ECE594I Notes set 13: Two-port Noise Parameters

Transcription

1 C594 otes, M. Rodwell, copyrighted C594 Notes set 13: Two-port Noise Parameters Mark Rodwell Uiversity of Califoria, Sata Barbara , fax

2 Refereces ad Citatios: C594 otes, M. Rodwell, copyrighted Sources / Citatios : Kittel ad Kroemer : Thermal Physics Va der Ziel : Noise i Solid - State Devices Papoulis : Probabil ity ad Radom Variables (hard, comprehes ive) Peyto Z. Peebles : Probabili ty, Radom Variables, Radom Sigal Priciple s (itroduct ory) Wozecraft & Jacobs : Priciple s of Commuicat ios gieeri g. Motchebak er : Low Noise lectroi c Desig formatio theory lecture otes : Thomas Cover, Staford, circa 1982 Probabilit y lecture otes : Marti Hellma, Staford, circa 1982 Natioal Semicoductor Liear Applicatio s Notes : Noise i circuits. Suggested refereces for study. td Va der Ziel, Wozecraft & Jacobs, Peebles, Kittel ad Kroemer Papers by Fukui (device oise), Smith & Persoik (optical receiver desig) Natioal Semi. App. Notes (!) Cover ad Williams : lemets of formatio Theory

3 Two-Port Noise Descriptio C594 otes, M. Rodwell, copyrighted Through the methods of circuit aalysis, the iteral oise erators of a circuit ca be summed ad represete d by two oise erators ad. The spectral desities of The cross spectral ad desity must also must be calculated ad specified. be calculated ltdad specified.

4 Calculatig Total Noise C594 otes, M. Rodwell, copyrighted f S the erator ktr N = 4, just has thermal oise, Represet the combiatio of amplifier voltage ad curret oise by a sigle source Total = N + N Z We ca ow calculate 2 S = Z g S, total, amplifier 2 = Z S g the spectral + 2 Re S + 2 Re S { Z } * desity of this ( R jx ) { } g total oise :

5 Sigal / Noise Ratio of Geerator C594 otes, M. Rodwell, copyrighted V ad are i series ad see the same load impedace. sigal,, total, The ratios of powers delivered by these will ot deped upo the load. Therefore cosider t he aviable oise powers. The sigal power available from the erator is 2 Psigal available = Vsigal RMS / 4R,, f we cosider a arrow badwidth betwee ( the P the available oise power from N, is 2 = [ ] = S ( jf ) Δf / 4R oise, available, erator, f sigal Δf / 2) ad ( f sigal + Δf / 2), The sigal/oise ratio of the erator is the SNR = P 2 2 P sigal, available V sigal, RMS / 4R V sigal, RMS / 4R = = S ( jf ) Δf / 4R kt Δf oise, available, erator,

6 Sigal / Noise Ratio of Geerator+Amplifier C594 otes, M. Rodwell, copyrighted Sigal power available from the erator Noise power available from erator : Poise av, : P V / 4R sigal, available = 2 sigal, RMS = S Δf / 4R, V Noise power available from amplifier : Poise, av, Amp = S Δ, total, amplifier = kt Δf f / 4R Sigal/oise ratio icludig amplifier oise : SNR = = P S oise, avail, total V 2 P sigal, available V sigal, RMS / 4R = + P S Δf / 4R + S 2 sigal, RMS Δf / 4R oise, avail, amp / 4R + kt Δf total, Δf / 4R

7 C594 otes, M. Rodwell, copyrighted Noise Figure: Sigal / Noise Ratio Degradatio Noise figure = sigal/oise sigal/oise ratio ratio before before addig addig amplifier amplifier Sigal/oise ratio before addig amplifier : SNR = V 2 sigal, RMS kt Δf / 4R Sigal/oise ratio after addig amplifier : SNR = S total V 2 sigal, RMS Δf / 4R / 4R + kt Δf Noise figure = F = S total Δf / 4R kt Δf + kt Δf S / 4R total Noise figure = 1 + = 1 + kt amplifier available iput oise kt power

8 Calculatig Noise Figure C594 otes, M. Rodwell, copyrighted Noise figure = 1 + S total / 4 kt R We also kow that : S = Z total, amplifier g + 2 S 2 Re { S Z * }, g We ca calculate from this a expressio for oise figure : F = 1 + S + Z s 2 S + 2 Re 4kTR * ( Z S ) s

9 Miimum Noise Figure C594 otes, M. Rodwell, copyrighted Noise figure varies as a fuctio of Z = R + jx : F = 1 + S 2 Z S 2 Re Z S * + + ( ) s 4kTR s After some calculus, we ca fid a mimimum oise figure ad a erator impedace which gives us this miimum : F mi 1 = 1 + 4kT 2 S S ( m [ S ] ) Re [ S ] S m [ ] 2 S m[ S ] Z opt = Ropt + jx opt = j S S S Pit Poits which to remember : () (a) gives a miimum F varies F (c). with Z, (b) hece there is a optimum Z

10 Noise Figure i Wave Notatio C594 otes, M. Rodwell, copyrighted Writte F = F mi istead i terms of wave 4 r Γ s Γ opt + [ ] 2 [ ] 2 1 Γs 1 Γopt 2 parameters, These describe cotous i the Γs plae of costat oise figure :" oise figure circles", i.e. a descriptio of with source the reflectio variatio of coefficie t. oise figure

11 Low-Noise Amplifier Desig C594 otes, M. Rodwell, copyrighted Desig steps are 1) i-bad stabilizatio: this is best doe at output port to avoid degradig oise 2) iput tuig for F mi 3) output tuig (match) 4) out-of-bad of stabilizatio Note that tuig for miimum oise figure requires a *mismatch* o the amplifier iput; amplifier gai therefore must lie below the trasistor MAG/MSG. Note that tuig for miimum oise figure implies that amplifier iput is mismatched: iput reflectio coefficiet is therefore ot zero! Discrepacy i iput oise-match & gai-match ca be reduced by addig source iductace Z s =Z o Z s oise match V

12 xample LNA Desig: 60 GHz, 130 m SiGe BJT C594 otes, M. Rodwell, copyrighted gai & oise circles after iput matchig ote compromise betwee gai & oise tuig

13 Friis Formula for Noise Figure C594 otes, M. Rodwell, copyrighted Available gai : power gai of the amplifier with the * output * matched P power available from the amplifier output G = AVA A = P power available from the erator AVG to the load Noise figure of a cascade of amplifiers F total = F F2 1 + G F 1 G A1 GA 1 A2... Here the oise figures ad available gais of each amplifier are calculated a source impedace equal to the output impedace of the prior stage. give usig The Friis expressio will ot be prove here due to time limits.

14 Noise Measure C594 otes, M. Rodwell, copyrighted Oe peculiarit y of oise figure is that ay active device has poorer oise figure tha a simple wire coectig iput ad output. We eed to amplify a sigal to use it, ad that comes at the cost of icreased oise relative to the sigal. Clearly F is ot a the best figure - of - merit for a low - oise amplfier! Defie F = F F as the oise figure of a ifiite F G A F G A F G A cascade of idetical amplifiers : The * oise measure * is M = F 1 the defied as so : Maso proves that M is a etwork ivariat, i.e. is ivariat with respect to embeddig the device i a lossless reciprocal etwork. This implies i particular that t M is the same for a FT i commo - source cofigurat ios. / commo - gate ad commo - drai

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