standing wave coil frequency

[Montec]

Hello all
Here are some simple equations for designing a compact "resonant" toroid.

     T_R = 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 T_R > 3  will make for a better coil )

    D₁ = T_R/π√(dL_w/(T_R-1))  (√ = square root, Ï€ = "pi") This single layer toroid approximation is valid when D₂ >> d.

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

    D₂ = D₁/T_R

    N = Ï€(D₁ - D₂)/d  Number of loops

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

    f_c = (.9c/L_w)sin(acrtan(P/Ï€D₂))

    N_n-N_n+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]

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

[Montec]

Hello Magluvin

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

[Montec]

Hello all
Here are some more equations that deal with "slow" waves in coils

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

         C = Speed of light
         Ó© = "theta" =  arctan(P/Ï€D₂)
         D₂ = Coil diameter
         P = pitch of coil winding

Some other equations for V_p

    V_p ≈ μ_oμ_rCND₂/4L  An approximate value for V_p.

         Î¼_o = permeability of space = 0.000001256636  or 4Ï€-7 (4"pi"-7)

         Î¼_r = 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)

     V_p ≈ 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.

[Montec]

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.)