EE 330 Lecture 24. Amplification with Transistor Circuits Small Signal Modelling

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1 EE 330 Lecure 24 Amplificaion wih Transisor Circuis Small Signal Modelling

2 Review from las ime Area Comparison beween BJT and MOSFET BJT Area = 3600 l 2 n-channel MOSFET Area = 168 l 2 Area Raio = 21:1

3 Review from las ime Operaing Poin of Elecronic Circuis Ofen ineresed in circuis where a small signal inpu is o be amplified The elecrical por variables where he small signal goes o 0 is ermed he Operaing Poin, he Bias Poin, he Quiescen Poin, or simply he Q-Poin By seing he small signal o 0, i means replacing small volage inpus wih shor circuis and small curren inpus wih open circuis When analyzing small-signal amplifiers, i is necessary o obain he Q-poin When designing small-signal amplifiers, esablishing of he desired Q-poin is ermed biasing Capaciors become open circuis (and inducors shor circuis) when deermining Q-poins Simplified dc models of he MOSFET (sauraion region) or BJT (forward acive region) are usually adequae for deermining he Q-poin in pracical amplifier circuis

4 Amplificaion wih Transisors From Wikipedia: Generally, an amplifier or simply amp, is any device ha changes, usually increases, he ampliude of a signal. The "signal" is usually volage or curren. I is difficul o increase he volage or curren very much wih passive RC circuis olage and curren levels can be increased a lo wih ransformers bu no pracical in inegraed circuis Power levels can no be increased wih passive elemens (R, L, C, and Transformers) Ofen an amplifier is defined o be a circui ha can increase power levels (be careful wih Wikipedia and WWW even when some of he mos basic conceps are discussed) Transisors can be used o increase no only signal levels bu power levels o a load In ransisor circuis, power ha is delivered in he signal pah is supplied by a biasing nework

5 Amplificaion wih Transisors IN Amplifier RL + - OUT Usually he gain of an amplifier is larger han 1 OUT = AIN Ofen he power dissipaed by R L is larger han he power supplied by An amplifier can be hough of as a dependen source ha was discussed in EE 201 Inpu and oupu variables can be eiher or I or mixed

6 Applicaions of Devices as Amplifiers I C, I D Logic Circuis Linear Circuis C Logic Circuis Typical Regions of Operaion by Circui Funcion MOS Bipolar Triode and Cuoff Sauraion and Cuoff CE, DS Linear Circuis Sauraion Forward Acive

7 Consider he following MOSFET and BJT Circuis BJT MOSFET CC R R 1 Q 1 () () EE Assume BJT operaing in FA region, MOSFET operaing in Sauraion Assume same quiescen oupu volage and same resisor R 1 Noe archiecure is same for BJT and MOSFET circuis One of he mos widely used amplifier archiecures

8 Consider he following MOSFET and BJT Circuis BJT CC R 1 MOSFET R 1 () Q 1 () EE MOS and BJT Archiecures ofen Idenical Circui are Highly Nonlinear Nonlinear Analysis Mehods Mus be used o analyze hese and almos any oher nonlinear circui

9 Mehods of Analysis of Nonlinear Circuis KCL and KL apply o boh linear and nonlinear circuis Superposiion, volage divider and curren divider equaions, Thevenin and Noron equivalence apply only o linear circuis! Some oher analysis echniques ha have been developed may apply only o linear circuis as well

10 Mehods of Analysis of Nonlinear Circuis Will consider hree differen analysis requiremens and echniques for some paricularly common classes of nonlinear circuis 1. Circuis wih coninuously differenial devices Ineresed in obaining ransfer characerisics of hese circuis or oupus for given inpu signals 2. Circuis wih piecewise coninuous devices Ineresed in obaining ransfer characerisics of hese circuis or oupus for a given inpu signals 3. Circuis wih small-signal inpus ha vary around some operaing poin Ineresed in obaining relaionship beween small-signal inpus and he corresponding small-signal oupus. Will assume hese circuis operae linearly in some suiably small region around he operaing poin Oher ypes of nonlineariies may exis and oher ypes of analysis may be required bu we will no aemp o caegorize hese scenarios in his course

11 1. Nonlinear circuis wih coninuously differenial devices Analysis Sraegy: Use KL and KCL for analysis Represen nonlinear models for devices eiher mahemaically or graphically Solve he resulan se of equaions for he variables of ineres

