Log Periodic Golden Ratio Coaxial Waveguide

[GRON]

This Documentation describes Open Hardware, and is licensed under the
CERN Open Hardware License.












Correction: Capacitor C1 should be in 1000pF range, 100.0-10,000pF, 15-30kV






All pairs of adjacent rings heterodyne in this manner. This image shows only one example.







This Documentation describes Open Hardware, and is licensed under the
CERN Open Hardware License.


More to follow.

[GRON]

Log Periodic Golden Ratio Coaxial Waveguide, Part II

This Documentation describes Open Hardware,
and is licensed under the CERN Open Hardware License


The Wave Articulation Matrix is composed of eight concentric cylinders of ferrous metal.
All eight cylinders have equal mass and equal surface area.



1. Let's assemble the next element around the last completed element.





2. Wrap dielectric material around until we have reached the diameter for the next conductor.





3. Wrap a rectangle of ferrous metal to form a cylinder. This unit was assembled using 0.002 inch-thick Stainless Steel foil, available from Grainger. Ensure that the metal forms a solid, conducting cylinder. Here, the metal is taped together with highly conductive carbon tape (the type used to mount samples in an SEM). If there is a gap between the ends of the metal, it will form a Split Ring Resonator (Parallel LC circuit for U.H.F) -- we do not want that.





4. Finish with a layer of dielectric material.







The envelope of the unit is a Hyperbolic Horn.





Method of Operation
The waveguide can be excited either magnetically or dielectrically. The dielectric method is as follows:

In the initial condition, the central conductor (cylinder zero) is connected to a 1000pF capacitor charged to 15-30kV. A flux of dielectric induction radiates out from this central cylinder in all directions. This flux induces a charge distribution in the surrounding cylinders (we shall call these the Parasitic Elements), and appears to pass through them. The flux is zero within these conductor.

When the triode fires, this flux collapses.

We are interested in the waves which are thus formed in the spaces between the Parasitic Elements.

Whether these are TE, TM, TEM, Longitudinal, or Standing Waves, let us hypothesize that their wavelengths are in some way proportional to the circumferences and/or lengths of the Parasitic Elements.

If this is the case, then when the waves of any two adjacent cylinders heterodyne, they will produce waves with wavelengths proportional to the next larger and smaller cylinders. This is because of the Golden Ratio Log Periodic geometry of the unit.


More to follow.

This Documentation describes Open Hardware, and is licensed under the CERN Open Hardware License

[Dave45]

wow how did I miss this thread
please continue

[MonsieurM]

thank you for sharing

looking forward to read more and learn more from this thread

[Michael John Nunnerley]

Nice

Looks good, but not sure about your half bridge driver, would be easier to use a half bridge driver chip

Mike

[GRON]

Thank you. Can you recommend a good one?

[GRON]

Derivation of the Geometry of the Structure

This documentation describes Open Hardware,
and is licensed under the CERN Open Hardware License



Let’s make a Golden Spiral.



Technically, a Golden Spiral grows by a factor of Phi every quarter cycle. Each quarter cycle, the amplitude multiplies by Phi.

Phi = The Golden Ratio = (1 + sqrt(5) )/2

Just to make things simple, let’s have our spiral grow by a factor of Phi each full cycle, instead of each quarter cycle.

Let’s also look at our spiral sideways, and allow it to exist in the dimension of time.



Each time the wave completes a cycle, the amplitude has multiplied by Phi.

The envelope of this wave is an Exponential Curve: Phi^x

Golden Spirals are found in many places in nature, where living things grow. This wave is experiencing Exponential Growth.

Can our wave grow in any other ways? Yes, its frequency can grow as well as its amplitude. Let’s have the frequency grow in the same way as the amplitude. Each time the wave completes one cycle, its frequency will grow by a factor of Phi. That is, each time the wave completes a cycle, its Period will divide by Phi.

Now what does this wave look like?



This wave is a very special wave. It is like a Golden Spiral within a Golden Spiral.

Because we have allowed the frequency to grow as well as the amplitude, the envelope of the wave is no longer an exponential curve. It is a Hyperbola.

An exponential curve can keep growing forever, and keep getting bigger and bigger. A Hyperbola, on the other hand, has an asymptote.





What does this mean?

It means this:

A wave whose amplitude grows like a Golden Spiral (Exponential curve), can continue growing forever, and always remain finite.

A wave whose amplitude *and frequency* both grow like Golden Spirals will have a Hyperbolic envelope, not an Exponential one. That means that the wave will achieve an infinite amplitude within a finite amount of time. The amount of time required to do this is equal to the period of the wave which initiated the growth process, plus Phi times that period.



