noise_notes_set7_new

noise_notes_set7_new - ECE594I notes M Rodwell copyrighted...

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ECE594I notes, M. Rodwell, copyrighted ECE594I Notes set 7: Shot Noise Mark Rodwell University of California, Santa Barbara [email protected] 805-893-3244, 805-893-3262 fax
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ECE594I notes, M. Rodwell, copyrighted References and Citations: Devices State - Solid in Noise : Ziel der Van Physics Thermal : Kroemer and Kittel : Citations / Sources g. ngineeri ns ommunicat f rinciple cobs ozencraft ory) (introduct s Principle Signal Random Variables, Random ty, Probabili : Peebles Z. Peyton ive) comprehens (hard, Variables Random and ity Probabil : Papoulis 982 rca tanford ellman artin otes cture robabilit 1982 circa Stanford, Cover, Thomas : notes lecture theory n Informatio Design c Electroni Noise Low : er Motchenbak ng. Engineeri ions Communicat of s Principle : Jacobs & Wozencraft d f t d circuits. in Noise : Notes ns Applicatio tor Linear Semiconduc National 1982 circa Stanford, Hellman, Martin : notes lecture y Probabilit design) receiver (optical Personik & Smith noise), (device by Fukui Papers Kroemer and Kittel Peebles, Jacobs, & Wozencraft Ziel, der Van study. for references Suggested Theory n Informatio of Elements : Williams and Cover ) (! Notes App. Semi. National
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ECE594I notes, M. Rodwell, copyrighted Shot Noise ( idealized) rocess ealized n rst ocus events. emission t independen with process idealized on first Focus ns proximat me ith his late ill e tors. semiconduc in ansport carrier tr to ions, approximat some with this, relate will We 2. 1 region from emission of y probabilit a is there , period time small some in observed that, Suppose 1 1 p τ / flux electron average 1 1 p r = = charge electron write here clarity we notational for / current DC average 1 1 q p q I = = = ). 1 ( for shorthand a as use not and p q
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ECE594I notes, M. Rodwell, copyrighted Shot Noise (idealized) ) 1 ( period the is period Time . increments time small consider Now t i t t i t t i Δ + < < Δ Δ Δ Then . period other any in emitted electrons of # the of t independen is each in emitted electrons of # The ) 1 t t Δ Δ ) ( ) ( electrons) ( 2) k p k p k p t t i i = = Δ Δ robabilit f ch rials e here ecause ) 1 ( / ) 1 / ( 1 1 p p k t t k τ Δ = Δ . y probabilit of each trials ) / ( are there because 1 p t Δ
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ECE594I notes, M. Rodwell, copyrighted Shot Noise (idealized) here ses nl nsider e < > ariance d ean ith aussian : work g simplifyin Gaussian, a to converge will on distributi the ) 1 ( , 1 ) / ( where cases only consider we If τ p p t p << >> Δ ) / ( variance and ) / ( mean with Gaussian ) ( t p t p k p i t Δ Δ = Δ : ns fluctuatio and values mean the separately Consider t k k E k E k k Δ = = = = Δ . in flux electron mean ] [ where flux, in n fluctuatio ] [ k k k = Δ 2 variance with Gaussian is σ
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ECE594I notes, M. Rodwell, copyrighted Shot Noise [ ] j i j i j i k k E t t 2 eriod ime me r the ut for 0 : and steps time g differenin For = Δ Δ Δ Δ [ ] k i i k k E 2 eneral o :
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noise_notes_set7_new - ECE594I notes M Rodwell copyrighted...

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