--- title: "NMR Power Saturation Analyzer Interactive Lab | Sandbox Physics" description: "More drive can yield less response. 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." canonical_url: "https://sandboxphysics.com/labs/nmr-power-saturation/" language: "en" page_type: "lab" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/labs/nmr-power-saturation/" last_modified: "2026-10-18" --- 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. > Interactive simulation: open this page in a web browser to change the parameters and run the model. 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 amplitude Reach exact steady state Average 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](https://sandboxphysics.com/labs/cw-nmr-spectrometer/) [Compare pulsed free induction](https://sandboxphysics.com/labs/nmr-free-induction-spectrometer/) [Magnetic-resonance evidence](https://sandboxphysics.com/stories/quantum-evidence/magnetic-resonance-beams-absorption-induction/) [Bloch 1946 · equations and steady state](https://journals.aps.org/pr/pdf/10.1103/PhysRev.70.460) [Purcell, Torrey & Pound · original absorption report](https://journals.aps.org/pr/abstract/10.1103/PhysRev.69.37) [TeachSpin CW bridge manual](https://faculty.cst.temple.edu/~tuf43817/PHYS4796/Spring2025/Pulse_NMR.pdf) [NIST reference constant](https://physics.nist.gov/cuu/Constants/Table/allascii.txt) Physics tutorial ## NMR Power Saturation Analyzer **Background** 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. **Why it matters** A constant is inferred through a calibrated response and retained observations. 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 misconception** Recovering a source parameter independently confirms the law. **Better mental model** These synthetic records test a measurement and inference workflow. They are not historical observations, a parameter confidence interval, or external scientific certification. ### Run the experiment 1. 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. 2. 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. 3. 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. Physical conclusion 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. Quantum & fields · Starter path ## Start from a single measurement Predict outcomes and collect counts, building from one qubit to wave packets, bound states and two-photon interference. [Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare it with the frequency of acquired shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/) 1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/) 2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/) 3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/) 4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/) 5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/) 6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/) [View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)