D. Edward Mitchell 16:00, 14 April 2020 (UTC) Hello World!    groupKOS Developer Share —usually UNDER CONSTRUCTION

Hexatron Ring Amplifier

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edit template Prelude   Assembly   Resonant Array   Ring Amp   Suspension   Power   Sensor Matrix   Processing   The Story

Fig. 1. A logic-chip differential ring oscillator with inductive loading on the 'X' flip-flop latching feed-back circuit. The 'X' on a schematic 'unwinds' when the gates point opposite directions, to form the 'X' into a loop. The ring amp will oscillate about an average frequency established mostly by the inductive loading of the 'X.'

Power-transistor ring-amplifier version

In later designs beyond the logic-chip prototypical version illustrated in Fig. 1, the electrical path to energize a copper loop on the donut also happens one half-loop at a time. When a half-loop is energized by a fast power switch, a current-shunt at the other end of the half loop is sensed and conditioned to switch the second half of the copper-loop halves.

A current shunt at the end of the 2nd half-loop of a pair then physically routes the voltage signal forward in the ring of copper-pairs. Three copper pairs form three phases of a ring-oscillation. The physical-routing of the output forward or reverse around the ring will produce right- or left-hand rotation on the torus, selectable with the routing choice.

Ring oscillators are implicitly noisy, inherent to the design, as the switching transistors inject noise from the circuit environment. All present signals in the ring circuit are amplified in proportion to how closely the regularity of the signal matches the natural oscillating frequency of the ring oscillation.

But the noise is not in amplitude in the ring signal, but as timing jitter on 'when' a ring-section inverts. This jitter will disappear when an oscilloscope of the ring signal is switched to triggered-mode, to start a trace on the scope when the signal starts... but and all the jitter is lost! The jitter is rather studied with a categorization of all the cycle-periods, the duration of a power-transistor's on-time, or off time.

The jitter is studied on a time-forward ring oscillation, because anything that affects the magnetic environment of the ring, anything within some effective proximity, will affect the spectral profile of the system pulse noise under study.


When a ring of inverters change polarity in a fast tail-chase, a signal injected into the ring manifests in a timing-variation of the power-switch. Any signals matching the regularity of the ring will get regularly accumulated as regular variations in 3-phase symmetry.

Donut coil symmetries

There are only two general classes of ways to wind three independent coils on a donut without crossing. Loops can be placed on the donut surface without touching, and symmetrically, as either a group of links or a group of knots. The 'link' class are loops on a donut that do not cross themselves as a closed loop. The 'knot' class will entwine with itself on a donut, passing between its own helices of earlier trips winding around the donut ring.

The resonant-X physical resonator element is one half of a copper loop, hammered into stiffened shape from thin copper tubing (1/8" dia. or smaller).

The copper half-loop is formed on the surface of a torus; a dielectric donut, or non-conducting torus form.

A second copper half-loop of complementing symmetry completes a resonating element on a donut.

Two more pairs of half-loops form two more copper resonators that are entangled as three non-touching electrical loops (as a link or knot).

The half-loops of each pair are each configurable electrically to provide additive or subtractive contributions to system self-resonance.

How a ring amp amps

When a ring of inverters change polarity in a fast tail-chase, a signal injected into the ring manifests in a timing-variation on the power-transistor. Any signals matching the regularity of the ring will get regularly accumulated as regular variations in 3-phase symmetry.


Donut links

Nine copper loops as links on an invisible donut are positioned as Villarceau circles a.k.a. a fiber bundle, a.k.a. a fibration of a 3-space torus from a 4-space sphere. The 'fibers' of 'fibration' are the rings on a donut.

Smooth 'links' on a donut, that also entangle with themselves without touching or crossing, are selected for study of a rotary 'entanglement' per se, where resonant elements will resonate while going through each the other links. Intuition loudly dictates magnetic entanglement will follow link entanglement. What's your intuitor say? Don aght groupKOS doght cφm

There is one link symmetry on a donut that is chosen for resonant study; the Villarceau circle.

Donut knots

A 3-groups of smooth 13:8 torus knots, showing detanglement (ordering) of left- and right-hand current direction when the knots are energized in bipolar connection, each from the outer periphery of the knots, at hexagonal connection points.

Smooth and entangled 'knots' on a donut have a lot of knot groups, each created at a different 'knot ratio,' which sets the slope of the helix winding around the donut ring.

The knot ratio of 13:8, which is adjacent Fibonacci numbers, will wind smoothly on a donut and provide a number of gee-wiz symmetries taunting my inner Develoepr.

A simple cousin of the 13:8 magic is the 3:2 torus knot, and will likely be a first prototype due to its fewer, more affordable and easier fabrication.

The 13:8 3-knot group has a mysterious dissonance pattern that alternately creates chiral-bandings that are dis-entangled along the donut surface into alternate lanes of similar helical chirality (direction of current flow) in groups of four loops. The 13:8 is perfectly dis-entangled.

Intuition prefers the 13:8 to studies because there is more copper on the donut surface. That may or may not have any significance to the end design of evolved versions.