模拟集成电路设计精粹课件4

Noise performance of elementary transistor stagesWilly SansenKULeuven, ESAT-MICAS Leuven, Belgiumwilly.sansen@esat.kuleuven.beWilly Sansen10-05

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SNR and SNDRvOUTSNR 0.1% SNDR 1% distortion 0.1% distortion

0 0 vIN

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Table of contents Definitions Noise Noise Noise Noise Noise

of noise

of an amplifier of a follower of a cascode of a current mirror of a differential pair noise matching

Capacitive

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Noise versus timevN

t vN2 vN2 is the average noise power

tRef. Van der Ziel (Prentice Hall 1954, Wiley 1986), Ott (Wiley 1988)Willy Sansen10-05

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Noise versus frequencyvN2

Noise density V2/Hz1/f noise dvN2

VRMS/√Hzwhite noise

f

Integrated noise VRMSv12=

f1 vN2=

df

f2

∫

f2

f1

dvN2 df=

(f2- f1) dvN2Willy Sansen10-05

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Noise of a resistor is thermal noisedvR2

dvR2= 4kT R dfdepends on T, not on IR for R= 1 k

is white

R

dvR2= 4 nVRMS/ Hz at T= 300 K or 27oC

R

diR2

diR2=

dvR2 R2

=

4kT R

df

is white

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Integrated Noise of Resistor - 1dvRs2 RS vout CL f BW dvRs2= 4kT RS df vRs=2

A

vin

BW=

1 2π RSCL

∫0

∞

dvRs

2

1+ (f/ BW) 2Willy Sansen10-05

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Integrated Noise of Resistor - 2A vRs2= fπ BW BWn= BW 2

∫0

∞

dvRs2 1+ (f/ BW) 2∞

0

∫ 1+x

dx

2

π= 2

vRs2= 4kT RSBWπ df 2 vRs2= kT CLWilly Sansen10-05

CL= 1pF vRs= 65µVRMS

048

Noise density vs integrated noiseA dvRs2= 4kT RS df

f BW BWn

vRs=

2

∫0

∞

dvRs2 1+ (f/ BW) 2

kT= CL

Noise density (V2/Hz)~ RS (or 1/gm) Integrated noise (VRMS)~ 1/CLWilly Sansen 049

10-05

A resistor also has 1/f noisedvRf2

dvRf2=

VR2

KFRR AR

df f

is 1/f

VR -

+

R

KFRSi≈ 2 10 -21 Scm2 KFRpoly≈ 10 KFRSi

for R= 1 k with 20

‘s of 50 /

and 1µm wide and VR= 0.1 V

dvRf2= 16 nVRMS/ Hz at 1 HzRef. Vandamme, ESSDERC‘04Willy Sansen10-05

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Noise of a diode is shot noiseID diD2

diD2= 2q ID dfq= 1.6 10-19 C

is white

depends on ID, not on T

for ID= 50µA

diD2= 4 pARMS/ HzWilly Sansen10-05

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A diode also has 1/f noiseID diDf2

diDf2= ID

KFD df AD f

is 1/f

KFD≈ 10 -21 Acm2

For a diode of AD= 5 x 2µm= 10µm2 and ID= 0.1 mA diDf2= 1 nARMS/ Hz at 1 HzWilly Sansen10-05

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Noise of a MOSTdvG2+ vin RG+ vGS gmvGS rDS diDS2+ vout -

dvG2= 4kT RG df diDS2=

4kT 2 df= 4kT gm df RCH 3Ref. Van der Ziel, Prentice Hall 1954, Wiley 1986.Willy Sansen10-05

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MOST: equivalent input noise: whitedvieq2+ vin RG+ vGS gmvGS rDS+ vout -

dvieq

2=

4kT (Reff ) df

2/3 Reff=+ RG gm

Hi Freq.: diieq2= (CGSω)2 dvieq2 is correlated

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Poly Gate resistance rG in a MOST

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Substrate resistances rB in a MOST

Ref. Chang, Kluwer 1991Willy Sansen10-05

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