The Matrix
Calculations for the apparatus — what a choke and a cell ring at, what the water is doing, what the circuit is asking of the drive.
Every calculation here shows the formula it used, the method in words, what it assumes, and where the formula came from. A number without its working is an assertion; this archive does not make those anywhere else, and will not make them here.
Simulators — build a circuit from parts and see what the whole thing does. Parts — the library behind every form. Saved circuits.
Measurements — what was recorded at the bench, kept separate from what is predicted here.
50 calculations in the catalogue. The rest are planned — see docs/PLAN-MATRIX-ENGINE.md.
Design — whole systems, step by step
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Design a VIC: cell, choke, Q and step charging VIC standard physics
Given this tube, this water and a target frequency, what choke does it need, how sharply will it ring, and will it step-charge?
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Simulate a VIC: chokes, cell and pulsed drive VIC standard physics
With these chokes, this cell and this drive, where does the loop ring, what does the drive draw, and does the cell step-charge?
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VIC-5: will the phase-locked loop find this cell's resonance? VIC standard physics
With these chokes and this cell, where is the resonance — and can this PLL reach it, hold it, and build the rise inside each gate?
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With the legs firing in turn through their load resistors, how far does each pulse charge this cell, what does the supply deliver, and does anything build up against the water's leak?
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Steam resonator: how fast, and by what, the water heats WFC standard physics
With this voltage across this plate cell at this frequency, how fast does the water reach the boil — and is it the dipoles or the current doing it?
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What does this mix of carrier, metal and surfactant weigh, how thick is it, does it flow smoothly at this pump rate, and what does it do to the water's permittivity?
Water and dielectric
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Water permittivity at temperature WFC standard physics
What is the dielectric constant of the water in the cell once it has warmed up?
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Complex permittivity and loss (Cole-Cole) WFC standard physics
How much of the energy put into the cell is stored, and how much just heats the water?
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Dissolved solids to conductivity WFC standard physics
What conductivity does a TDS reading in ppm correspond to?
The cell
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Coaxial cell capacitance WFC standard physics
What is the capacitance of a tube-in-tube cell with water between the walls?
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Flat-plate cell capacitance and field WFC standard physics
What is the capacitance of a flat-plate cell, and how hard is the field across the water?
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Concentric-sphere cell capacitance WFC standard physics
How much capacitance does a sphere inside a sphere hold, with this water between them?
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Leak resistance across a tubular cell WFC standard physics
Through what resistance does the charge on this tube leak away, given the water's conductivity?
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Leak resistance across a plate cell WFC standard physics
Through what resistance does the charge on these plates leak away, given the water's conductivity?
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Leak resistance across a spherical cell WFC standard physics
Through what resistance does the charge on a sphere-in-sphere cell leak away?
Resonance
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Series LC resonant frequency VIC standard physics
At what frequency will this choke and this cell ring together?
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Inductance needed for a target frequency VIC standard physics
What choke do I need to make this cell resonate where I want it?
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Q factor and voltage rise VIC standard physics
How sharp is the resonance, and how much voltage appears across the cell?
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Damping and ringdown VIC standard physics
After a pulse, does this loop ring or sag, at what frequency, and for how many cycles?
Chokes and coils
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Coil inductance (Wheeler) VIC standard physics
How much inductance will this coil have when I have wound it?
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Coil self-resonance VIC standard physics
Above what frequency does this choke stop behaving as an inductor?
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Inductance of a winding on a core VIC standard physics
What inductance do these turns have on this core?
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Two chokes on one core VIC standard physics
With the charging and blocking chokes coupled, what inductance does the loop see, and what does the blocking choke present?
Transformer and core
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Transformer step-up to the cell VIC meyer
What voltage reaches the cell for a given turns ratio, and what current does that cost?
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Minimum turns before core saturation VIC standard physics
How many primary turns does this core need before it saturates?
Step charging and gating
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Resonant build-up under a gated drive VIC standard physics
Driven on resonance, how many cycles does the cell voltage take to climb toward Q times the drive — and how far does it get before the gate closes?
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Step charging accumulation VIC derived
Does the cell voltage climb over a gated pulse train, or fall back between pulses?
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Pulse train timing VIC standard physics
How long is each pulse, how long the gap, how many pulses fit in one gate, and what fraction of the time is the drive on?
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Current and power under a pulsed drive VIC standard physics
At the drive frequency, what current does the loop draw, what power does it dissipate, and what does that average out to over the pulse train?
Phase-locked loop
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Phase-locked loop: lock, hold and damping VIC standard physics
With this VCO, phase detector and loop filter, how far can the loop lock from, how far can the resonance drift, and how fast does it settle?
Dual switchover
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Dual switchover: one leg's pulse into the cell VIC derived
When a switch leg connects the cell to the supply through its load resistor, how far does the cell charge, what current flows, and what does each pulse cost?
Electrical particle generator
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Magnetic flux through a coil EPG standard physics
How much magnetic flux links a coil sitting in a field of a given strength, area and angle?
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Induced EMF from a changing flux EPG standard physics
What voltage does a coil see while the flux through it changes?
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Solenoid inductance with a core EPG standard physics
What inductance does this coil have, wound on this core?
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Mutual inductance between two coils EPG standard physics
How strongly are these two coils coupled?
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Coulomb force between two charges EPG standard physics
How hard do two charges at this separation push, or pull, on each other?
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Electric field across a gap EPG standard physics
How strong is the field between two electrodes at this voltage and spacing?
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Townsend ionisation coefficient EPG standard physics
How fast does ionisation multiply along the field at this pressure and field strength?
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Breakdown voltage — Paschen's law EPG standard physics
At what voltage does this gap break down and sustain its own discharge?
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Particle magnetisation and saturation EPG standard physics
How far toward saturation does a magnetic particulate go in this field, at this temperature?
EPG field geometry and coupling
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Where along the tube should the output coil sit to get the strongest signal?
EPG fluid chemistry
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Slurry density EPG derived
How dense is the medium once the metal particulate and surfactant are in it?
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Slurry viscosity EPG standard physics
How much does suspending the particulate thicken the carrier?
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Flow regime in the tube EPG standard physics
Is the medium flowing smoothly through the tube, or turbulently — and how fast?
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Permittivity of a metal-loaded fluid EPG standard physics
How much does suspending metal particles in the water raise its dielectric constant?
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Surface tension with a surfactant EPG standard physics
How far does this much surfactant lower the water's surface tension, and is it past the point of doing any more?
Steam resonator
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Heating water with a field: dielectric or conduction WFC standard physics
At this field and frequency, how fast does the water between the plates heat — and is it the dipoles or the ions doing it?
Gas output and efficiency
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Gas yield and Faraday efficiency WFC standard physics
How much gas can this current possibly produce, and how much of that did the cell actually make?
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Coefficient of performance WFC standard physics
How much energy is in the gas produced, against the electrical energy it took?
Multi-cell arrays
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Multi-cell array WFC standard physics
What does ganging cells in series or parallel do to the capacitance and the resonance?