Understanding Noise in Active Devices: MOSFETs Schematics & Analysis
Explore the principles of noise in active devices, focusing on MOSFETs, with valid schematics and frequency-dependent models. Learn about thermal noise, flicker noise, and the relationship between noise expressions in MOSFETs. Discover equivalent gate noise and the equivalence between output-referred and input-referred noise models in microelectronic system design.
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Noise in active devices MOSFETs This noise schematization is valid up to a frequency that depends on the process and device length. Generally, for integrated MOSFETs, it is possible to use this single-source model up to frequencies of several hundred MHz P. Bruschi Design of Mixed Signal Circuits 1
Mosfet Thermal noise 8 3 = ( ) f S kTg m Typically: In T m g 1 1.5 m = + 1 mB g m m Being frequency independent, thermal noise is the origin of the broad-band noise in MOSFETs A more general expression: = ( ) 4 S f kTg In T n m 1 R 2 3 = = 4 4 S kT kTG = 1 m In R n P. Bruschi Microelectronic System Design 2
Mosfet flicker noise Frequently used by designers of analog integrated circuits N 1 f f = 2 m ( ) S f g In F WL Nfis a parameter that depends on the process N-MOS: Nfn P-MOS: Nfp ( m) 2 2 V Dimensions of Nfare: k I C 1 f A more general expression of the flicker PSD (can be used in SPICE) fi = ( ) f S In F 2 eff L OX P. Bruschi Microelectronic System Design 3
Relationship between the two noise expressions N 1 f = 2 g I f = 2 m ( ) S f g m D In F WL 2 N WL f N C I 1 1 f W L f f OX = ( ) f 2 = S C I In F OX D 2 L k = = k I C 1 1 1 f fi =2 N fi = ( ) f S f 2 OX In F C 2 eff L OX P. Bruschi Microelectronic System Design 4
Equivalent gate noise ? Substituting inwith a single voltage source in series with the gate gives a contribution that depends on the resistance (R) seen by the gate. 1 = = = dn i i dn i m gs g v m n g v n + 1 j Rc gs P. Bruschi Microelectronic System Design 5
Equivalence between the output referred and input referred noise models input referred model output referred model v + gn i R j Rc 1 1 n = g = dn i g v i m 1 m n gn + + j c 1 1/ j Rc R gs gs gs Independent of R, as required for the equivalence with the output referred model, which results in: dn i By setting: = j c v = i dn i v g = i gn gs n n m n P. Bruschi Microelectronic System Design 6
Equivalence between the output referred and input referred noise models = j c v i gn gs n i = n v = i v g n g n n m m Note that ignis dependent on vn (they are correlated stochastic processes) P. Bruschi Microelectronic System Design 7
Transformations between drain noise current and gate noise voltage i = = i v g n v n n m n g m ( ) 2 m g S f ( ) f ( ) f ( ) f = = In 2 m S S g S In Vn Vn 8 3 N WL f 1 8 3 = ( ) f Vn T S kTmg 1 f = ( ) f S kTg m Thermal noise: In T m m N 1 f = ( ) f Vn F S f = 2 m ( ) S f g Flicker noise: In F WL P. Bruschi Microelectronic System Design 8
Noise in BJTs Since the BJT has a non negligible base current, it is necessary to use two distinct current noise sources for the base and the collector Simplified BJT noise model Collector noise current Base flicker noise = 2 S qI I InC C = 2 + B S qI k InB B fB f Only shot noise (broad-band) Base shot noise (broad-band) P. Bruschi Microelectronic System Design 9
MOSFET vs BJT Let us consider only the drain (in) and collector (inc) noise sources. = 2 3 n MOS ( ) f 4 S kTg = 2 S qI In T m InC C kT q I V n MOS = 1 m = = = I m T g V g C g C m m T 2 kT q 1 2 = = 2 S qg kTg n BJT = = n BJT ( ) f 4 S kTg InC m m InC m P. Bruschi Microelectronic System Design 10
BJT input referred noise voltage nC i g = v n 1 z 1 r + j c m v z be = n bn v i in be in + v v v if z R be S n in S The noise voltage source vnis the only significant contribution to the input referred noise V I 1 = = 2 kT T 2 S kTg BJT: Vn C m 1 g V Much more noise for the same static current consumption! = 4 4 S kT kT TE I MOSFET Vn m D P. Bruschi Microelectronic System Design 11
The Noise Efficiency Factor (NEF) Since the single-BJT amplifier offers an excellent trade-off between noise and power consumption, in 1987 M. Steyaert (KU Leuven University) proposed a FOM (figure of merit) called NEF to characterize all voltage amplifiers in terms of noise efficiency Total rms noise of the amplifier under consideration rms rti V = NEF V 4 kT B T Effective noise bandwidth and total current consumption of the amplifier under consideration 2 I supply Denominator = 2 rms bjt V Input rms voltage of a BJT with same current and BW of the amplifier P. Bruschi Microelectronic System Design 12