The geometry of the Wave Articulation Matrix is shaped like this wave.





The wave can also be flipped around. Now it is a "chirp".







This documentation describes Open Hardware,
and is licensed under the CERN Open Hardware License

[Dave45]

Your waveguide is very interesting, have you done any testing you would be willing to share.

If a waveguide such as yours were inserted into a liquid dielectric and froze at full power would it continue to draw or focus energy when the prime mover was removed.

[Dave45]

Your dielectric version is cool but the magnetic version is intriguing are you using concentric coils?
It would seem a magnetic version would have a broader impact because of the compression caused by the magnetic field but this is your build I could be wrong.
Creating a waveguide seems more plausible that just pulsing a coil and hoping for the best.
It will be interesting to see where this goes ,
Thanks

[morpher44]

bashar STA thread

This is so weird to me. I was writing about this same idea, but
on a "cone" shaped coil.
You could wind several coils, each a PHI ratio of each other and
get them to self-oscillate and heterodyne.

I built two such coils on a cone, one at the hydrogen line,
and one a PHI ratio up the cone and a phi ratio frequency higher.
They both self oscillate. The tuning is a bit tricky.
I believe I spaced them too far apart for the transformer-mixing
effect to be most effective.
I have to re-think the geometry ... but
this idea is AWSOME.
100 monkeys indeed.

I had this idea after realizing the
Hubbard coils are phi ratios in order to
create "heterodyned" frequencies.

[GRON]

Right On

Right on. I believe that if you heterodyne two waves which are Golden Ratio to each other, you create many many sidebands, both higher and lower in frequency, all Golden Ratio to the next and previous in the sequence. Theoretically, you create a infinite number of sidebands.

If I am not mistaken, the Lakowski Multi-Wave Oscillator is a set of Split Ring Resonators which are all Golden Ratio to each other.





There are many structures, many ways to implement this principle.

[GRON]

Your dielectric version is cool but the magnetic version is intriguing are you using concentric coils?
It would seem a magnetic version would have a broader impact because of the compression caused by the magnetic field but this is your build I could be wrong.
Creating a waveguide seems more plausible that just pulsing a coil and hoping for the best.
It will be interesting to see where this goes ,
Thanks

There are no coils in this device.

[GRON]

Your waveguide is very interesting, have you done any testing you would be willing to share.

If a waveguide such as yours were inserted into a liquid dielectric and froze at full power would it continue to draw or focus energy when the prime mover was removed.

That is a very interesting question. I have no idea.

I will post data of initial experiments when they are complete.

[GRON]

Eric Dollard's Comments, Projective Geometry

I wrote a letter to Eric Dollard, showing him the WAM. He had many insightful things to say.

One of his suggestions was to look at the structure of the WAM in terms of Projective Geometry. Particularly, Rudolph Steiner (and George Adams') conception of Space and Counter-Space.



0. Euclidian Space has its points and lines on an Infinite Plane. Counter-Space has its planes enveloping and approaching a Point at Infinity.


1. Eric Dollard, in a letter to me:

[…]

Your Structure represents a TRANSFORMATION between two situations: the Infinite Plane, and the Point at Infinite Distance. See Rudolph Steiner, Projective Geometry.

[...]


2. Lawrence Edwards, from "The Vortex of Life: Nature's Patterns in Space and Time": pp. 22-24

Before going any further we must spend a short time considering the polar opposite qualities of space. George Adams' work on what he sometimes called positive and negative Euclidian space, or extensive and intensive space, was one of the outstanding contributions to the thought of our century. […]

As was pointed out earlier in this chapter, projective geometry sees the primary elements of space as being threefold -- point, line and plane -- and it has frequently been shown that the first and last of these stand in polar opposite relation to one another. If in any figure made up of points, lines, and planes, we interchange the functions of point and plane, we come upon a new figure which is in every respect the polar opposite of the first one, the lines playing a similar role in each of hem. And we find that the new figure is an inside-out equivalent of the first one.

It became an important task for George Adams to apply this process not to any particular figure, but to our concept of the whole of space itself. An observer in extensive space feels himself point-centered in the middle of his universe, and he looks out through the extent of space to an infinitude without -- the so-called Plane at Infinity of our ordinary projective textbooks. In intensive space he has to regard himself as a planar entity, in some sense a peripheral being, gazing inward to a point-centered infinitude, the infinitude within. In extensive space we find it convenient, and natural, to see our objects as being made up from points (atoms if you like) while the planes are formed from, and implied by, myriads of points. Whereas in intensive space the fundamental building blocks for our figures will be enveloping planes.

