Lilienfeld 1925 Quantify Available Power Gain

# Quantify Available Power Gain: Turn a Validated Modulation Into an Amplification Verdict

Step 22 asked a binary question: does terminal current change with control bias in a way that leakage and drift cannot explain? A pass there is necessary but not sufficient to call the device an amplifier. Correlation between a control signal and an output signal is also produced by capacitive feedthrough, rectification, and source-impedance loading — mechanisms the epilogue to the original fourteen-step sequence already named as the exact confounds a real amplification claim must rule out. Step 23 closes that loop: it takes a Step 22 pass and asks the decisive question directly, in watts, not in volts or in significance.

The criterion is available power gain, not voltage gain. A device can show a large voltage swing at its output while delivering less power than the input signal supplied, in which case it is a transformer or an impedance-mismatched attenuator, not an amplifier. Lilienfeld's disclosure claims the control electrode commands a load current larger than the signal current it draws; Step 23 is the arithmetic that either supports or refutes that specific claim for this specimen, under this bias point, at this frequency.

## 1. Define gain from available power, not from voltage ratios

Available power from a source is the maximum power it could deliver into a conjugate-matched load, not the power it happens to deliver into whatever load is connected:

$$ P_{avail,in}=\frac{v_{s}^{2}}{8\,\mathrm{Re}\{Z_{s}\}}, $$

where $v_s$ is the open-circuit signal amplitude at the control port and $Z_s$ is the source impedance driving it, including the signal generator and any series network. The available output power at the load, with the device's small-signal output resistance $R_{out}$ and the actual load $R_L$ it drives, is

$$ P_{L}=\frac{i_{L}^{2}R_{L}}{2}, $$

measured directly rather than inferred, and the quantity that decides the amplification question is

$$ G_{avail}=\frac{P_{L}}{P_{avail,in}}. $$

$G_{avail}>1$ means the load receives more signal power than the control source could possibly have delivered under any passive network, which cannot happen without the device supplying energy from its own DC bias. $G_{avail}\le 1$ means a passive network could in principle reproduce the output, and no claim of amplification is supported regardless of how large the output voltage looks.

Available power gain measurement at the Lilienfeld control port and load A signal path diagram shows a source with its own impedance driving the control electrode, the device drawing DC bias power separately, and a load resistor at the output, with the available input power and the delivered load power each defined as a distinct quantity whose ratio is the available power gain. AMPLIFICATION IS A POWER QUESTION, NOT A VOLTAGE QUESTION Compare power the load actually receives against the maximum the source could ever deliver SIGNAL PATH AND POWER BUDGET SIGNAL SOURCE v_s, Zs P_avail,in 13 11 12 control port draws P_avail,in DC BIAS supplies the energy any gain must draw from LOAD RL receives PL G_avail = PL / P_avail,in Measured directly from v_s, Zs, i_L, and RL — never assumed from a voltage trace alone. G_avail ≤ 1: a passive network could reproduce the output. No amplification claim is supported. G_avail > 1: the load power exceeds what the source could deliver under any passive match. WHY THIS IS NOT STEP 22 AGAIN STEP 22tested whether a terminal-current change exists and survives leakage and drift controlsSTEP 23takes that validated change and asks whether it constitutes net delivered power, in wattsCONSEQUENCEa Step 22 pass with G_avail ≤ 1 is real correlation but not amplification

## 2. Measure every quantity the ratio depends on — do not assume any of them

$Z_s$ is not the signal generator's nameplate output impedance alone; it is the impedance actually presented to the control port, including any coupling network, cabling, and the Step 20-measured control-port input impedance in parallel if the port is resistive at the test frequency. Measure $v_s$ as the open-circuit signal amplitude with the device disconnected, not as a dial setting. Measure $i_L$ directly, with a calibrated current sense in the load branch, at the same frequency and amplitude used for $v_s$.

$R_{out}$ is not a datasheet parameter for this device; it must be extracted from the Step 19 baseline slope at the operating point together with a small-signal load-variation measurement, because a historical, hand-built structure has no guaranteed output impedance. Report every one of $v_s$, $Z_s$, $i_L$, $R_L$, and the derived $R_{out}$ individually, so that a skeptical reader can recompute $G_{avail}$ from primary quantities rather than trusting a single asserted ratio.

## 3. Use the smallest signal that still resolves above the Step 19 and Step 20 floors

The measurement must stay in the small-signal regime that the Step 19 baseline and Step 20 leakage characterization were built on; a large test signal risks exercising nonlinearity that the linear gain definition above does not capture, and risks the same stress and drift concerns Steps 20 through 22 already bounded. Choose the smallest input amplitude that keeps $i_L$ resolvable above the instrument and fixture noise floor established in Step 20's blank measurement, and verify that halving the input amplitude halves the measured $i_L$ within uncertainty. A gain estimate taken outside this linear range is not comparable to the small-signal $\delta I_{min}$ and $f_{leak,max}$ thresholds the whole Step 19–22 arc was built around, and must be reported as a large-signal result with that caveat stated explicitly.

