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**Unformatted text preview: **Last Time Planck Blackbody Radiation Stefan-Boltzmann Law Radiation energy flux density U B J T = 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 & 2.82 & 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 = 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 = '/ 2 n f nc L = 1 '/ 2 f c L = 2 2 '/ 2 f c L = 2 f For energy >> & And energy within f is: ( ) / 2 / ' f f L f c = This energy is absorbed by resistors in time t = L/c, and power within f Thermal Electrical Noise Transmission line photon modes: 2 f In thermal equilibrium the absorbed energy should equal to the emitted: This energy is absorbed by resistors...

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