3. Me:

I hypothesize that the transformation from the Infinite Plane to the Point at Infinity, expressed as the Log Periodic Golden Ratio configuration of the WAM, can also be expressed as a Linear Algebra Matrix using homogenous coordinates. See:

algebra

It may then be possible to create other WAM configurations by first writing them as a transformation matrix, and then expressing this matrix as a three dimensional physical structure.


4. Me:

If you look at the WAM sideways, you will see a vortex with its bottom point at infinity. This is precisely the form taken by water when you stir it around to make a vortex.

Lawrence Edwards discusses this type of vortex on pages 164-167 of the above book.

[GRON]

New Wiring Diagrams

Attached to this post are the updated wiring diagrams.

Here are the notes:





ASSEMBLY NOTES


1. The Wave Articulation Matrix is composed of eight concentric cylinders of ferrous metal, such as iron, steel, or stainless steel.

2. All eight cylinders have equal mass and equal surface area.

3. The cylinders are whole circles -- they are not Split Ring Resonators. If a cylinder is made by rolling up a rectangle of metal foil, then the two meeting edges must be seam-welded, soldered, or connected with conductive glue.

4. The Wave Articulation Matrix can be described as a Log-Periodic structure, as in a "Log Periodic Antenna". The Log Base used here is the Golden Ratio.



(c) Creative Commons 2012-2013
This documentation describes Open Hardware, and is licensed under the CERN Open Hardware License, v1.1.






FIRING CIRCUIT OPERATION

1. Capacitor C1 is charged through resistor R1 by the High Voltage Supply.

2. Because WAM cylinder zero (the innermost cylinder) is connected to the high voltage side of capacitor C1, and cylinder seven (the outermost cylinder) is held at a low voltage, an Electric Field exists in the space between these two cylinders.

3. When the pulse generator causes the Triode to go into conduction, this Electric Field collapses, producing wave phenomena.

4. The WAM can be thought of as a wave guide. It has been suggested by Eric Dollard that it exists in the form of a Mode Changer. Not all waves will necessarily be TEM waves. It may be instructive to think of longitudinal waves as described by Tesla in his paper "On the Energy Dissipation of the Hertz Resonator", propagating in a vector orthagonal to the surface of the innermost cylinder. It may be most illuminating to conceive of the interference patterns of these waves as Standing Waves in space, like the standing waves on a transmission line when there is an impedance mismatch between source and load.

5. The pulse generator switches the Triode OFF, capacitor C1 charges up again, and the process repeats.




FIRING CIRCUIT NOTES

1. The Spark Gap is merely a safety mechanism. It acts like a blow-off valve. Its purpose is to protect the Triode from being damaged, should an excessively high voltage develop on cylinder zero for some reason. The electrodes of the spark gap should be separated at a distance such that it will not fire during normal operation, but will discharge the voltage on cylinder zero should it exceed the maximum rated plate voltage of the Triode.

2. The bottom of the innermost cylinder (cylinder zero) is connected to capacitor C1. The top of this cylinder is connected to the Triode or Switching Device.

2. Cylinders 1-6 provide the output of the device. They may be tied together electrically.

3. Cylinder seven (the outermost cylinder) is connected to +12V positive bias.

4. The cathode of the Triode is not grounded. It is positively biased at +12V.

5. Capacitor C1 should be a vacuum capacitor, to allow for the most rapid discharge.

6. It is desirable that the Triode or Switching Device switch from OFF to ON as quickly as possible (fast rise time). What we wish to achieve is the sudden, rapid collapse of a strong Electric Field.

7. The Switching Device does not have to be a Triode. Any high voltage, high speed switching device will be appropriate.

8. The WAM can be scaled to any size. However, for practical sizes (for example, lambda = 60 cm) the waves generated will be in the microwave range. Therefore, the length of any connecting wires becomes significant.

9. Values for R1 and C1 should be chosen such that the capacitor's Time Constant allows it to be fully recharged in between discharge pulses.

10. The Pulse Generator can be a square wave generator operating at approximately 1-2 MHz. It is generally recognized that the 1.995-2.000 MHz HAM band is used for Experimental work. These frequencies are available to any operator holding a General Class or higher HAM license.

11. It may be necessarry to insert a non-inductive resistor between the top of cylinder zero, and the plate of the triode, in order to prevent too much plate current from flowing.



(c) Creative Commons 2012-2013
This documentation describes Open Hardware, and is licensed under the CERN Open Hardware License v1.1.