CONTINUOUS NUCLEAR RESONANCE / SATURATION

NMR Power Saturation Analyzer

Lock to resonance and step the calibrated RF nutation rate. Record the rise and fall of the absorptive voltage, infer the critical drive, and see which relaxation information remains inseparable.

DRIVE / BALANCE / INFER

More drive can yield less response.

Source longitudinal time · excluded from fit

T_1/\mathrm{s}

0.35

Source homogeneous transverse time · excluded from fit

T_2/\mathrm{ms}

25

Source receiver scale · excluded from fit

G/\mathrm{\mu V}

300

Source in-phase baseline · excluded from fit

b_I/\mathrm{\mu V}

2

Calibrated single-exposure noise

\sigma/\mathrm{\mu V}

1

Independent settled repeats

n

8

Calibrated RF nutation frequency

r=\Omega/(2\pi)\;(\mathrm{Hz})

1.6

Moving the frequency or drive probe retains records. Source changes clear current records; a saved comparison is retained.

A homogeneous Bloch reservoir, exact resonance lock and fully settled independent exposures. Calibrated nutation frequency is proportional to the co-rotating RF field, not watts. The voltage maximum identifies a relaxation-time product; unknown receiver scale prevents separate recovery of both times. This is a synthetic bridge experiment, not a power calorimeter.

Nominal vertical static field, transverse sample coil. Continuous RF and a matched reference arm feed a balanced bridge; the residual reaches a phase-referenced receiver. Ideal cancellation and flat calibrated gain, not a solved RF circuit. Cable motion is schematic. $B_0=0.35\,\mathrm{T},\quad f_{\rm ref}\simeq14.902\,\mathrm{MHz}$

CONTINUOUS DRIVE / SETTLED VOLTAGE EXPOSURES

Find the drive that turns the curve.

Set frequency and RF amplitudeReach exact steady stateAverage independent IQ voltages

61 independent settled exposures span calibrated nutation rates from zero to twelve hertz, at exact resonance. Rate is proportional to RF field; drive power is proportional to its square for an unchanged coil. No watt calibration or resonance-lock hardware is solved.

Ready. Predict, then acquire.

RAW VOLTAGES / SEPARATE SOURCE EXPECTATION

The voltage rises, then falls.

$r/\mathrm{Hz},\quad I,Q\;(\mathrm{\mu V})$

Teal: absorptive in-phase voltage. Gold: dispersive quadrature voltage. Dots: observations. Thin lines: source expectations. Purple dashes: record-only fit. Gray: exact saved records. Constant receiver baselines are retained and fitted.

RESIDUALS / COMPUTED FROM RETAINED VOLTAGES

What the fit leaves behind.

$(I-I_{\rm fit}),\;(Q-Q_{\rm fit})\quad(\mathrm{\mu V})$

Only recorded coordinates appear. No residual is generated before a supported fit. A small residual shows consistency with this response family, not independent confirmation of the physical law.

INFERENCE / SOURCE PARAMETERS EXCLUDED

Inferred critical nutation rate

\text{—}

Inferred relaxation-time product

\text{—}

Inferred in-phase baseline

\text{—}

Retained complex exposures

0

Voltage residual RMS

\text{—}

Unknown amplitude and baseline are profiled out. Only the relaxation-time product is identified. A linear unsaturated-response comparison rejects records without a resolved turnover. Search bounds and weak-information thresholds are diagnostic heuristics, not confidence intervals.

Latest raw observations

Index	$r/\mathrm{Hz}$	$I/\mathrm{\mu V}$	$Q/\mathrm{\mu V}$

SAVED COMPARISON / LIMITS & SOURCES

Single homogeneous, noninteracting resonance with exponential Bloch relaxation. No static field distribution, molecular shifts or coupling, heating, diffusion, radiation damping, finite settling, bridge imbalance, drive leakage, phase error or RF circuit loading. Receiver gain is assumed flat over the narrow carrier span. The bridge measures response voltage, not absorbed watts or individual nuclear outcomes.

Compare: absorption and dispersion Compare pulsed free induction Magnetic-resonance evidence Bloch 1946 · equations and steady state Purcell, Torrey & Pound · original absorption report TeachSpin CW bridge manual NIST reference constant

Start with the essentials

Focus question: More drive can yield less response.
One-sentence intuition: Keep source assumptions separate from estimates made from records.

Core mathematical model

A critical RF amplitude

\begin{aligned}I(r)&=b+\frac{a r}{1+(r/r_c)^2}\\r_c&=\frac{1}{2\pi\sqrt{T_1T_2}}\end{aligned}

At exact resonance the absorptive voltage is largest at the critical calibrated nutation rate. The field is a co-rotating amplitude, half the peak linearly oscillating field.

One identifiable product

T_1T_2=\frac{1}{(2\pi r_c)^2}

A source scale is not supplied to inference. Different lifetimes with the same product and a compensating unknown gain give the same voltage curve.

Voltage is not absorbed power

\frac{P_{\rm abs}}{M_0B_0}=\Omega v=\frac{\Omega^2T_2}{1+\Omega^2T_1T_2}

Normalized absorbed power increases toward a plateau while the voltage component can decrease. No sample magnetization density, volume or watt calibration is supplied.

Common difficulties

A simulation supplies its law

Typical misconceptionRecovering a source parameter independently confirms the law.

Better mental modelThese synthetic records test a measurement and inference workflow. They are not historical observations, a parameter confidence interval, or external scientific certification.

Run the experiment

01
Scan through the turnover
Acquire the full calibrated drive range, including zero drive and the high-drive tail.
What to observe: The unknown baseline and scale are fitted along with the critical drive. Residuals come from the retained voltages.
02
Test non-identifiability
Save the reference, then choose the same-product preset and acquire again.
What to observe: The source times differ but the mean voltage curves coincide. Neither time is separately reported.
03
Separate response from energy
Compare the declining voltage tail with the power equation.
What to observe: A weaker voltage is not proof that less energy is being absorbed. The analyzer is not a calorimeter.