Tesla's transmission waveguide equations

[uep57]

 I comment here for transmission lines is a wide known theme for electrical-electronic  engineers, is wide known the common transmission lines have a propagation speed less than speed light, however there is other special transmission line is missing in common circuits theory can have propagation speed too much greater than light speed without limits and the more greater you want, that's the Nikola Tesla transmission line, or analog computers as named in other terms, and I wait this can help to free energy designers, however I start showing the common transmission line and the equations get the maximal propagation of the wave you can get in too much books or google, however you must understand this for understand the Tesla's setup, first we have a line can to have any geometry, 2 parallel wires, coaxial, etc,...that line have series inductance and parallel capacity and you can see it as infinite capacitors and infinite inductors , for know inductance and capacity at any distance you must measure the total series inductance Ls and total parallel capacity Cp of the line and divide by the total length of the line, let L = Ls/s, C = Cp/s, where s is the total length of the line, so in any dx segment of the line you have Cdx capacity and Ldx inductance. The following is take a differential segment of the line and write the equations , solve it and know all the properties of this waves, however as you can see in the attached image is not needed solve the wave equation for get the propagation speed, just divide both equations for get dx/dt and the maximal propagation speed , and, as you can see the limit is the light speed in vacuum, er is the relative dielectric permittivity of the insulation media. This wave is known as a transverse wave has electrical and magnetical fields at 90º of space phase shift and 90º of time phase shift as you can deduce from this equations, this is the artificial waveguide made for the man and not as the nature propagates electricity, artificial as the Hertz experiment where sender and receiver are magnetically coupled as a wireless transformer
The Nikola Tesla's transmission line is the  opposite case of the classical line, is the way the nature propagate electricity in storms  using the Schumman resonant cavity Earth-Ionosphere or the way telecommunications can be made by capacitive coupling between antennas, this transmission line  has series capacity and parallel inductance, this line is missing in the classical text books of transmission lines and if you google for some web sites you will find this line in too much experiments and practical setups but is missing the math can proof its amazing properties, first as in the case of the common line we must get its parameters of capacity and inductance for a differential segment dx, now all is opposite, the total series capacity C must be divided by the number of total capacitors for get capacity in a dx segment, is C * N, but N = s/dx, where s is the total length of the line, the same for the inductance in a dx segment will be L * N = L * s/dx. Then we can write the equations of this new differential circuit and as you can see in the image there is another equations, the wave equation is a partial derivate of fourth order and according to math can be reduced to  4 first order equations of first order and get 4 propagation speeds, 2 real and 2 complex phase conjugates, however here we calculate the positive real speed. In this case is not easy get the propagation speed without solve the wave equation, so we can think one particular solution  I(x,t) = Imax * Sin(kx – wt) imposes the condition I(0,0)=0 A and a sine waveform, replacing in the main equation we get some relations of the parameters, other condition is in the load: I(s,0) =0 imposes there is not load and output terminals are open, then we have all the solved parameters for get in that conditions the maximal propagation speed vp is shown at the end and as you can see this propagation speed "increases with the length" of the line as if this line was a "wave accelerator", so here is open the option not only the wave can get a speed more greater than light speed, as L and C have tendence to zero the speed of the wave have tendence to infinite, for example if the line have a length of 1 meter, total series capacity of 1 pf, total parallel inductance of 0.1 nHy we get : vp= 34c, 10 meter of the same line will get : vp =340c.This wave is known as longitudinal waves  have properties you can deduce from this equations are the electrical and magnetical fields have the same time phase shift violates the Faraday principle and too much other amazing properties of this waves you can deduce from this math.

[uep57]

This is a video I've made on the same theme, there is some words in spanish you can translate

https://www.youtube.com/watch?v=aKX13NFZMic

Regards

[uep57]

This is the english version of the video

https://youtu.be/zZ-EFwdV49o

Bye

[Void]

Thank you. That is very interesting indeed!

[AlienGrey]

This is the english version of the video

https://youtu.be/zZ-EFwdV49o

Bye

so now you have found that complicated video what are you going to d ith it ?