Phased-Conjugate Image Powering with a Ferroelectric Capacitor (Four-Wave Mixing in Practice)

A clear, hands-on explainer of the “phase-conjugate replica image” idea often associated with Tom Bearden—refined here into a practical four-wave mixing (FWM) experiment using a ferroelectric capacitor (e.g., barium-titanate based). We’ll cover what it is, why three injected tones are required, and how to probe for a “sweet spot” where the device appears to deliver a stronger discharge than the charge you supplied.

Concept diagram: three tone generators F1, F2, and F3=F1−F2 feed a nonlinear barium-titanate capacitor; a cap-dump circuit extracts pulsed energy to a storage battery. — Concept sketch: two phase-locked pumps at `F1` and `F2`, plus a seed at `F3 = F1 − F2`, all injected into a nonlinear (ferroelectric) capacitor. The medium produces a conjugate (fourth) wave internally. A “cap-dump” stage harvests the pulses.

Safety & Scientific Honesty

Use low voltages while exploring (bench supplies, function generators). Add fuses and current-limits.
Claims of “overunity” are hypotheses here. Do full power accounting: measure instantaneous V×I into and out of the device and integrate over time.
Not all “supercapacitors” use barium titanate. For strong nonlinearity, use a ferroelectric/ceramic capacitor (BaTiO₃ or similar) or a supercap specifically built with a ferroelectric composite.

1) The Core Idea, Cleaned Up

Nonlinear medium: A ferroelectric dielectric (e.g., barium titanate) is strongly nonlinear. When driven with multiple tones, it mixes them.
Bearden’s step (two tones): Drive with F1 and F2. The medium generates a difference-frequency component (F1 − F2) among others.
The missing step (seed tone): Inject a third tone F3 that equals the expected difference (F3 = F1 − F2) and is phase-aligned. This “seeds” the nonlinear process. With all three present, the medium can form a strong phase-conjugate replica (the fourth wave) that returns energy coherently.
Why ferroelectric capacitors: They already store charge and sit between your sources and the load; the emerging conjugate wave interacts inside the dielectric, so you avoid complicated external feedback networks.

2) Lab Setup

Instruments

Two function generators with phase-lock (or one dual-channel generator): produce F1 and F2.
Third generator or synthesized output for F3 = F1 − F2 (can be derived in the same instrument if it allows internal mixing).
Digital scope (2–4 channels), current shunt (low-ohm), and a precise DMM.

Device Under Test (DUT)

Nonlinear cap: a BaTiO₃ ceramic/ferroelectric capacitor or a composite “supercap” known to include ferroelectric material.
Injection network: series resistors (to prevent source fighting), small signal diodes (optional) to steer paths, and a star ground/reference node.
Cap-dump: a synchronous MOSFET or SCR dump (with diode) into a storage element (e.g., a low-ESR electrolytic or a small battery) for pulsed extraction.

3) Frequencies, Phases, and Levels

Start band: Explore roughly 10 kHz → 1 MHz. Ferroelectrics often show strong dispersion in this region—your “sweet spot” lives here.
Set pumps: Choose F1 and F2 close enough that F3 = F1 − F2 is within your generator’s range (e.g., 400 kHz and 410 kHz → 10 kHz seed).
Phase-lock: Ensure F1 and F2 are phase-locked. Then align the seed F3 so its phase reinforces the internally generated difference component.
Amplitudes: Keep F1 and F2 moderate (e.g., 1–5 V_pp each to start). Make the seed F3 lower (≈10–30% of the pump amplitude).

4) Wiring (text schematic)


      CH1 (F1) ──┬─[R]──► DUT (ferroelectric capacitor) ◄──[R]─┬── CH2 (F2)
                 │                                          │
                 └─[R]──► CH3 (F3 = F1−F2, phase-aligned) ──┘
      
      DUT node ──► Cap-Dump (MOSFET/SCR) ──► Storage cap/battery (through diode)
      Return/ground: common star point; scope uses x10 probes with short leads.

Resistors (100–1kΩ) isolate the sources so they don’t drive each other. Keep leads short; ferroelectrics can be very reactive at HF.

5) Finding the “Sweet Spot”

Characterize baseline: With only F1 present, measure charge time and dump energy E into your storage element. Repeat for F2 alone.
Two-tone mix: Apply F1 and F2 (phase-locked). Sweep their frequency while monitoring any growth at F1 − F2.
Add the seed: Inject F3 = F1 − F2. Adjust its phase until you see maximum coherent response (look for a clean, larger-than-expected pulse at the dump node).
Tune for peak: Nudge all three frequencies together (keeping F3 equal to the difference). You are hunting for a point where the DUT’s effective behavior looks “super-capacitive” (i.e., stronger discharge pulse for a given small charge input).

6) Measuring Gain Correctly

Instantaneous power method: Record V(t) and I(t) for each input channel into the DUT and for the dump output. Compute P(t) = V(t)·I(t), then integrate over identical windows: E = ∫P(t)dt.
Subtract losses: Include resistive heating (series resistors), gate drive power (if any), and capacitor ESR.
Look for artifacts: Phase errors, scope math bandwidth limits, probe ground loops, and diode recovery can all mimic “excess” energy. Verify with a second method if you see surprising results.

7) Why This Arrangement Helps

All in one medium: The nonlinear mixing and energy storage occur inside the same ferroelectric dielectric, so the conjugate component “arrives” where it can be harvested—no lossy external feedback loop.
Seeded FWM: Injecting the seed F3 aligns the process and can dramatically strengthen the phase-conjugate wave, compared with relying on spontaneous difference-frequency generation alone.
Cap-dump timing: By dumping on the peak of the coherent pulse, you convert reactive surges into useful DC while disturbing the mixing process as little as possible.

8) Practical Tips

Try different ferroelectric parts (C0G/NP0 ceramics are linear—avoid; look for high-K dielectrics or explicit BaTiO₃ ferroelectrics).
Keep the DUT cool; ferroelectric properties shift with temperature. Log temp during sweeps.
Add a narrow band-pass (centered at F3) between the DUT node and the dump to reduce pump leakage into the storage element.
Experiment with small reverse bias on the DUT (DC offset) to pre-polarize domains and stabilize the phase alignment.

What Success Looks Like

A narrow, repeatable pulse at the dump node that grows strongly only when all three tones are present and phase-aligned.
Effective “apparent capacitance” increase: for the same small charge energy, you observe a disproportionately larger discharge pulse (after careful accounting).
Robustness across repeats: moving a few kHz off the sweet spot should reduce the effect sharply—strong frequency/phase selectivity is a good sign.

If you reach this point, you’ve likely found a genuine nonlinear-mixing resonance. From there, refine the dump timing, minimize losses, and document everything.