ECEN326: Electronic Circuits Fall 2017

Transcription

1 EEN36: Electronic ircuits Fall 07 ecture 5: Frequency esponse a Palero Analo & Mixed-al enter Texas A&M University

2 Announceents HW5 due / Exa /6 9:0-0:0 (0 extra utes) losed book w/ one standard note sheet 8.5 x front & back Br your calculator overs throuh ecture 6 aple Exa posted on website ead azavi hapter

3 Aenda Frequency esponse oncepts Hih-Frequency Models of Transistors Frequency esponse Analysis Procedure E and taes B and G taes and D (Follower) taes ascode taes Differential Pairs Additional Exaples 3

4 Hih Frequency oll-off of Aplifier As frequency of operation creases, the aplifier a decreases This lecture analyzes this frequency response issue H Frequency esponse 4

5 Exaple: Huan oice I Natural oice Telephone yste Natural huan voice spans a frequency rane fro 0Hz to 0KHz, however conventional telephone syste passes frequencies fro 400Hz to 3.5KHz. Therefore phone conversation differs fro face-to-face conversation. 5

6 Exaple: Huan oice II Path traveled by the huan voice to the voice recorder Mh Air ecorder Path traveled by the huan voice to the huan ear Mh Air Ear kull ce the paths are different, the results will also be different. H Frequency esponse 6

7 Ga oll-off: iple ow-pass Filter o Z Z s s s s s s s Z H s o s s s for susoidal steady - state response s j H j j In this siple exaple, as frequency creases the ipedance of decreases and the voltae divider consists of and attenuates to a reater extent at the put. 7

8 Ga oll-off: oon ource =0 D s H s s s D s D D This circuit has a pole at p The capacitive load,, is the culprit for a roll-off sce at hih frequency, it will steal away soe sal current and shunt it to round. 8

9 Frequency esponse of the tae D D ecall the Power is To fd the half - power (-3dB) pot relative to the low - frequency a D D proportional to olv for D oltae D At low frequency, the capacitor is effectively open and the a is flat. As frequency creases, the capacitor tends to a short and the a starts to decrease. A special frequency is ω=/( D ), where the a drops by 3dB (half-power). In this sle-pole circuit, this is also the pole frequency. 9

10 Exaple: elationship between Frequency esponse and tep esponse H s j t t 0 exp u t The relationship is such that as creases, the bandwidth drops and the step response becoes slower. H Frequency esponse 0

11 Bode Plot When we hit a zero, ω zj, the Bode anitude rises with a slope of +0dB/dec. When we hit a pole, ω pj, the Bode anitude falls with a slope of -0dB/dec 0 ) ( p p z z s s s s A s H

12 Exaple: Bode Plot =0 H s s s This circuit has a p D s D The circuit only has one pole (no zero) at /( D ), so the slope drops fro 0 to -0dB/dec as we pass ω p. D pole at H Frequency esponse

13 Pole Identification Exaple I ircuit transfer functions can be well approxiated by consider that if a node the sal path has a sall-sal resistance j and capacitance j parallel to an A round, then it contributes a pole of anitude ( j j ) - p =0 p D p p D H Frequency esponse 3

14 Pole Identification Exaple II D p p p p D H Frequency esponse 4

15 ircuit with Float apacitor The pole of a circuit is coputed by fd the effective resistance and capacitance fro a node to GOUND. The circuit above creates a proble sce neither teral of F is rounded. While we could always derive the transfer function fro the sall-sal odel, there is a useful Miller s Theore which can be used to approxiate the circuit s poles 5

16 6 6 Miller s Theore If A v is the a fro node to, then a float ipedance Z F can be converted to two rounded ipedances Z and Z. v F A Z Z v F A Z Z / H Frequency esponse where should be the sae both circuits A A Z Z Z Z Z Z I I v v F F F F v F F F F A Z Z Z Z Z Z I I should be the sae both circuits

17 Miller Multiplication Z j F Equivalent to an put cap that is Av jf Ao jf Ao the orial ultiplied by Follow a siilar procedure, the put cap is the orial F F A ultiplied by o A o With Miller s theore, we can separate the float capacitor. However, the put capacitor is larer than the orial float capacitor. We call this Miller ultiplication. 7

18 Exaple: Miller Theore A v D D F Note, this is only a (often ood) approxiation of the transfer function Uses only the low-frequency a Nelects a zero D D F D 8

19 Hih-Pass Filter esponse o s s s s s s s Z Z Z The voltae division between a resistor and a capacitor can be confiured such that the a at low frequency is reduced. H Frequency esponse 9

20 Exaple: Audio Aplifier p, 0Hz i i p, 0kHz i 79. 6nF i 00K / nF In order to successfully pass audio band frequencies (0 Hz-0 KHz), lare put and put capacitances are needed. H Frequency esponse 0

