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Johnson Noise: Determinations of k and Absolute Zero Edwin Ng | 12 - - PowerPoint PPT Presentation
Johnson Noise: Determinations of k and Absolute Zero Edwin Ng | 12 - - PowerPoint PPT Presentation
Johnson Noise: Determinations of k and Absolute Zero Edwin Ng | 12 December 2011 Nyquists Theory of Johnson Noise Johnson noise is thermal noise in circuits Nyquists Theory of Johnson Noise Johnson noise is thermal noise in circuits
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Nyquist’s Theory of Johnson Noise
Johnson noise is thermal noise in circuits Two resistors R connected by a wire: I = V2/2R
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Nyquist’s Theory of Johnson Noise
Johnson noise is thermal noise in circuits Two resistors R connected by a wire: I = V2/2R By equipartition, each mode at frequency f has
energy kT
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Theory of Johnson Noise (cont.)
For an RC circuit,
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Theory of Johnson Noise (cont.)
For an RC circuit, Governing formula for Johnson-Nyquist noise:
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Johnson Noise Setup
Adapted from MIT Department of Physics, “Johnson Noise and Shot Noise” (2011).
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Johnson Noise Setup
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Gain and Frequency Band Calibration
Will measure RMS voltage through band pass
filter (from ~1kHz to ~50kHz)
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Gain and Frequency Band Calibration
Will measure RMS voltage through band pass
filter (from ~1kHz to ~50kHz)
Define gain ratio g(f) = Vout(f)/Vin(f)
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Gain and Frequency Band Calibration
Will measure RMS voltage through band pass
filter (from ~1kHz to ~50kHz)
Define gain ratio g(f) = Vout(f)/Vin(f) Integrate the Johnson noise with G(R, C) integral
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Gain and Band Calibration (cont.)
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Measuring RMS Voltages
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Measuring RMS Voltages (cont.)
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Resistance Measurements
Measure RMS voltages of various resistors across
~1kΩ to ~1000 kΩ at T = (23.6 ± 0.2) °C
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Resistance Measurements
Measure RMS voltages of various resistors across
~1kΩ to ~1000 kΩ at T = (23.6 ± 0.2) °C
Governing equation:
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Resistance Measurements
Measure RMS voltages of various resistors across
~1kΩ to ~1000 kΩ at T = (23.6 ± 0.2) °C
Governing equation: Need to determine C
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Determination of Capacitance
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Determination of k with Resistances
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Temperature Measurements
Measure RMS voltages of 500 kΩ resistors across
temperature range -196°C to 150°C
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Temperature Measurements
Measure RMS voltages of 500 kΩ resistors across
temperature range -196°C to 150°C
Governing equation:
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Temperature Measurements
Measure RMS voltages of 500 kΩ resistors across
temperature range -196°C to 150°C
Governing equation: Tc measured in Celsius: T0 is absolute zero
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k and T0 with Temperature
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Conclusions
Best estimate on k
(1.361 ± 0.026rand. ± 0.081syst.) x 10-23 J/K Correct value: 1.381 x 10-23 J/K (≈ 1.5% error)
Determination of absolute zero
T0 = (-274.3 ± 9.3) °C Correct value: -273.15 °C (≈ 2.0% error)
Verified existence and behavior of Johnson-
Nyquist noise
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