Chapter 17 Amplifier Frequency Response

Transcription

1 hapter 7 Amplifier Frequency epone Microelectronic ircuit Deign ichard. Jaeger Travi N. Blalock 8/0/0 hap 7-

2 hapter Goal eview tranfer function analyi and dominant-pole approximation of amplifier tranfer function. Learn partition of ac circuit into low and high-frequency equivalent. Learn the hort-circuit time contant method to etimate upper and lower cutoff frequencie. Develop bipolar and MOS mall-ignal model with device capacitance. Study unity-gain bandwidth product limitation of BJT and MOSFET. Develop expreion for upper cutoff frequency of inverting, noninverting and follower configuration. Explore high-frequency limitation of ingle and multiple tranitor circuit. 8/0/0 hap 7-2

3 hapter Goal (contd. Undertand Miller effect and deign of op amp frequency compenation. Develop relationhip between op amp unity-gain frequency and lew rate. Undertand ue of tuned circuit to deign high-q band-pa amplifier. Undertand concept of mixing and explore baic mixer circuit. Study application of Gilbert multiplier a balanced modulator and mixer. 8/0/0 hap 7-3

4 Tranfer Function Analyi H Zl H Z H Z H F L Pk L P L P L Zk L Z L Z L F... 2 ( ( 8/0/0 ( ( ( ( ( H F L F mid A b n n b b b a m m a a a D N A v A mid i midband gain between upper and lower cutoff frequencie. H Pl H P H P H F... 2 ( ( j H F H Pi H Zi, << for,i l ( ( L F mid A L A ( j L F for,j k ( ( H F mid A H A L Pj L Zj, >> hap 7-4

5 Low-Frequency epone F ( L P2 L P2 Pole P2 i called the dominant low-frequency pole (> all other pole and zero are at frequencie low enough to not affect L. If there i no dominant pole at low frequencie, pole and zero interact to determine L. A ( A F ( A Z Z2 L mid L mid P A P2 A ( j mid For j, at L, L 2 ( L 2 2 ( Z2 ( L 2 2 ( P L Z 2 2 L P 2 2 ( Z Z2 Z 2 2 Z L L ( P P2 P P2 2 4 L L ( ( Pole L > all other pole and zero frequencie L P P2 Z Z2 In general, for n pole and n zero, L n Pn 2 2 n Zn 2 8/0/0 hap 7-5

6 Low-Frequency epone 8/0/0 hap 7-6

7 Tranfer Function Analyi and Dominant Pole Approximation Example Problem: Find midband gain, F L ( and f L for A ( L 0. Analyi: earranging the given tranfer function to get it in tandard form, A ( 200 ( 00 L Now, ( 0 ( 000 A ( A F ( L mid L ( 00 F ( A 200 L ( 0( 000 mid and Zero are at 0 and -00. Pole are at -0, -000 f ( Hz L 2 π ( ( 000 All pole and zero frequencie are low and eparated by at leat a decade. Dominant pole i at 000 and f L 000/2π 59 Hz. For frequencie > a few rad/: A ( 200 L 000 ( 8/0/0 hap 7-7

8 High-Frequency epone F ( L ( / P3 H P3 Pole P3 i called the dominant highfrequency pole (< all other pole. If there i no dominant pole at low frequencie, pole and zero interact to determine H. A H ( A mid F H ( (/ A Z (/ Z2 mid (/ P (/ P2 For j, at H, A A ( j mid H 2 ( ( ( H 2 / 2 Z2 ( ( ( H 2 / 2 P2 2 ( 2 / 2 H Z ( 2 / 2 H P H H H Z Z2 Z Z H H H P P2 P P2 Pole H < all other pole and zero frequencie H In general, P P2 Z Z2 H 2 2 n 2 Pn n Zn 8/0/0 hap 7-8

9 High-Frequency epone 8/0/0 hap 7-9

10 Direct Determination of Low-Frequency Pole and Zero: -S Amplifier V o ( I o ( g 3 m V g ( D (/ g m ( V 3 D g ( 3 ( D 3 V G g ( ( V i ( I G 2 3 (/ V g ( V g -V 2 S (/g 2 m S V A v ( o ( A F ( V ( mid L i A g mid D G m ( 3 G I V g ( 8/0/0 hap 7-0

11 Direct Determination of Low-Frequency Pole and Zero: -S Amplifier (contd. F L ( ( I G 2 (/ 2 S (/g 2 m S ( 3 D 3 The three zero location are: 0, 0, -/( S 2. The three pole location are: (, I G (/g 2 m, ( S 2 D 3 Each independent capacitor in the circuit contribute one pole and one zero. Serie capacitor and 3 contribute the two zero at 0 (dc, blocking propagation of dc ignal through the amplifier. The third zero due to parallel combination of 2 and S occur at frequency where ignal current propagation through MOSFET i blocked (output voltage i zero. 8/0/0 hap 7-

12 Short-ircuit Time ontant Method to Determine L Lower cutoff frequency for a network with n coupling and bypa capacitor i given by: n L i is i Midband gain and upper and lower cutoff frequencie that define bandwidth of amplifier are of more interet than complete tranfer function. where is i reitance at terminal of ith capacitor i with all other capacitor replaced by hort circuit. Product is i i hort-circuit time contant aociated with i. 8/0/0 hap 7-2

13 Etimate of L for -E Amplifier Uing ST method, for, ( ( E S I B in 2 B r π For 2, r 2S 4 ie π th 4 β o r π ( I B 4 β o For 3, 3S 3 ( 3 i ( r 3 o 3 L i f 735Hz L is i 8/0/0 hap 7-3

