EECE 311 Lecture 3, Spring 2012

EECE 311: Electronic Circuits Part 3 2 Common Source Amplifier with Source Resistance Small Signal Model at Low Freq: What does RL model? Note that vi ≠ vgs Common Source with Source Resistance  The current flows in RS  Voltage gain:  Reduced by factor (1+ gm RS)  What is the input resistance? 3 mvgs g    S  gs m S gs m gs i v g R R g v v v     1 L gs m o g v R v   S m L m i o R g R g v v   1 Common Source with Source Resistance Do not neglect channel length modulation (ro)  Thevenin - Norton 4 Common Source with Source Resistance Do not neglect ro  ro causes the gain to drop (further) 5 1 1 m o gs o L S m o L gs o L o L S m o S i gs S gs o L S o m o L m L i o L S m o S L S m S o g r v i r R R g r R v v R i r R R g r R v v R i v r R R v g r R g R v r R R g r R R R g R r                                 i Common Source with Source Resistance Do not neglect ro  What is the input resistance?  What is the output resistance? 6 Common Source with Source Resistance Do not neglect ro  Output resistance? 7 Common Source with Source Resistance Do not neglect ro  Output resistance  RXY = RX + RY + gm RX RY  Ro = ro + RS + gm ro RS  Looking into the drain of a MOSFET, with gate at DC (no signal), and resistance RS between source and ground, a resistance ro + RS + gmroRS is seen (from drain to ground). 8 BJT Common-Emitter with RS Small-Signal Equivalent Circuit 9 Input Resistance of CE with RS Ri = vi / ii vp = rp ii vi = vp + Rs (ii + gm vp) = rp ii + RS (ii + gm rp ii) vi / ii = rp + RS (1 + gm rp) But gm rp = b : Ri = vi / ii = rp + (b + 1)RS 10 BJT Base Reflection Rule  The resistance seen looking into the base is: rp + (b + 1) times the resistance between the emitter and ground …the resistance in the emitter appears (b + 1) times larger when looking into the base. Fine print: The above rule applies when ro is very large (negligible Early Effect) 11 BJT Common-Emitter Small-Signal Equivalent Circuit  Voltage gain:  Similar to MOSFET result 12 1 o m L m i S v g R g v R     BJT Common-Emitter with RS Output Resistance Hint: Recycle! Output resistance: use MOSFET result after noting that rp and RS are connected in parallel for the Ro calculation (when vi is set to zero): Ro = ro + (rp // RS) + gm ro (rp // RS) 13 14 Common-Gate Amplifier with Active Load from S to D appears controlled source a circuit : equivalent that in the small - signal Note i m i gs g v v v   15  Input Resistance: m i i i i m i g i v R g v i  1     Voltage gain: L m m i i L i o v L i o R g g i i R v v A R i v       Output resistance:     o i m R g v 0  Current gain: 1   i i o A i i Common-Gate Amplifier Resistance Looking into MOSFET Source Terminal  The resistance seen looking into the MOSFET source with gate at DC levels (no signal) is equal to 1/gm  Does NOT apply when ro is not neglected (not )  1/gm becomes an approximation 16 17  Input Resistance Note • We calculated Rin and not Ri • Rin depends on RL Common-Gate Amplifier (with ro) 1 1 // when 0 1 i o i m i o i L i o L i i m i o i o L in i m o o in o L m o m v v i g v r v R i v R i i g v r v r R R i g r r R r R g r g                        18 0 0 L L i R i i        Open-Circuit Voltage Gain  Voltage Gains (RL connected) o o i in v v sig i sig in s v v v R G A v v v R R       Note • Av , Gv are positive (non- inverting) o i L v i R  i o L in v v R R  L , which is also equal to L v vo in L o R