21 apacitive oupl vs. Direct oupl apacitive coupl, also known as A coupl, passes A sals fro Y to X while block D contents. This technique allows dependent bias conditions between staes. Direct coupl does not. Allows for hih ( D ) (a), while also allow a hih put stae ate bias for ood put sw Due to direct coupl, ust trade-off A for put stae bias/sw apacitive oupl Direct oupl

22 Typical Frequency esponse ower orner Often due to A coupl Upper orner Often due to load/parasitic capacitors H Frequency esponse

23 Aenda Frequency esponse oncepts Hih-Frequency Models of Transistors Frequency esponse Analysis Procedure E and taes B and G taes and D (Follower) taes ascode taes Differential Pairs Additional Exaples 3

24 Hih-Frequency Bipolar Model b je At hih frequency, capacitive effects coe to play and je are the junction capacitances b represents the base chare to enerate the non-unifor chare profile required for proper operation (hapter 4) H Frequency esponse 4

25 Hih-Frequency Model of Interated Bipolar Transistor ce an terated bipolar circuit is fabricated on top of a substrate, another junction capacitance exists between the collector and substrate, naely. 5

26 Exaple: apacitance Identification H Frequency esponse 6

27 MO Intrsic apacitances For a MO, there exist oxide capacitance fro ate to channel, junction capacitances fro source/dra to substrate, and overlap capacitance fro ate to source/dra. 7

28 Gate Oxide apacitance Partition and Full Model Assu bulk is an A round The ate oxide capacitance is often partitioned between source and dra. In saturation, ~ ate, and ~ 0. They are parallel with the overlap capacitance to for G and GD. H Frequency esponse 8

29 Exaple: apacitance Identification H Frequency esponse 9

30 Transit Frequency Transit frequency, f T, is defed as the frequency where the current a fro put to put drops to. I I I ett the anitude equal toat r r s T H Frequency esponse r r Z T s r r I s Z Nelect T yields I Z I I G T G T Nelect GD G ett the anitude equal toat G s s I Z T yields 30

31 Exaple: Transit Frequency alculation The transit frequency creases draatically as the channel lenth is shrunk, allow for uch faster transistors with MO scal Note, this nelects soe advanced device physics (carrier velocity saturation) which slows this rate of frequency crease W nox G TH G Wox (talked ab 474) 3 W nox G TH f T T Wox 3 3n G TH ft 4 f G n T T 65n TH G 400c 00 6GHz /(. s) H Frequency esponse 3

32 Aenda Frequency esponse oncepts Hih-Frequency Models of Transistors Frequency esponse Analysis Procedure E and taes B and G taes and D (Follower) taes ascode taes Differential Pairs Additional Exaples 3

33 Analysis uary The frequency response refers to the anitude of the transfer function. Bode s approxiation siplifies the plott of the frequency response if poles and zeros are known. In eneral, it is possible to associate a pole with each node the sal path. Miller s theore helps to decopose float capacitors to rounded eleents. Bipolar and MO devices exhibit various capacitances that liit the speed of circuits. H Frequency esponse 33

34 Hih Frequency ircuit Analysis Procedure Detere which capacitor ipact the low-frequency reion of the response and calculate the low-frequency pole (nelect transistor capacitance). alculate the idband a by replac the capacitors with short circuits (nelect transistor capacitance). Include transistor capacitances. Mere capacitors connected to A rounds and oit those that play no role the circuit. Detere the hih-frequency poles and zeros. Plot the frequency response us Bode s rules or exact analysis. H Frequency esponse 34

35 Aenda Frequency esponse oncepts Hih-Frequency Models of Transistors Frequency esponse Analysis Procedure E and taes B and G taes and D (Follower) taes ascode taes Differential Pairs Additional Exaples 35

36 Frequency esponse of tae with Bypassed Deeneration Input A oupl X X s X s i X is s i i The put A coupl fors a hih-pass filter which should be desed for a certa iu cut-off frequency H Frequency esponse 36

37 frequency - off should also be desed to set the iu cut The pole frequency b p b b D b D X s s s 37 Frequency esponse of tae with Bypassed Deeneration Ma Aplifier In order to crease the idband a, a capacitor b is placed parallel with s. 37 H Frequency esponse

38 Unified Model for E and taes H Frequency esponse 38

39 39 39 Unified Model Us Miller s Theore H Frequency esponse Y X Thev Thev r r r DB G D GD Y D GD X Thev Thev

40 Unified Model Us Miller s Theore p, p, Thev XY XY H Frequency esponse 40

41 Exaple: E tae =k I 00 A ff 0 ff 30 ff p, p, 56MHz.59GHz The put pole is the bottleneck for speed. H Frequency esponse 4