## 4. Separate real gain from the confounds the epilogue already named

Rerun the specific null checks the amplification epilogue identified, now with power rather than voltage as the test quantity:

  • Capacitive feedthrough: repeat the measurement with the DC bias removed from the 11↔12 path while leaving the control-port signal and load connected. Any $i_L$ that persists is feedthrough, not amplification, and must be subtracted or shown to be negligible relative to the biased-condition $i_L$.
  • Rectification: check whether $i_L$ contains energy at harmonics of the drive frequency disproportionate to a linear response; a nonlinear rectifying path can produce an output-frequency component that looks like gain on a simple peak-reading meter but fails a narrowband power measurement at the drive frequency itself.
  • Source-impedance loading: confirm $P_{avail,in}$ was computed from the actual $Z_s$ presented to the port, not a nominal source impedance, since underestimating $Z_s$ inflates $P_{avail,in}$ in the wrong direction and makes a real gain look smaller, while overestimating it can manufacture an apparent gain that disappears under a correctly measured source impedance.
Linearity check and confound subtraction for the available power gain measurement A log-log plot of load current against input signal amplitude shows a linear small-signal region bounded by the Step 20 noise floor and a nonlinear large-signal region, beside a bar comparison of the biased load current against the feedthrough-only load current with the DC bias removed, leading to a disposition table for the amplification verdict. A GAIN NUMBER IS ONLY TRUSTWORTHY INSIDE THE LINEAR, UNCONFOUNDED REGIME Verify proportionality, then subtract feedthrough before reporting a verdict LOAD CURRENT VERSUS INPUT AMPLITUDE input signal amplitude, log scale load current, log scale Step 20 noise floor linear region, slope confirms proportionality large-signal, nonlinear BIASED VERSUS FEEDTHROUGH-ONLY load current at the drive frequency DC bias on bias removed i_L, biased feedthrough only Any bias-removed current must be subtracted or shown negligible. AMPLIFICATION VERDICT PASSlinearity confirmed, feedthrough subtracted, G_avail > 1 with stated uncertaintyHOLDG_avail near unity, linearity marginal, or feedthrough comparable to biased signalREJECTG_avail ≤ 1, dominant harmonic content, or gain only outside the confirmed linear range

## 5. Sweep frequency and operating point before generalizing the verdict

A single frequency and bias point cannot support a general amplification claim. Repeat the measurement across the bandwidth relevant to the intended application — audio frequencies for the loudspeaker-coupled stages the original disclosure diagrams — and across the bias range Step 21 already certified as leakage-safe. Report $G_{avail}$ as a function of frequency and of control bias, not as a single headline number, because a structure with large parasitic capacitance between the control foil and the film can show gain that falls sharply with frequency for reasons unrelated to the underlying field-effect mechanism.

## 6. State the verdict with the same discipline as Step 22

Report pass, hold, or reject exactly as Step 22 did: alongside the full set of measured primary quantities, the linearity check, the feedthrough subtraction, and the frequency and bias dependence, not as an isolated ratio. A single favorable $G_{avail}$ value computed at one convenient frequency and bias point, without the confound checks in §4, is not a verdict — it is exactly the kind of unsupported claim the historical record around this device has repeatedly produced, and which this project exists to avoid repeating.

## 7. Minimum Step 23 record

Retain:

  • device genealogy and the registered Step 15–22 geometry, coverage, material, isolation, baseline, leakage, protocol, and modulation results;
  • measured $v_s$, $Z_s$ (including any coupling network), $i_L$, $R_L$, and the extracted $R_{out}$, each reported individually;
  • the computed $P_{avail,in}$, $P_L$, and $G_{avail}$ with full uncertainty propagation from every input quantity;
  • the linearity sweep confirming proportionality between input amplitude and $i_L$, and the amplitude range over which it held;
  • the bias-removed feedthrough measurement and the subtraction or negligibility justification;
  • any harmonic-content check used to rule out rectification;
  • $G_{avail}$ reported as a function of frequency and control bias, not as a single value;
  • temperature, humidity, elapsed time, and cable-motion controls through the run;
  • the final pass, hold, or reject disposition for the amplification claim, stated with its supporting measurements.

The historical geometry and the claimed effect are grounded in [J. E. Lilienfeld, US Patent 1,745,175](https://patents.google.com/patent/US1745175A/en), which describes the control electrode commanding output variations reproduced at greater scale. The requirement to measure gain from available power rather than from voltage ratios, and to rule out feedthrough, rectification, and impedance mismatch before accepting a gain claim, follows standard small-signal amplifier characterization practice and the same low-level measurement discipline applied throughout Steps 18–22 from the [Keithley Low Level Measurements Handbook](https://www.tek.com/en/documents/product-article/keithley-low-level-measurements-handbook---8th-edition).

## Quantify Available Power Gain’s Place in the Process Lineage

Step 22 established that a terminal-current change correlates with control bias and survives leakage and drift controls. Step 23 now asks the question that correlation alone cannot answer: does the load receive more signal power than the control source could possibly supply, measured in watts rather than inferred from voltage traces, with capacitive feedthrough and rectification explicitly ruled out and the result reported across frequency and bias rather than at one convenient point. Only a specimen that passes both Step 22's modulation test and Step 23's power-gain test supports the amplification claim the original fourteen-step construction and operating sequence set out to demonstrate.

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