Reply #2 on: April 03, 2011, 11:15:17 PM »

#### MrMag

• Hero Member
• Posts: 754
##### Re: standing wave coil frequency
« Reply #3 on: April 04, 2011, 01:14:12 AM »
I agree, thank-you Montec

#### Montec

• Newbie
• Posts: 34
##### Re: standing wave coil frequency
« Reply #4 on: April 04, 2011, 07:08:23 PM »
Hello all
The approximate inductance (L) of a toroidal coil can be calculated by the following.

L = Î¼oÎ¼rr2N2/D

Î¼o = permeability of space = 0.000001256636  or 4Ï€-7 (4"pi"-7)

Î¼r = relative permeability of toroidal core  (air = 1, other ferromagnetic cores will be based on core alloy)

r = radius of toroid minor axis (what you wind the wire around) plus 1/2 the wire diameter , both in (m)

N = number of turns (wraps around minor axis)

D = diameter of major axis (distance across toroid, center to center of minor axis) in (m)

A formula derived from the above is:

L = Î¼oÎ¼rNA/P  (Somewhat more useful)

A = area across the minor axis in (m2) (Ï€r2 of coil cross section)

P = pitch of coil winding (distance between wraps at major axis center line) in (m)

This shows that coil inductance is directly related to the number of turns and area within the turn. But is indirectly related (inverse) to the pitch of the coil. A multi- layer coil increases "N"  and "r" is then an averaged layer-radius of the coil.

The inductance of a coil allows the calculation of reactance (resistance) at a desired operating frequency. So a high frequency transformer needs less wire to act as resistance at an operating frequency. This keeps the current flow within the specs for the wire.

@ stevenfrank38, MrMag
Thanks for the encouragement.

#### Free Energy | searching for free energy and discussing free energy

##### Re: standing wave coil frequency
« Reply #4 on: April 04, 2011, 07:08:23 PM »

#### Montec

• Newbie
• Posts: 34
##### Re: standing wave coil frequency
« Reply #5 on: April 21, 2011, 07:21:32 PM »
Hello all
Here are some simple equations for designing a compact "resonant" toroid.

TR = D1/D2 = 1 + 2d/x  (Toroid ratio between major and minor diameters)

D1 = Major diameter

D2 = Minor diameter

d = diameter of wire

x = distance between wire loops on the outside of the toroid  ( I assume x < d for a TR > 3  will make for a better coil )

D1 = TR/Ï€âˆš(dLw/(TR-1))  (âˆš = square root, Ï€ = "pi") This single layer toroid approximation is valid when D2 >> d.

Lw = length of wire used to wrap the toroid = .9C/fc
C = speed of light
fc = designed frequency of the toroid.

D2 = D1/TR

N = Ï€(D1 - D2)/d  Number of loops

P = d(TR/(TR-1) Average pitch for the toroid

fc = (.9c/Lw)sin(acrtan(P/Ï€D2))

Nn-Nn+1 = 2Ï€  The difference between loop counts (N) where "d" remains constant for a multilayer (n) toroid.

Corrections for a previous post.  (need that "pi" in there)

f = (.9c/Lc)sin(acrtan(P/Ï€D))
a = arctan(P/Ï€D)

#### Magluvin

• Hero Member
• Posts: 5832
##### Re: standing wave coil frequency
« Reply #6 on: April 22, 2011, 03:13:42 AM »
I like pi.

Thanks for the info. very useful.

Came up with an idea to use(home made) ferrofluid as a core material. The core shell can be made so the fluids can be changed to easily experiment with different materials and mixtures. Would be a real time saver, along with only having to wind it 1 time.  ;]  Just thoughts

Mags

#### Free Energy | searching for free energy and discussing free energy

##### Re: standing wave coil frequency
« Reply #6 on: April 22, 2011, 03:13:42 AM »

#### Montec

• Newbie
• Posts: 34
##### Re: standing wave coil frequency
« Reply #7 on: April 22, 2011, 07:01:18 AM »
Hello Magluvin

A TR ratio of "pi" or 2"pi" has crossed my mind.

#### Montec

• Newbie
• Posts: 34
##### Re: standing wave coil frequency
« Reply #8 on: April 23, 2011, 07:39:11 AM »
Hello all
Here are some more equations that deal with "slow" waves in coils

Vp = Csin(Ó©)  Slow wave velocity in a coil

C = Speed of light
D2 = Coil diameter
P = pitch of coil winding

Some other equations for Vp

Vp â‰ˆ Î¼oÎ¼rCND2/4L  An approximate value for Vp.