12 2. Circuis wih piecewise coninuous devices e.g. f x Analysis Sraegy: f x x x 1 1 f x x x 2 1 Guess region of operaion region 1 region 2 Solve resulan circui using he previous mehod erify region of operaion is valid Repea he previous 3 seps as ofen as necessary unil region of operaion is verified I helps o guess righ he firs ime bu a wrong guess will no resul in an incorrec soluion because a wrong guess can no be verified

13 Deermine boundary of region where small signal analysis is valid 3. Circuis wih small-signal inpus ha vary around some operaing poin Ineresed in obaining relaionship beween small-signal inpus and he corresponding small-signal oupus. Will assume hese circuis operae linearly in some suiably small region around he operaing poin Analysis Sraegy: Use mehods from previous class of nonlinear circuis More Pracical Analysis Sraegy: Deermine he operaing poin (using mehod 1 or 2 discussed above afer all small signal independen inpus are se o 0) Develop small signal (linear) model for all devices in he region of ineres (around he operaing poin or Q-poin ) Creae small signal equivalen circui by replacing all devices wih small-signal equivalen Solve he resulan small-signal (linear) circui Can use KCL, DL, and oher linear analysis ools such as superposiion, volage and curren divider equaions, Thevenin and Noron equivalence

14 Consider he following MOSFET and BJT Circuis BJT CC R 1 MOSFET R 1 () Q 1 () EE MOS and BJT Archiecures ofen Idenical Circui are Highly Nonlinear Nonlinear Analysis Mehods Mus be used o analyze hese and almos any oher nonlinear circui

15 Small signal operaion of nonlinear circuis = M sinω Nonlinear Circui M is small If M is sufficienly small, hen any nonlinear circui operaing a a region where here are no abrup nonlineariies will have a nearly sinusoidal oupu and he variance of he magniude of his oupu wih M will be nearly linear (could be viewed as locally linear ) This is ermed he small signal operaion of he nonlinear circui When operaing wih small signals, he nonlinear circui performs linearly wih respec o hese small signals hus oher properies of linear neworks such as superposiion apply provided he sum of all superimposed signals remains sufficienly small Oher ypes of small signals, e.g. square waves, riangular waves, or even arbirary waveforms ofen are used as inpus as well bu he performance of he nonlinear nework also behaves linearly for hese inpus Many useful elecronic sysems require he processing of hese small signals Pracical mehods of analyzing and designing circuis ha operae wih small signal inpus are really imporan

16 Small signal operaion of nonlinear circuis = M sinω Nonlinear Circui M is small Pracical mehods of analyzing and designing circuis ha operae wih small signal inpus are really imporan Two key quesions: How small mus he inpu signals be o obain locally-linear operaion of a nonlinear circui? How can hese locally-linear (al small signal) circuis be analyzed and designed?

17 Consider he following MOSFET and BJT Circuis BJT CC R 1 MOSFET R 1 () Q 1 () EE One of he mos widely used amplifier archiecures

18 Small signal operaion of nonlinear circuis = M sinω Nonlinear Circui M is small Example of circui ha is widely used in locally-linear mode of operaion R M -M Two mehods of analyzing locally-linear circuis will be considered, one of hese is by far he mos pracical

19 Small signal operaion of nonlinear circuis = M sinω Nonlinear Circui M is small Two mehods of analyzing locally-linear circuis for small-signal exciaions will be considered, one of hese is by far he mos pracical 1. Analysis using nonlinear models 2. Small signal analysis using locally-linearized models

20 Small signal analysis using nonlinear models R By selecing appropriae value of, will operae in he sauraion region Assume operaing in sauraion region M = M sinω M is small OUT - M DD = -I R OUT DD D μc W 2L μcox W 2L 2 OX I - - D IN SS T I μc W 2L DQ M μ COX W 2L 2 OX - - R OUT DD IN SS T sin SS Termed Load Line 2 SS T 2 R T

21 Small signal analysis example = M sinω M is small R OUT OUT DD DD μcox W 2L μcoxw 2L SS M sin T SS T 2 M sin 1- SS T 2 R 2 R Recall ha if x is small 1+x 2 1+2x μcoxw 2 2M sin OUT DD SS T 1- R 2L SS T μc W μc W 2 sin 2 2 OX OX M OUT R DD SS T R SS T 2L 2L SS T μc W 2 μc W OX 2L L OX R R sin OUT DD SS T SS T M

22 Small signal analysis example = M sinω R By selecing appropriae value of, will operae in he sauraion region Assume operaing in sauraion region μc W 2 μc W OX 2L L OX R R sin OUT DD SS T SS T M

23 Small signal analysis example R Assume operaing in sauraion region = M sinω μc W 2 μc W OX 2L L OX R R sin OUT DD SS T SS T M Quiescen Oupu ss olage Gain μc W L OX A R v SS T μc W 2L 2 OX R OUTQ DD SS T A sin OUT OUTQ M Noe he ss volage gain is negaive since + T <0!

