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Hi Jon,
This is above my pay grade so I asked the new o1 model from OpenAI. I posted your comment along with the diagram and scope shots.
I'd be interested in others thoughts.
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Below is a summary of what is actually going on in this “slow‐ramp” test, why your capacitor ends up with more apparent stored energy than your scope math says you put in, and why there is no need to invoke “the Aether” (or any other unseen energy source) to explain it. In short, the measured “COP ≈ 90” arises from incomplete measurement of the true input power/energy and from overlooking how the amplifier, coil, and parasitic coupling really behave in the time domain.
1. Why the capacitor’s voltage rises
Even with a “slow” or relatively low‐dV/dt ramp, there is still an electric‐field coupling from the primary inductor  to the open‐circuited capacitor . This coupling can be broken down into:
1. Capacitive coupling from the coil’s windings and/or leads to .
2. Displacement current (sometimes called “displacement current through parasitic capacitances”) from the amplifier’s output node and coil windings into the capacitor node.
Because of these parasitic coupling paths, a small displacement current can flow into  even though it appears “open‐circuited.” On a scope plot, it can easily look like “charge separation with no conduction current,” but in reality the coil, wiring, test leads, and the capacitor physically create stray/pickup paths.
2. The huge “87.8 A” calculation
You computed I = C\,\Delta V/\Delta t \approx 88\,\mathrm{A} based on
I \;=\; \frac{(550\,\mu\mathrm{F})(2.953\,\mathrm{V})}{18.5\,\mu\mathrm{s}} \;\approx\; 88\,\mathrm{A}.

That equation is correct only if the capacitor current truly flows through a single well‐defined conduction path that you have measured. But in this experiment:
1. A Class‐D power amplifier can (and does) deliver short, high‐peak current pulses into reactive loads, especially if there is any pulse or ramp edge.
2. The circuit layout almost certainly has stray and distributed impedances that you are not measuring with your single “current sense” approach. In particular:
• Your R1 or CH2 measurement might not register the fast spike(s).
• The amplifier itself may deliver pulses outside the bandwidth or sample window you are capturing with the scope’s math channel.
• Your scope probe on  is high‐impedance, but there is still stray conduction/current flow in the cables and amplifier output stage.
Hence the true current path responsible for charging  is simply “hiding” in plain sight within the distributed circuit geometry. It is not that “88 A mysteriously appears.” It is that short bursts of current do flow, but your scope’s measurement method is missing them.
3. Why the scope math suggests only 26.8 µJ in
You mention measuring

which integrates to

Yet the capacitor’s energy is
\[
U_{C_1} \;=\;\tfrac12\,C\,V^2
\;=\;\tfrac12\times 550\times 10^{-6}
\times (2.953)^2
\;\approx\; 2.4\,\mathrm{mJ}.
\]
And you note that , giving “COP ≈ 90.”
Missing or mis‐measured input
What is really happening is that your scope’s math trace is almost certainly not capturing the real (and sometimes very brief) current/voltage pulses that the Class‐D amplifier is generating. A Class‐D stage can switch large current in tens of nanoseconds or microseconds, and typical “Power = Voltage × Current” scope math may only be capturing the lower‐amplitude portion or the time‐averaged portion.
So your actual energy input is being under‐reported by orders of magnitude. Once you sum up all the energy delivered—including the brief spikes or transitions that your math trace might be missing—the real input to the circuit comes out comparable to (or greater than) the  stored on . This resolves the “Where did all that energy come from?” question by conventional circuit theory.
4. Slow‐ramp vs. fast‐pulse
You note that a slower ramp also leads to the capacitor being charged. That is not surprising. Even when dV/dt is smaller, any finite “ramp” across an inductor + capacitor arrangement (with a parasitic coupling path) can result in net charge buildup. Whether the waveform edges are “fast” or “slow,” the principle is the same: the amplifier and coil geometry provide a path for displacement current into . The main difference is that with a slower ramp, the absolute current peaks can be lower (though still possibly short spikes on transitions), and the total time is longer.
5. There is no need for an “Aether” hypothesis
From standard electromagnetics:
1. Displacement currents flow whenever there is a time‐varying electric field. Even in “open” circuits, you can get net charge on a conductor or capacitor by virtue of parasitic capacitances.
2. A Class‐D amplifier plus an inductive load can have high instantaneous current pulses that do not show up if you are only looking at a lower‐bandwidth or time‐averaged trace.
3. Apparent “over‐unity” or “COP > 1” arises routinely when the experimenter’s measurement method does not capture all real input power/energy. This is not a condemnation—it is easy to make these errors with modern power scopes that average or sample in ways that miss fast edges.
Everything we see in these waveforms is consistent with normal conservation of energy once the full circuit parasitic paths and the high‐speed amplifier switching dynamics are properly accounted for. Put differently, the amplifier really is delivering the current/energy that shows up as voltage on . It just does so in short bursts and via stray coupling paths that are subtle to measure.
Bottom line
1. The capacitor is being charged from the amplifier/coil system via normal electromagnetic coupling (not from “outside” or “the Aether”).
2. The “88 A” is simply the instantaneous current demanded by ; short bursts of current do flow, but are missed by your scope’s power measurement.
3. The “COP ≈ 90” is an artifact of under‐measuring the true input energy.
No new physics is required—just the usual Maxwell‐based explanation of parasitic coupling, displacement currents, and the pitfalls of incomplete power/energy measurements in pulse or Class‐D driven circuits.
------------------------- edit added screenshots for the Tex format calculations
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Topic: partzmans board ATL (Read 36174 times)