42 Exaple: Half Width tae W X p, p, XY XY W ox G TH In 474 we will learn that all MO caps are W DB G Wox W 3 W A D GD j P D ov jsw ov W F a, reduces by / Assu is still hih: The put pole creases by ~4X The put pole creases by ~x onstant a-bandwidth product! H Frequency esponse 4

43 Direct Analysis of E and taes For a detailed direct sall-sal analysis, see azavi.4.4 as b Direct analysis yields different pole locations and an extra zero. H Frequency esponse s a ThevXY XY s s s bs p p p p p p Us a "doant pole"approxiation as Thev XY as s bs p Thev b XY p and s Thev bs To fd the poles, we can write where p p s p b a XY p p s Exact Expression 43

44 Direct Analysis of E and taes w/ Doant Pole Approxiation p p XY Thev Thev XY XY Thev Thev XY Thev z XY XY XY p will be lower due to the additional ter p is at a uch hiher frequency due to pole splitt Discussed ore when we talk ab stability H Frequency esponse 44

45 Exaple: E and Direct Analysis (Doant Pole Approxiation) Thev G, DB, XY r DB O r O GD GD p p r r r r O ro ro XY ro ro ( r O O r O XY XY O XY O ( XY XY ) ) H Frequency esponse 45

46 Exaple: oparison Between Different Methods 0 G GD DB ff 00 ff 50 ff 50 K iple Miller theore analysis vastly overestiates the put pole at a lower frequency Miller s Exact Doant Pole p, 57MHz p, 64MHz p, 49MHz p, 48MHz 4.53GHz p, 4.79GHz p, 46 46

47 Input Ipedance of E and taes Z s r Z G D GD s Z At low frequencies : has a pole at r r Approxiate as purely capacitive 47

48 Aenda Frequency esponse oncepts Hih-Frequency Models of Transistors Frequency esponse Analysis Procedure E and taes B and G taes and D (Follower) taes ascode taes Differential Pairs Additional Exaples 48

49 ow Frequency esponse of B and G taes A = re s is s i As with E and staes, the use of capacitive coupl leads to low-frequency roll-off B and G staes (althouh a B stae is shown above, a G stae is siilar). H Frequency esponse 49

50 Frequency esponse of B tae r O p, X X X p, Y Y No Miller effect Input pole is ~f T (very hih frequency) Y H Frequency esponse 50

51 Frequency esponse of G tae p, Xr O X G B X r O p, Y Y GD Y DB iilar to a B stae, the put pole is on the order of f T, so rarely a speed bottleneck. H Frequency esponse 5

52 Exaple: G tae Pole Identification r O MOFET aps p, X B GD p, Y DB GD G DB H Frequency esponse 5

53 Exaple: Frequency esponse of G tae B G GD ff 80 ff DB ff K d H Frequency esponse p, X p, Y 5.3GHz 44MHz Input pole is ~f T Output pole liits bandwidth 53 53

54 Aenda Frequency esponse oncepts Hih-Frequency Models of Transistors Frequency esponse Analysis Procedure E and taes B and G taes and D (Follower) taes ascode taes Differential Pairs Additional Exaples 54

55 Eitter and ource Followers The follow will discuss the frequency response of eitter and source followers us direct analysis, as this circuit typically has poles that are close toether Eitter follower is treated first and source follower is derived easily by allow r to o to fity 55

56 Direct Analysis of Eitter Follower For detailed analysis, see azavi.6 Assu that as a s bs b H Frequency esponse r r z Generally, this yields close poles, necessitat a direct solution approach 56

57 Direct Analysis of ource Follower tae Tak r G GD B as G bs s a b GD GD G GD GD B B G B H Frequency esponse 57

58 Exaple: Frequency esponse of ource Follower G GD DB ff 50 ff 80 ff 00 ff 50 H Frequency esponse p p.79ghz.79ghz j j.57ghz.57ghz oplex onjuate Poles 58 58

59 59 59 Exaple: ource Follower bs as s G ) )( ( DB GD B GD GD DB GD B G GD G GD b a H Frequency esponse r O

60 Input apacitance of Eitter/ource Follower r O Us Miller Theore with A v GD G H Frequency esponse 60

61 Exaple: ource Follower Input apacitance GD r O r O G H Frequency esponse 6

62 Output Ipedance of Eitter Follower Need to consider the put resistance of the previous stae, Nelect H Frequency esponse I X X r r ow Frequency: r s s Hih Frequency: r r e Output ipedance enerally oes up w/ frequency! 6

63 Output Ipedance of ource Follower Nelect GD Output ipedance enerally oes up w/ frequency! I X X G G s s ow Frequency: Hih Frequency: H Frequency esponse 63