24 Small signal analysis example R Assume operaing in sauraion region = M sinω A sin OUT OUTQ M μc W L OX A R v SS T μc W 2L 2 OX R OUTQ DD SS T Bu his expression gives lile insigh ino how large he gain is! And he analysis for even his very simple circui was messy!

25 Small signal analysis example = M sinω R A sin OUT OUTQ M M -M OQ M =0

26 R Small signal analysis example = M sinω OX v SS T M -M A sin OUT OUTQ M μc W A R L OQ M

27 R Small signal analysis example = M sinω OX v SS T M -M A sin OUT OUTQ M μc W A R L OQ M

28 = M sinω R Small signal analysis example M -M A sin OUT OUTQ M μc W L OX A R v SS T OQ M Serious Disorion occurs if signal is oo large or Q-poin non-opimal Here clipping occurs for high

29 = M sinω R Small signal analysis example M -M A sin OUT OUTQ M μc W L OX A R v SS T OQ M Serious Disorion occurs if signal is oo large or Q-poin non-opimal Here clipping occurs for low

30 = M sinω R Small signal analysis example A sin OUT OUTQ M Bu recall: μc W L OX A R v SS T Thus, subsiuing from he expression for I DQ we obain A v SS 2I R DQ T I DQ μ COX W 2L 2 SS T Noe his is negaive since + T < 0

31 Small signal analysis example = M sinω R A v 2I R SS DQ T Observe he small signal volage gain is wice he Quiescen volage across R divided by + T Can make A large by making + T small This analysis which required linearizaion of a nonlinear oupu volage is quie edious. This approach becomes unwieldy for even slighly more complicaed circuis A much easier approach based upon he developmen of small signal models will provide he same resuls, provide more insigh ino boh analysis and design, and resul in a dramaic reducion in compuaional requiremens

32 Small signal analysis example (Consider wha was negleced in he previous analysis) = M sinω R A sin OUT OUTQ M However, here are invariably small errors in his analsis A sin + ε OUT OUTQ M To see he effecs of he approximaions consider again μcox W 2 OUT DD M sin SS T R 2L μc sin 2 sin OXRW OUT DD M SS T M + SS T 2L μc 1 cos 2 OXRW 2 2 sin 2 OUT DD M SS T M + SS T 2L 2 2 μcoxrw 2 M μcoxw μcoxrw 2 OUT + SS T SS T R M sin M cos 2 2L 2 L 4L Noe presence of second harmonic disorion erm!

33 R = M sinω Small signal analysis example Nonlinear disorion erm A sin OUT OUTQ M A sin + ε OUT OUTQ M 2 μcoxrw 2 M μcoxw μcoxrw 2 OUT + SS T SS T R M sin M cos 2 2L 2 L 4L 2 μcoxrw M + 2L 2 2 OUTQ DD SS T μcoxw A SS T R L A μc RW 4L OX 2 M sin cos 2 A A O UT O UTQ M 2 M

34 = M sinω R Small signal analysis example Nonlinear disorion erm sin cos 2 A A O UT O UTQ M 2 M 2 μcoxrw M + 2L 2 2 OUTQ DD SS T μcoxw A SS T R L Toal Harmonic Disorion: Recall, if x A μc RW 4L OX 2 M b sin hen k kωt+ k 2 k THD k0 b Thus, for his amplifier, as long as says in he sauraion region μcoxw R A M 2M A2 4L M THD A A μc W R L Disorion will be small for M << + T M OX SS T SS T Disorion will be much worse (larger and more harmonic erms) if leaves sauraion region. 1 2 b k

35 Consider he following MOSFET and BJT Circuis BJT CC R 1 MOSFET R 1 () Q 1 () EE One of he mos widely used amplifier archiecures Analysis was very ime consuming Issue of operaion of circui was obscured in he deails of he analysis

36 End of Lecure 24