EE 230 Lecture 33 Nonlinear Circuits and Nonlinear Devices Diode BJT MOSFET
Review from Last Time: n-channel MOSFET Source Gate L Drain W L EFF Poly Gate oxide n-active p-sub depletion region (electrically induced) Bulk
Review from Last Time: Voltage Variable Resistor R 2 A =1+ V R 1 R2 A=1+ V R FET Applications include Automatic Gain Control (AGC) R FET 1 L V -V µc W GS T OX
Review from Last Time: MOS Transistor Models simplifications I=0 G µc W 2 ( ) 2L Saturation OX I= V -V D GS T With λ=0 Saturation Region Model good enough for many analog applications
Review from Last Time: MOS Transistor Models (Summary) µc W OX V -V 1+λV 2L ( 2 ) ( ) GS T DS D V CONT FET S
Review from Last Time: MOS Transistor Applications (Digital Circuits) V DD V DD R Y R Y A M 1 A B 1 2 B M 2 A B Y A B Y Can be extended to arbitrary number of inputs But the resistor is not practically available in most processes and static power dissipation is too high
MOS Transistor Applications (Digital Circuits) DD X 2 1 Y Assume 1 ~ V H = V DD Assume 0 ~ V L = 0V MOSFET Models
MOS Transistor Applications (Digital Circuits) DD 2 Assume 1 ~ V H = V DD X Y Assume 0 ~ V L = 0V 1 MOSFET Models Assume V T1 ~V DD /5 n-channel device Assume V T2 ~ - V DD /5 p-channel device
MOS Transistor Applications (Digital Circuits) DD DD 2 2 X Y X Y 1 1 ~ V H = V DD 0 ~ V L = 0V 1 If X=V DD, then V GS1 =V DD >V T1, V GS2 =0 > V T2 S 1 closed, S 2 open Y = 0V~ 0
MOS Transistor Applications (Digital Circuits) DD DD 2 2 X Y X Y 1 1 1 ~ V H = V DD 0 ~ V L = 0V If X=0V, then V GS1 =0V<V T1, V GS2 =-V DD < V T2 S 2 closed, S 1 open Y = V DD ~ 1
MOS Transistor Applications (Digital Circuits) DD X Y X 2 Y 0 1 1 0 1 Truth Table Performs as a digital inverter
MOS Transistor Applications (Digital Circuits) A 0 0 1 1 B 0 1 0 1 Y 1 0 0 0 Truth Table Performs as a 2-input NOR Gate Can be easily extended to an n-input NOR Gate
MOS Transistor Applications (Digital Circuits) A 0 0 1 1 B 0 1 0 1 Y 1 1 1 0 Truth Table Performs as a 2-input NAND Gate Can be easily extended to an n-input NAND Gate A B Y
MOS Transistor Applications (Digital Circuits) DD DD X M 2 Y A M 3 M 4 M 1 Y M 1 B M 2 Termed CMOS Logic Widely used in industry today (millions of transistors in many ICs using this logic Almost never used as discrete devices
Bipolar Transistor B: Base C: Collector E: Emitter
Bipolar Transistor npn pnp
Bipolar Transistor npn pnp p-type silicon n-type silicon
Vertical npn BJT Base Emitter Collector n+ buried collector implant Buried collector Vertical npn BJT
Lateral pnp BJT BE E C CB Lateral pnp BJT
Bipolar Transistor I C I B5 npn I B4 I B3 I B2 I B1 V CE
Bipolar Transistor C I C B I B V CE V BE E pnp
Bipolar Transistor C B E C npn CE
Bipolar Transistor C npn CE Most analog or linear applications based upon Forward Active region Most digital applications involve Saturation and Cutoff regions and switching between these regions as the Boolean value changes states
Bipolar and MOS Region Comparisons I C Saturation Forward Active V CE MOSFET BJT Cutoff Cutoff Saturation Triode Cutoff Forward Active Saturation
Bipolar Transistor I C I B5 I B4 I B3 I B2 I B1 V CE npn
Bipolar Transistor Multi-Region Model I VBE = V VCE V t CE C JSAEe B VAF VAF JSA I B = β E e V 1 + BE V t = βi 1 + V BE >0.4V V BC <0 Forward Active V t = kt q V BE =0.7V V CE =0.2V I C <βi B Saturation I C =I B =0 V BE <0 V BC <0 Cutoff
Bipolar Transistor I C I B5 I B4 I B3 I B2 I B1 V CE npn
Bipolar Transistor I C = J JSA I B = β V t = S A kt q E e V V E BE t e = βi V V BE t B Simplifier Basic Multi-Region Model V BE >0.4V V BC <0 Forward Active V BE =0.7V V CE =0.2V I C <βi B Saturation I C =I B =0 V BE <0 V BC <0 Cutoff
Small-signal Operation of Nonlinear Circuits Small-signal principles Example Circuit Small-Signal Models Small-Signal Analysis of Nonlinear Circuits
Small-signal Operation of Nonlinear Circuits Small-signal principles Example Circuit Small-Signal Models Small-Signal Analysis of Nonlinear Circuits
Small-Signal Principle y Nonlinear function y=f(x) Y -point X x
Small-Signal Principle y Region around -Point y=f(x) Y -point X x