64 Active Inductor If < / (not usually true) Eitter Follower z r p r r If > / (eneral case) ource Follower z p G G The plot above shows the put ipedance of eitter and source followers. ce a follower s priary duty is to lower the driv ipedance ( >/ ), the active ductor characteristic on the riht is usually observed. H Frequency esponse 64

65 Exaple: Output Ipedance r O M 3 only I X X r G 3 r s O O G 3 s 3 Note: This nelects the capacitors fro M and M H Frequency esponse 65

66 Aenda Frequency esponse oncepts Hih-Frequency Models of Transistors Frequency esponse Analysis Procedure E and taes B and G taes and D (Follower) taes ascode taes Differential Pairs Additional Exaples 66

67 Frequency esponse of ascode tae Assue (W/) = (W/) A v, XY For cascode staes, there are three poles and Miller ultiplication is saller than the E/ stae. H Frequency esponse x XY 67

68 68 68 Poles of Bipolar ascode, r X p, Y p, p H Frequency esponse oparable to f T

69 69 69 Poles of MO ascode, GD G X p, B GD G DB Y p, GD DB p H Frequency esponse

70 Exaple: Frequency esponse of ascode G GD DB K ff ff ff H Frequency esponse p, X p, Y p,.95ghz.73ghz 44MHz opare to siple p, p, Now put pole sets the bandwidth, and it has creased by 67% 64MHz Exact GHz

71 H 0 Differential Aplifiers 7 H Frequency esponse 7 MO ascode Exaple, GD G X p 3 3, DB GD GD G DB Y p, GD DB p Allows for a saller M Iproves put pole owers poles at nodes X and Y, but they should still be relatively hih

72 I/O Ipedance of Bipolar ascode A Z r s Z s (Nelect ) 7

73 I/O Ipedance of MO ascode 0 Z G (Nelect ) H Frequency esponse GD s Z GD DB 73 s

74 ascode Frequency esponse Take-Away Pots ascode aplifiers offer two ood properties Hih put ipedance to serve as a ood current source and/or aplifier eduction of the Miller effect and better hih-frequency perforance Ma cost is hiher voltae headroo to keep cascode transistor saturation Ipacts axiu put sw and distortion perforance 74

75 Aenda Frequency esponse oncepts Hih-Frequency Models of Transistors Frequency esponse Analysis Procedure E and taes B and G taes and D (Follower) taes ascode taes Differential Pairs Additional Exaples 75

76 Bipolar Differential Pair Frequency esponse Half ircuit b s a ThevXY XY Thev XY Thev XY as where s Thev bs XY ce bipolar differential pair can be analyzed us halfcircuit, its transfer function, I/O ipedances, locations of poles/zeros are the sae as that of the half circuit s (lide 43). H Frequency esponse 76

77 MO Differential Pair Frequency esponse Half ircuit ce MO differential pair can be analyzed us half-circuit, its transfer function, I/O ipedances, locations of poles/zeros are the sae as that of the half circuit s (lide 43). H Frequency esponse 77

78 78 78 Exaple: MO Differential Pair 3 3, , 3, ] ) / ( [ GD DB D p B GD G DB Y p GD G X p

79 oon Mode Frequency esponse M D D s s s ss will lower the total ipedance between pot P to round at hih frequency, lead to hiher M a which derades the M rejection ratio

80 Tail Node apacitance ontribution DB3 ource-body apacitance of M, M Dra-Body apacitance of M 3 Gate-Dra apacitance of M 3 M 3 is often a lare (wide) transistor order to have a sall copliance ( D ) voltae Watch for deraded hih-frequency M! H Frequency esponse 80

81 Aenda Frequency esponse oncepts Hih-Frequency Models of Transistors Frequency esponse Analysis Procedure E and taes B and G taes and D (Follower) taes ascode taes Differential Pairs Additional Exaples 8

82 Exaple: apacitive oupl (ow-frequency ut-off) I I.75A.3A 54Hz r B The hihest low-frequency pole ( = 54Hz) will set the low-frequency cut-off To fd : Y Thev s s s s B r E Hz

83 Exaple: I Aplifier ow Frequency Des MHz D A v F A v k D k.30k MHz The hihest low-frequency pole ( = 37.MHz) will set the low-frequency cut-off H Frequency esponse 83

84 Exaple: I Aplifier Midband Des 50 A v v v A v X A v A A v v D dB 3.77 H Frequency esponse 84 84

85 Exaple: I Aplifier Hih Frequency Des To et an accurate estiate for p and p, use the doant pole approxiation expressions on lide 44 p p Av GD G D GD Av GD G D GD D G GD DB GD where G GD G A v MHz.99GHz H Frequency esponse 85

86 Exaple: I Aplifier Hih Frequency Des H Frequency esponse 86 MHz A GHz MHz DB v GD D p p p

87 Next Tie Feedback azavi hapter 87