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Lecture07-04.2-Johnson_noise-Debye_model

# Lecture07-04.2-Johnson_noise-Debye_model - Last Time Planck...

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Unformatted text preview: Last Time Planck Blackbody Radiation Stefan-Boltzmann Law Radiation energy flux density U B J T σ = Peak frequency in spectrum tells temperature Big Bang: background radiation from expansion of universe Entropy of thermal photons: 2 4 3 2 60 B B k c σ π ≡ & 2.82 ω τ ≈ & Today Chapter 4 (part 2) Johnson noise, Debye model of phonons Johnson noise (thermal electrical noise) Phonons in solid: Debye model Heat capacity of a solid Thermal Electrical Noise V Planck law in one dimension Discovered by J.B. Johnson – noise <V 2 > ~ R (resistance) Explained by H. Nyquist (1928) Thermal Electrical Noise 2 4 V R f τ = Δ Nyquist theorem: Frequency bandwidth ' V I R R = + ( ) 2 2 2 ' ' ' V R P I R R R = = + For R=R’ the noise power is maximum in respect to R’ ( ) 2 2 2 4 2 V R V P R R = = The origin of “4” Thermal Electrical Noise Assume lossless transmission along line L – electromagnetic system in one dimension. Transmission line photon modes: One mode in frequency range '/ 2 f c L δ = '/ 2 n f nc L = 1 '/ 2 f c L = 2 2 '/ 2 f c L = 2 f τ Δ For energy τ ω >> & ε τ ≈ And energy within Δ f is: ( ) / 2 / ' f f L f c τ δ τ Δ = Δ This energy is absorbed by resistors in time Δ t = L/c’, and power within Δ f Thermal Electrical Noise Transmission line photon modes: 2 f τ Δ In thermal equilibrium the absorbed energy should equal to the emitted: This energy is absorbed by resistors...
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Lecture07-04.2-Johnson_noise-Debye_model - Last Time Planck...

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