EE 230 Lecture 33. Nonlinear Circuits and Nonlinear Devices. Diode BJT MOSFET


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1 EE 230 Lecture 33 Nonlinear Circuits and Nonlinear Devices Diode BJT MOSFET
2 Review from Last Time: nchannel MOSFET Source Gate L Drain W L EFF Poly Gate oxide nactive psub depletion region (electrically induced) Bulk
3 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
4 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
5 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
6 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
7 MOS Transistor Applications (Digital Circuits) DD X 2 1 Y Assume 1 ~ V H = V DD Assume 0 ~ V L = 0V MOSFET Models
8 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 nchannel device Assume V T2 ~  V DD /5 pchannel device
9 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
10 MOS Transistor Applications (Digital Circuits) DD DD 2 2 X Y X Y ~ 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
11 MOS Transistor Applications (Digital Circuits) DD X Y X 2 Y Truth Table Performs as a digital inverter
12 MOS Transistor Applications (Digital Circuits) A B Y Truth Table Performs as a 2input NOR Gate Can be easily extended to an ninput NOR Gate
13 MOS Transistor Applications (Digital Circuits) A B Y Truth Table Performs as a 2input NAND Gate Can be easily extended to an ninput NAND Gate A B Y
14 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
15 Bipolar Transistor B: Base C: Collector E: Emitter
16 Bipolar Transistor npn pnp
17 Bipolar Transistor npn pnp ptype silicon ntype silicon
18 Vertical npn BJT Base Emitter Collector n+ buried collector implant Buried collector Vertical npn BJT
19 Lateral pnp BJT BE E C CB Lateral pnp BJT
20 Bipolar Transistor I C I B5 npn I B4 I B3 I B2 I B1 V CE
21 Bipolar Transistor C I C B I B V CE V BE E pnp
22 Bipolar Transistor C B E C npn CE
23 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
24 Bipolar and MOS Region Comparisons I C Saturation Forward Active V CE MOSFET BJT Cutoff Cutoff Saturation Triode Cutoff Forward Active Saturation
25 Bipolar Transistor I C I B5 I B4 I B3 I B2 I B1 V CE npn
26 Bipolar Transistor MultiRegion 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
27 Bipolar Transistor I C I B5 I B4 I B3 I B2 I B1 V CE npn
28 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 MultiRegion 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
29 Smallsignal Operation of Nonlinear Circuits Smallsignal principles Example Circuit SmallSignal Models SmallSignal Analysis of Nonlinear Circuits
30 Smallsignal Operation of Nonlinear Circuits Smallsignal principles Example Circuit SmallSignal Models SmallSignal Analysis of Nonlinear Circuits
31 SmallSignal Principle y Nonlinear function y=f(x) Y point X x
32 SmallSignal Principle y Region around Point y=f(x) Y point X x
33 SmallSignal 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
34 SmallSignal 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
35 SmallSignal 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 smallsignal coordinate system
36 SmallSignal Principle y Linear Model at point y=f(x) Y point y=f(x) X INT yy xx f x x=x X yy = ( ) f = x x x=x xx
37 SmallSignal Principle y Linear Model at point y=f(x) Y point y=f(x) X INT yy xx f x x=x X yy = ( ) f = x x x=x xx
38 SmallSignal Principle Changing coordinate systems: y SS =yy yy ( xx ) x=x x SS =xx x f = f y = SS x x=x x SS
39 SmallSignal Principle SmallSignal 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 firstorder terms x=x x SS
40 SmallSignal Principle y point y SS y=f(x) Observe: y x SS yy f = x x=x ( xx ) x x f y y xx x = + x=x ( ) f y f x xx x ( ) ( ) = + x=x SmallSignal Model: y SS f = x x=x x SS Mathematically, small signal model is simply Taylor s series expansion at the point truncated after firstorder terms
41 SmallSignal 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
42 Smallsignal Operation of Nonlinear Circuits Smallsignal principles Example Circuit SmallSignal Models SmallSignal Analysis of Nonlinear Circuits
43 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
44 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
45 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 12V 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
46 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
47 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
48 Smallsignal Operation of Nonlinear Circuits Smallsignal principles Example Circuit SmallSignal Models SmallSignal Analysis of Nonlinear Circuits
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