Î¼o = permeability of space = 0.000001256636  or 4Ï€-7 (4"pi"-7)

Î¼r = relative permeability of core

N = number of turns

L = coil inductance  This may vary along the length of the coil by winding a non-uniform coil. (Or by placing magnets when using a ferromagnetic core)

Vp â‰ˆ CD2P/4A       Another approximation

A = Ï€D2   Area within the coil loop.

Now the big question is what happens when you have two "slow" waves traveling in the opposite directions within the same space.
Time for some experimentation it seems.

#### Free Energy | searching for free energy and discussing free energy

##### Re: standing wave coil frequency
« Reply #8 on: April 23, 2011, 07:39:11 AM »

#### Montec

• Newbie
• Posts: 34
##### Re: standing wave coil frequency
« Reply #9 on: April 24, 2011, 08:25:08 PM »
Hello all

I should also add that the inductance of coil A can be changed by shorting a contra-wound coil B. (I have measured this with an induction meter.)

#### gyulasun

• Hero Member
• Posts: 4063
##### Re: standing wave coil frequency
« Reply #10 on: April 24, 2011, 09:11:10 PM »
Hello all

I should also add that the inductance of coil A can be changed by shorting a contra-wound coil B. (I have measured this with an induction meter.)

Yes but my understanding in that case is that you waste power by using up some part of the magnetic flux for "heating" the counterwound coil wire.

#### Free Energy | searching for free energy and discussing free energy

##### Re: standing wave coil frequency
« Reply #10 on: April 24, 2011, 09:11:10 PM »

#### Montec

• Newbie
• Posts: 34
##### Re: standing wave coil frequency
« Reply #11 on: April 24, 2011, 10:27:48 PM »
Hello gyulasun

Yes but my understanding in that case is that you waste power by using up some part of the magnetic flux for "heating" the counterwound coil wire.

True, but speaking in Amp-turns you could change the inductance of a 10 amp 100 turn coil with a 1 amp 1000 turn coil; or change the resonant frequency of a tank circuit with just a switch (or modulate the tank circuit with an electronic switch).

#### Montec

• Newbie
• Posts: 34
##### Re: standing wave coil frequency
« Reply #12 on: December 27, 2011, 09:31:59 PM »
Hello and Happy Holidays to all

"Slow" wave or Phase coupling between two air coils can be accomplished by matching the phase velocity (Vp) of the coils. This will maximize the coupling. Basically you are just matching the ratio of the pitch and coil diameter.
P1 = Pitch of coil 1 (Distance between adjacent loops in the coil)
D1= Diameter of coil 1
P2 = Pitch of coil 2.
D2 = Diameter of coil 2.
Then
P1/D1 = P2/D2

Since P1/D1 is (when looking at a right triangle) the tangent (opposite over adjacent) of the acute angle then Vp = CsinÓ¨ = Csin(arctan(P1/Ï€D1))
where
Vp = Phase velocity of the signal within the coil
C = Speed of light
Ó¨ = Acute angle

When using two wires of different gages (wire diameter) then the gage of the wire can replace the pitch in the above equation if the coil is wound tightly.
G1 = gage of wire 1
G2 = gage of wire 2
then
D1 = G1((G2+G1)/(G2-G1)) Diameter of coil 1
D2 = G2((G2+G1)/(G2-G1)) Diameter of coil 2

The diameter of the form used to wind the inside coil is
D = G1((G2+G1)/(G2-G1) - 1)

A thin layer of tape may be used to separate the inside and outside coils, or they may be contra-wound.

#### Tito L. Oracion

• Hero Member
• Posts: 2203
##### Re: standing wave coil frequency
« Reply #13 on: December 28, 2011, 12:27:30 AM »
Hi good day

But This is what Tesla said:
â€œToday's scientists have substituted mathematics for experiments, and they wander off through equation after
equation, and eventually build a structure which has no relation to reality.â€

But still the formula of the vibration is missing.

At least your a scientist . joke

But i believe you a little

#### verpies

• Hero Member
• Posts: 3464
##### Re: standing wave coil frequency
« Reply #14 on: December 31, 2011, 04:18:55 PM »
Yes but my understanding in that case is that you waste power by using up some part of the magnetic flux for "heating" the counterwound coil wire.

If the counterwound coil is shorted by a capacitor than this capacitor will give back the energy induced in that coil during the next quarter of the cycle.  The resistive RI^2 losses in that coil do not have to be high if the induced current is low and voltage is proportionally high (this is the same voltage that appears across that shorting capacitor).