R A A R R r    i o m i o g v r v v   o m R i o vo g r v v A L      1 19 (by inspection) o o R r   Output Resistance  Rout = output resistance with vsig = 0  Common Gate Characteristics  Large Output Resistance  Small Input Resistance  Unity Current Gain Good current buffer  Ro = output resistance with vi = 0 calculation: XY out o S m o S R R r R g r R    20 Common-Gate at High Frequency (no ro) 1 Pole Frequency: 1 1 2 / / p in s m f C R g         2 Pole Frequency: 1 2 p out L f C R   1 2 1 1 o m sig p p V A V s s                  Node equation at S (after Norton transformation): sig s in s m s s s V V sC V g V R R    1 o m L s out L V g R V sC R   1 1 s sig m s in s V V g R sC R    Node equation at D: o out o m s L V sC V g V R   Note: body is grounded 21  Considering ro by OCTC: Resistance seen by // in s in C R R  Note • No Miller (multiplication) effect • Larger bandwidth than Common-Source     1 2 // // H in s in out out L f C R R C R R         Resistance seen by // out out L C R R  22 Common-Base Amplifier Small Signal Model: 23 / / ( / /input resistance of the CG) 1 o L in m o r R R r r g r       Input Resistance • very small input resistance ( ) when is very large (no Early Effect) 1 in i e e o r R R r r r       24     by inspection? similar to MOSFET with replaced by / / / / / / o o out s e out o e m o e R r R R R r R r R r g r R r           Output Resistance 25 Cascode Amplifier  Common-Source + Common-Gate 26  Input Resistance: by inspection in R    Output Resistance:  The last stage is a common-gate   CG out out S o m o S CG R R R r g r R     the signal source resistance of the common-gate stage is the output resistance of the common- source stage. 2 2 2 1 2 2 1 2 CS CS out o o m o o o o m o o R R r g r R r r g r r       27 Voltage Gain L o o d vo i d i R v v v A v v v      Input resistance of CG is the load on the CS stage It happens to be when the load of the CG is an open circuit   Open-Circuit Voltage Gain of Cascode L v vo L o R A A R R    Voltage Gain with Load Connected   1 1 // CG CG vo m o in A g r R        2 2 1 1 2 1 m o m o m o g r g r g r     28 Rsig vsig Q1 Q2 Cdb2 Cdb1 Cgs2+Csb2 Cgd2 Cgs1 Cgd1 CL RL  Cascode High Frequency Response 29 Rsig Q1 Q2 Cgs1 RL  Resistance seen by Cgs1 30 Rsig Q1 Q2 Cdb1+Cgs2+Csb2 RL  Resistance seen by Cdb1+Cgs2+Csb2 31 Rsig Q1 Q2 CL+Cgd2+Cdb2 RL  Resistance seen by CL+Cgd2+Cdb2 32 Rsig Q1 Q2 Cgd1 RL  Resistance seen by Cgd1 33       1 1 2 2 2 2 1 * 2 1 2 2 1 2 2 1 2 * * 1 OCTC: // // // = 1 // // gs CS CG CS db gs sb L gd db gd C sig in sig o L in o o C C C m o L out cascode L o o m o o C C C C sig m sig R R R R r R R R R r R g r R R R R r r g r r R R R g R R                             1 1 1 2 2 2 * XY 1 1 2 2 2 2 1 // This is an R 1 CG CS gs gd db gs L gd db in o H gs C db gs sb L gd db gd C C C C C C R R R C R C C C R C C C R C R               We use the results derived previously for input and output resistances of common- source and common-gate stages 34 Cascode Current Source  Large Output Resistance Serves well as a current source (load) for an amplifier 35 BJT Cascode   1 1 1 2 2 2 2 ( ) 2 2 1 2 // of CB when load is open circuit is 1 v m o in v vo vo CB m o vo v vo A g r r R r A A A g r A A A            36  Open-Circuit Voltage Gain  Input Resistance by inspection 1 Rin r   Output Resistance       ' ' ' 1 2 2 2 2 1 // 1 (1 ) out e m e o e o out m o o o R R g R r R r r r R r g r r