654_ch2 - ECE 654 Prof. S. Mohammadi Solid State Devices II...

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ECE 654 Solid State Devices II Prof. S. Mohammadi - 31 - Chapter 2 Noise in Electronic Devices Introduction In this chapter we discuss different noise sources at both low and high frequencies and introduce noise small signal modeling. Noise modeling provides an insight into device noise optimization. Fundamental Noise Sources Let us consider various noise mechanisms that may exist in electronic devices. 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
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ECE 654 Solid State Devices II Prof. S. Mohammadi - 32 - in fact average current (or voltage) is zero V(t) C(t) or t but you can go to frequency domain and plot mean-square value of the noise signal f 2 R i f 2 R v noise spectral density f R kT i R Δ = 4 2 f kTR v R Δ = 4 2 bandwidth of interest (ckt or measurement) 0 = = R R v i noise average is zero but average noise power is not?! why f kTR v R Δ = 4 2 assume a simple ckt of parallel RC
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ECE 654 Solid State Devices II Prof. S. Mohammadi - 33 - 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
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ECE 654 Solid State Devices II Prof. S. Mohammadi - 34 - C kT df f v RC j v R C = Δ + = 2 0 2 2 1 1 ω filtering function f v R Δ 2 f constant white noise f v R Δ 2 f non-white R V R C C V Assuming white noise = R v R 2 constant π d f v C kT R + Δ = 0 2 0 2 2 0 2 2 RC 1 0 = × Δ = RC f v C kT R 2 2 2 f kTR v R Δ = 4 2 kTR f v R 4 2 = Δ f integrate f Δ noise spectral density
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ECE 654 Solid State Devices II Prof. S. Mohammadi - 35 - * 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 0 = F V Ef - e + h 0 > F V Ef 0 > F V current flow special case assume that electrons are very well controlled / behaved and cross the junction in a very uniform manner
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Solid State Devices II Prof. S. Mohammadi - 36 - 1 mA current b 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
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654_ch2 - ECE 654 Prof. S. Mohammadi Solid State Devices II...

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