Lect2UP290_(100328)

# Lect2UP290_(100328) - Lecture 290 Low Power and Low Noise...

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Lecture 290 – Low Power and Low Noise Op Amps (3/28/10) Page 290-1 CMOS Analog Circuit Design © P.E. Allen - 2010 LECTURE 290 – LOW POWER AND LOW NOISE OP AMPS LECTURE ORGANIZATION Outline • Review of subthreshold operation • Low power op amps • Review of MOSFET noise modeling and analysis • Low noise op amps • Summary CMOS Analog Circuit Design, 2 nd Edition Reference Pages 393-414 Lecture 290 – Low Power and Low Noise Op Amps (3/28/10) Page 290-2 CMOS Analog Circuit Design © P.E. Allen - 2010 REVIEW OF SUBTHRESHOLD OPERATION Subthreshold Operation Most micropower op amps use transistors in the subthreshold region. Subthreshold characteristics: The model that has been developed for the large signal sub- threshold operation is: i D = I t W L exp ± ² ² ³ ´ µ µ v GS - V T nV t ± ² ² ³ ´ µ µ 1 + v DS V A where v DS > 0 and V DS (sat) = V ON = V GS - V T = 2 nV t Small-signal model: g m = di D dv GS | Q = I t W L I t nV t exp ± ² ² ³ ´ µ µ v GS - V T nV t ± ² ² ³ ´ µ µ 1 + v DS V A = I D nV t = qI D nkT = I D V t C ox C ox + C js g ds = di D dv DS | Q · I D V A 100nA 1 μ A Weak Inversion Transition Strong Inversion Square Law Exponential i D v GS i D v DS V T 100nA v GS = V T v GS V T Fig. 7.4-0A 1V 2V 0 0 0 0

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Lecture 290 – Low Power and Low Noise Op Amps (3/28/10) Page 290-3 CMOS Analog Circuit Design © P.E. Allen - 2010 Boundary Between Subthreshold and Strong Inversion It is useful to develop a means of estimating when a MOSFET is making the transition between subthreshold and strong inversion to know when to use the proper model. The relationship developed is based on the following concept: We will solve for the value of v GS (actually v GS - V T ) and find the drain current where these two values are equal [ v GS (tran.) - V T )]. The large signal expressions for each region are: Subthreshold- i D ± I t W L exp ± ² ² ³ ´ µ µ v GS - V T nV t · v GS - V T = nV t ln ± ² ² ³ ´ µ µ i D I t ( W/L ) ± nV t ± ² ² ³ ´ µ µ 1 - I t ( W/L ) i D if 0.5 < i D /( I t W/L ). Strong inversion- i D = K'W 2 L ± ³ ´ v GS - V T 2 · v GS - V T = 2 i D K' ( W/L ) i D v GS V T i D = ( v GS - V T ) 2 K‘W 2 L i D = nV t v GS - V T I t W L exp ( ) i D (tran.) v GS (tran.) 070507-01 Lecture 290 – Low Power and Low Noise Op Amps (3/28/10) Page 290-4 CMOS Analog Circuit Design © P.E. Allen - 2010 Boundary Between Subthreshold and Strong Inversion - Continued Equating the two large signal expressions gives, nV t ± ² ² ³ ´ µ µ 1 - I t ( W/L ) i D = 2 i D K' ( W/L ) · n 2 V t 2 ± ² ² ³ ´ µ µ 1 - I t ( W/L ) i D 2 = 2 i D K' ( W/L ) Expanding gives, n 2 V t 2 ± ² ² ³ ´ µ µ I t 2 ( W/L ) 2 i D 2 - 2 I t ( W/L ) i D + 1 ± n 2 V t 2 = 2 i D K' ( W/L ) if ( I t W/L )/ i D < 0.5 Therefore we get, i D (tran.) = K'W 2 L n 2 V t 2 For example, if K’ = 120 μ A/V 2 , W/L = 100, and n = 2, then at room temperature the value of drain current at the transition between subthreshold and strong inversion is i D (tran.) = 120 μ A/V 2 100 2 4·(0.026) 2 = 16.22 μ A One will find for UDSM technology, that weak inversion or subthreshold operation can occur at large currents for large values of W/L .