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Unformatted text preview: ECE695F RFIC Prof. S. Mohammadi Noise in Integrated Circuits Fundamental Noise Sources Thermal Noise (Johnson Noise, Nyquist Noise) arises from thermally excited random motion of electrons in a conductive medium Properties of thermal noise 1) noise is white (?) 2) noise is proportional to temperature 3) not associated with DC current 4) can find it in any real physical resistor f Noise Spectral Density Representation of thermal noise R R 2 R i or 2 R v R does not mean the current is in certain direction 114  ECE695F RFIC Prof. S. Mohammadi in fact average current (or voltage) is zero V(t) C(t) or t but you can go to frequency domain and plot meansquare value of the noise signal f 2 R i f 2 R v noise spectral density f R kT i R = 4 2 f kTR v R = 4 2 bandwidth of interest (ckt or measurement) = = R R v i noise average is zero but average noise power is not?! why f kTR v R = 4 2 assume a simple ckt of parallel RC 115  ECE695F RFIC Prof. S. Mohammadi 2 C v 2 R v R C noiseless capacitor An equipartition theorem of statistical thermodynamic for each degree of freedom (or mode) in a given system, there is a thermal energy of kT 2 1 k: Boltzmann constant K J 23 10 38 . 1 Total energy of the system 2 2 1 2 1 C v C kT = = C kT v C = 2 total mean square voltage density integrated over all frequencies 116  ECE695F RFIC Prof. S. Mohammadi C kT df f v RC j v R C = + = 2 2 2 1 1 filtering function f v R 2 f constant white noise f v R 2 f nonwhite R V R C C V Assuming white noise = R v R 2 constant d f v C kT R + = 2 2 2 2 2 RC 1 = = RC f v C kT R 2 2 2 f kTR v R = 4 2 kTR f v R 4 2 = f integrate f noise spectral density 117  ECE695F RFIC Prof. S. Mohammadi * Actual power spectral density of thermal noise f constant THz h kT 6 for all practical purpose K J 23 10 38 . 1 sec 10 625 . 6 34 = J Plank constant Thermal noise is a white noise Shot noise * associated with DC current flow across a junction * arises from random nature of electrons and holes surmounting a potential barrier Ef e + h = F V Ef e + h > F V Ef > F V current flow 118  ECE695F RFIC Prof. S. Mohammadi special case assume that electrons are very well controlled / behaved and cross the junction in a very uniform manner 1 mA current uniform current pulses sec 10 6 . 1 10 1 10 6 . 1 16 3 19 = = = = I Q t t Q I every so many second one electron passes t i(t) sec 10 6 . 1 16 Fourier transform f I(f) no energy dc current GHz 6 10 6 GHz 6 10 12 no noise ! 119  ECE695F RFIC Prof. S. Mohammadi in reality carriers surmount the barrier in a random fashion t i(t) f I(f) dc current 1 current transit time in the depletion region : 1 hundreds of GHz So for all practical purposes shot noise is a white noise again it is better to talk about noise spectral density f I q i D n = 2 2 f constant 2...
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 Fall '09
 Mohammadi
 Integrated Circuit

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