Thermal noise measurement 2026-10-18
MIT's laboratory guide mounts resistors on an aluminum box beneath a metal beaker shield, with short twisted leads. Its SR560 amplifier uses nominal gain before a Krohn-Hite – band-pass filter; an oscilloscope reads root mean square voltage. Calibration sweeps an attenuated sinusoid and measures the actual gain . Students alternate the resistor and a short circuit, subtracting squared readings , and disconnect the ohmmeter during noise acquisition. Lead and input capacitance enter the gain-squared integral. With settings unchanged, varying electrical resistance or temperature tests the predicted mean square. The guide prescribes repeated readings and warns against averaging noise waveforms to zero. This is a documented teaching protocol, not a supplied dataset of measured outcomes.[ref]
The subtraction requires care: shorting the input changes the source electrical impedance. An amplifier's input current noise can therefore produce different voltage noise in the two configurations; a shorted baseline alone does not remove that contribution. Gain drift, interference and insufficient observation time also limit the inference. These are limitations of interpreting the measurement, not corrections that can be inferred from the nominal signal bandwidth alone. In an independent analysis one would compare the measured difference with
where represents the measured shunt capacitance and excludes that separately modeled shunt. If calibration already includes the same shunt response, applying the denominator again counts the attenuation twice. The thermal noise worked example and both original figures illustrate ideal models; they claim no measured agreement or measured value of the Boltzmann constant.
An authored teaching experiment uses an adjustable steady-voltage supply, a digital multimeter, fixed resistors, and a potentiometer or resistance decade box. Its original circuit uses a supply and , , and resistors; the student compares and electrical loads. The readout is load voltage, recorded against prediction and deviation. The student then removes the electrical load to measure the open-circuit voltage, disconnects the supply and substitutes a wire to measure the Thévenin resistance with the multimeter's resistance mode, and restores the supply for an independent method: adjust the variable electrical load until the voltmeter reads half the unloaded voltage. Finally the student builds the equivalent and repeats both load measurements. Its tables are blank recording forms, not reported observations. [ref]
The half-voltage inference assumes negligible voltmeter loading and positive . A finite voltmeter input electrical resistance actually gives an apparent unloaded reading
When the same voltmeter remains connected across a variable electrical load , the network sees . Setting its reading to , rather than to the true , gives
Thus the uncorrected half-reading method underestimates positive . In the original example, a stipulated gives and half-reading load , instead of . These are model predictions for a deliberately loading meter, not the specification or observed readout of the source experiment's instrument.
Finite readings can also estimate the terminal line without a physical short. For two distinct load settings with corrected delivered electric currents and terminal voltages ,
If the voltmeter remains across each electrical load, the delivered electric current is , including the meter branch. Omitting it biases the inferred slope.
Useful additional controls are to measure each resistor separately before assembly, verify terminal polarity, repeat an earlier load setting to detect supply drift, and compare a third setting with the inferred Thévenin terminal response. These are proposed controls, not reported outcomes of the source experiment. Closely spaced electric currents make the slope estimate sensitive to voltage resolution and measurement error; widely separated settings may trigger source current limiting or Joule heating that changes electrical resistance. Lead and contact electrical resistance, meter input uncertainty and rounding limit the inference. An ohmmeter injects its own test electric current; its reading on a powered network is not the suppressed-network ratio. Measurements with independent sources physically removed do not characterize an active dependent electrical source whose control or supply has also been disconnected.