r r                   CB formula 37 Common Drain (Source Follower) Small Signal Model: 38 Small-signal equivalent circuit:  Input Resistance in R   Voltage Gain o m gs L v g v R   Open-Circuit Voltage Gain 1 L o vo i R v A v     i gs o o o m L v v v v v g R     1 o m L v i m L v g R A v g R     39  Output Resistance 0 1 resistor appears from source to drain 1 i gs s o m gs m o m o m v v v v g v g v g R g        very small CD used with low impedance load Gain close to (but less than) one output "follows" the input Ro   40 Common Drain with channel length modulation (ro) Small Signal Model: 41 Equivalent Circuit:  Input Resistance in R   Voltage Gain  Open-Circuit Voltage Gain 1 1 L o m o vo i m o R v g r A v g r       ' ' 1 o m L v i m L v g R A v g R    42  Output Resistance 1 / / o o m R r g  43 Common Collector (Emitter Follower) ' // L L o R R r        ' ' ' 1 o m i L m i i L i L v g v i R g r i i R i R            ' 1 i i i L v r i i R      44  Input Resistance   ' 1 i in L i v R r R i        Voltage Gain     ' ' 1 1 L o v i L R v A v r R          Open Circuit Voltage Gain 1 o vo o e r A r r     Large Input Resistance  Open Circuit Voltage Gain nearly one: Signal at emitter “follows” signal at input 45  Output Resistance  Very Low Output Resistance   1 or i x i i i       1 o x r o i o x o v i r i r i r        not included / / 1 1 sig o o o e e R o r R r r r r r       x i sig v i r R      1 1 x o out o x sig v r R r i r R        46 Some Useful Transistor Pairings  Common Collector – Common Emitter Pairing   larger than that of CE 1 CE M in in G R R      Wide Bandwidth  Large Input Resistance 47  Darlington Pair 1 2 Effective      High-Performance Voltage Follower 48  Common Drain – Common Gate Pairing CD CG CG vo v vo vo A A A A     Infinite Input Resistance  Voltage gain ~ ½ CG  Very Good High Frequency Response 1 49  Common Collector – Common Base Pairing  PNP Common-Base Stage  Very Good High- Frequency Performance Improved Current Sources  Larger output resistance (current less dependent on voltage – closer to ideal)  Less dependence on transistor parameters (such as  in BJT)  Without sacrificing voltage range? Voltage across real current sources (VCS) cannot drop below a certain minimum 50 51  Cascode MOS Mirror  Large output resistance  But reduced range of VO min 3 4 2 2 since 2 2 O t ov G GS GS t ov v V V V V V V V       52  Improved Bipolar Current Mirror   2 1 1 REF C I I               Dependency on β decreased from 1/ β to 1/ β2 (error term is β times smaller)  But output resistance still the same (ro2)  What about voltage range?   2 1 1 2 / o C o REF I I I I       2 2 1 1 2 / 1 2 /       53  Wilson Current Mirror     2 1 1 2 1 1 1 C o REF C I I I I                                Dependency on β decreased from 1/ β to 1/ β2  Output resistance multiplied by β/2  But reduced range of Vo (Vomin = 1V)   2 2 1 2 1 2 1 2 1 1 2 /            54  Wilson MOS Mirror 3 3 3 2 3 3 1 1 3 3 2 1 m o o m o o o m m o m o o g R r g r r r g g R g r r        Large output resistance  But reduced range of VO 55  Improved Balanced Wilson MOS Mirror  Same as Wilson MOS current but with balanced drain voltages of Q1 and Q2. 56  Widlar Current Source  Can generate a small constant current using relatively small resistors. 1 2 2 BE BE E E V V I R       Output Resistance 1 // o m E o R g R r r    1 2 2 ln 1 ln 1 C C T T E E S S I I V V I R I I                