Wave Articulation Matrix Sean Logan KG7ARW

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Orientation of Structure and FET with respect to Power Supply Polarity

Parameters for COMSOL Simulation

Cylinders as quarter-wave resonators (The yellow cylinder is not actually there. It is shown to demonstrate the relationship between the wavelengths.)

Logo

Cylinders

Cylinder Dimensions, Algebraic

Cylinder Dimensions, Decimal

Hyperbola Equation



Introduction

Welcome. Please find information regarding an experimental electromagnetic resonator. Using the Golden Ratio (1.61803...) as the base of logarithms gives rise to a Geometric Series of sidebands when the waves heterodyne. The following paper describes the technology in more detail.

Golden Ratio Heterodynes (5 May 2019)

Experimental Data

Measurements preformed in a shielded anechoic chamber at PSU. Frequency sweeps with VNA. Spectrum Analyzer measurements with wideband noise source. Discussion of experimental data. Calculated vs. measured frequencies of resonance.

Experimental Data, (18 Jan 2019)

Design Specifications

Dimensions, Decimal, GIF file

Dimensions, Algebraic, 4 element

Dimensions, Algebraic, 8 element

Dimensions, Decimal, .dxf CAD file

Dimensions, Decimal, text file

Plastic fixture for holding cylinders, PNG file

Plastic fixture for holding cylinders, DXF file

Electronics

3D Renderings

Perspective Views 1

Perspective Views 2

Perspective Views 3

Math and Theory

curl B = dE/dt + J

Golden Ratio base Logarithms

How the waves heterodyne (text explanation)

How the waves heterodyne (gif)

Heterodynes in the frequency domain

Physical geometry derived from wave equation

Physical geometry derived from wave equation (2)

Golden Rectangle construction

Rectangles rolled up to make the cylinders

The whole structure fits within a Hyperbolic Horn, which is the shape of a vortex in water

A Golden Spiral can be thought of as a wave with an exponential envelope.

If the period of the wave shortens by a factor each cycle, then the wave has a hyperbolic envelope.

This image shows the meaning of the logarithm taken in the previous image.

Here you can see the relationship between the period of a given cycle of the wave, and all subsequent periods.

Exponential vs. Hyperbolic growth. Hyperbolas reach an asymptote, whereas exponential curves always remain finite.

The geometry of the structure can be derived from a spiral wrapped around a hyperbolic horn.

time-space.gif

Simpler form of the wave equation, with the asymptote at z=0. If this was a sound wave, it would sound like a chirp.



Fun Animations

CERN Open Hardware License v1.2

Copyright Sean Logan 2011-2019.

This documentation describes Open Hardware and is licensed under the CERN OHL v. 1.2.

You may redistribute and modify this documentation under the terms of the CERN OHL v.1.2. (http://ohwr.org/cernohl). This documentation is distributed WITHOUT ANY EXPRESS OR IMPLIED WARRANTY, INCLUDING OF MERCHANTABILITY, SATISFACTORY QUALITY AND FITNESS FOR A PARTICULAR PURPOSE. Please see the CERN OHL v.1.2 for applicable conditions.

LICENSE.pdf

HOWTO.pdf

CONTRIB.txt

CHANGES.txt

PRODUCT.txt

Et Cetera