Small-Signal Principle y Region around -Point y=f(x) Y -point X x Relationship is nearly linear in a small enough region around -point Region of linearity is often quite large Linear relationship may be different for different -points
Small-Signal Principle y y=f(x) Region around -Point Y -point X x Relationship is nearly linear in a small enough region around -point Region of linearity is often quite large Linear relationship may be different for different -points
Small-Signal Principle y -point y ss y=f(x) Y x ss X x Device behaves linearly in neighborhood of -point Can be characterized in terms of a small-signal coordinate system
Small-Signal Principle y Linear Model at -point y=f(x) Y -point y=f(x) X INT y-y x-x f x x=x X y-y = ( ) f = x x x=x x-x
Small-Signal Principle y Linear Model at -point y=f(x) Y -point y=f(x) X INT y-y x-x f x x=x X y-y = ( ) f = x x x=x x-x
Small-Signal Principle Changing coordinate systems: y SS =y-y y-y ( x-x ) x=x x SS =x-x x f = f y = SS x x=x x SS
Small-Signal Principle Small-Signal Model: y SS f = x Linearized model for the nonlinear function y=f(x) Valid in the region of the -point Will show the small signal model is simply Taylor s series expansion at the -point truncated after first-order terms x=x x SS
Small-Signal Principle y -point y SS y=f(x) Observe: y x SS y-y f = x x=x ( x-x ) x x f y y x-x x = + x=x ( ) f y f x x-x x ( ) ( ) = + x=x Small-Signal Model: y SS f = x x=x x SS Mathematically, small signal model is simply Taylor s series expansion at the -point truncated after first-order terms
Small-Signal Principle Goal with small signal model is to predict performance of circuit or device in the vicinity of an operating point Operating point is often termed -point Will be extended to functions of two and three variables
Small-signal Operation of Nonlinear Circuits Small-signal principles Example Circuit Small-Signal Models Small-Signal Analysis of Nonlinear Circuits
Small signal analysis example By selecting appropriate value of V SS, M 1 will operate in the saturation region Assume M 1 operating in saturation region V IN Consider three points on the input waveform V M t V IN =V M sinωt V M is small -V M µc W 2L =V -IR ( ) 2 OX I = V -V -V D IN SS T V OUT DD D µc W 2L ( ) 2 OX V = V V -V -V R OUT DD IN SS T
Small signal analysis example By selecting appropriate value of V SS, M 1 will operate in the saturation region Assume M 1 operating in saturation region V IN =V M sinωt V M is small V OUT V =V -IR OUT DD D µc W 2L ( ) 2 OX I = V -V -V D IN SS T µc W 2L µcoxw = VDD M ω 2L µ C W 2L ( ) 2 OX V = V V -V -V R OUT DD IN SS T 2 ( V sin t [ V + V ]) R SS ( V V ) 2 OX I D = SS + T T
Small signal analysis example V IN =V M sinωt V M is small V V OUT OUT µcoxw = VDD M ω 2L = V DD µcoxw 2L 2 ( V sin t [ V + V ]) R [ V + V ] SS T SS T 2 VM sinω t 1- [ VSS VT ] + 2 R V V OUT OUT = V = V DD DD V Recall that is x is small ( 1+x) 2 1+2x OUT µcoxw 2L µcoxw 2L = V DD µcoxw 2L [ V + V ] SS µc W 2L T 2 1-2V 2 OX [ V + V ] R [ V + V ] SS T µc L W SS M sinω t [ V + V ] T 2 SS 2V M R sinω T [ V + V ] 2 OX [ V + V ] R [ V + V ] R V sinω t SS T SS T SS M T t R
Small signal analysis example V IN =V M sinωt V OUT = V DD µcoxw 2L µc L W 2 OX [ V + V ] R [ V + V ] R V sinω t SS T SS T M uiescent Output ss Voltage Gain A µcoxw = [ VSS VT ]R L v + Alternately, substituting from the expression for I D we obtain A v = 2I [ V + V ] SS D R T
Small signal analysis example V IN =V M sinωt A v = 2I [ V + V ] SS D R T Observe the small signal voltage gain is twice the uiescent voltage across R divided by V SS +V T This analysis which required linearization of a nonlinear output voltage is quite tedious. This approach becomes unwieldy for even slightly more complicated circuits A much easier approach based upon the development of small signal models will provide the same results, provide more insight into both analysis and design, and result in a dramatic reduction in computational requirements
Small-signal Operation of Nonlinear Circuits Small-signal principles Example Circuit Small-Signal Models Small-Signal Analysis of Nonlinear Circuits