14 Etimate of L for -S Amplifier Uing ST method, For, ( S I G For 2, 2S S is S gm For 3, 3S 3 ( D 3 D ig I G ( r id 3 D o 8/0/0 hap 7-4

15 Etimate of L for -B Amplifier Uing ST method, For, S I ( E ( ie I E g m For 2, 2S 3 ( i 3 8/0/0 hap 7-5

16 Etimate of L for -G Amplifier Uing ST method, For, S I ( S ( is I S g m For 2, 2S 3 ( D id 3 D 8/0/0 hap 7-6

17 Etimate of L for - Amplifier Uing ST method, For, S I ( B ib r I B π β o E 3 For 2, 2S 3 ( E ie r π th 3 E β o 8/0/0 hap 7-7

18 Etimate of L for -D Amplifier Uing ST method, For, ( D S I G in I For 2, G 2S 3 S D out 3 S g m 8/0/0 hap 7-8

19 Frequency-dependent Hybrid-Pi Model for BJT apacitance between bae and emitter terminal i: π g m τ F apacitance between bae and collector terminal i: µ o µ ( V / φ B jc µo i total collector-bae junction capacitance at zero bia, Φ jc i it built-in potential. τ F i forward tranit-time of the BJT. π appear in parallel with r π. A frequency increae, for a given input ignal current, impedance of π reduce v be and thu the current in the controlled ource at tranitor output. 8/0/0 hap 7-9

20 Unity-gain Frequency of BJT The right-half plane tranmiion zero Z g m / µ occurring at high frequency can be neglected. β / r π ( µ π i the beta-cutoff / ( ( ( β β π µ π β β o r o 8/0/0 ( ( b I ( c I ( ( ( b I ( ( be V ( I c ( π µ π µ β β π µ π π µ µ r m g o r r g m g m β π µ π frequency where and f T T /2π i the unity gain bandwidth product. Above f T BJT ha no appreciable current gain. β β β β β T o ( µ π π µ π β β β m g r o o T ( hap 7-20

21 Unity-gain Frequency of BJT (contd. urrent gain i β o g m r π at low frequencie and ha ingle pole rolloff at frequencie > f β, croing through unity gain at T. Magnitude of current gain i 3 db below it low-frequency value at f β. g m π T 40I µ T µ 8/0/0 hap 7-2

22 High-frequency Model of MOSFET I ( d I ( b β( I ( g m V g ( GD ( g m GD ( GS GD I d ( T ( g T ( GS / GD g m T GS GD µ n ox " W ( f L V GS V TN T (2/3 ox "WL 3 µ n ( V V GS TN 2 L 2 8/0/0 hap 7-22

23 Limitation of High-frequency Model Above 0.3 f T, behavior of imple pi-model begin to deviate ignificantly from the actual device. Alo, T depend on operating current a hown and i not contant a aumed. For given BJT, a collector current I M exit that yield f Tmax. For FET in aturation, GS and GD are independent of Q-point current, o T g m I D 8/0/0 hap 7-23

24 Effect of Bae eitance on Midband Amplifier Bae current enter the BJT through external bae contact and travere a high reitance region before entering active area. r x model voltage drop between bae contact and active area of the BJT. To account for bae reitance r x i aborbed into equivalent pi model and can be ued to tranform expreion for -E, - and -B amplifier. r i g m v g m g r π v r m 'v π x be be r β g g o m ' m rπ π r x rπ r x r π ' rπ r x β o' βo 8/0/0 hap 7-24

25 Summary of BJT Amplifier Equation with Bae eitance 8/0/0 hap 7-25

26 Single-Pole High Frequency epone Let firt tart with a imple two reitor, one capacitor network. 2 2 v x 2 v i ( [ 2 ] 8/0/0 hap 7-26

27 Single-Pole High Frequency epone Subtituting j2πf and uing f p /(2π[ 2 ] (cont. v x 2 v i 2 j f f p Thi expreion ha two part, the midband gain, 2 /( 2, and the high frequency characteritic, /(jf/f p. 8/0/0 hap 7-27

28 Miller Effect We deire to replace xy with eq to ground. Starting with the definition of mall-ignal capacitance: Now write an expreion for the change in charge for xy: We can now find and equivalent capacitance, eq : 8/0/0 hap 7-28

29 -E Amplifier High Frequency epone uing Miller Effect Firt, find the implifed mallignal model of the -A amp. 8/0/0 hap 7-29

30 -E Amplifier High Frequency epone uing Miller Effect (cont. Input gain i found a Terminal gain i A i v b v i in i in r π r x r π 2 (r x r π i 2 (r x r π r π r x r π A bc v c g m r o 3 g m 3 g m L v b Uing the Miller effect, we find the equivalent capacitance at the bae a: eqb µ ( A bc π ( A be µ ( [ g m L ] π ( 0 µ ( g m L π 8/0/0 hap 7-30

31 -E Amplifier High Frequency epone uing Miller Effect (cont. The total equivalent reitance at the bae i The total capacitance and reitance at the collector i Becaue of interaction through µ, the two time contant interact, giving rie to a dominant pole p p r π 0 T eqb ( th r x inb ( i 2 r x r π r π 0 eq µ L eq r o 3 3 L r π 0 [ µ ( g m L π ] L [ µ L ] T [ µ ( g m L π ] L r π 0 [ µ L ] r π 0 ([ µ ( g m L π ] L r π 0 [ µ L ] 8/0/0 hap 7-3

32 Direct High-Frequency Analyi: -E Amplifier The mall-ignal model can be implified by uing Norton ource tranformation. B v v I B th i th I B I B v i th r r ( r th x π o r π th x 8/0/0 hap 7-32

33 Direct High-Frequency Analyi: -E Amplifier (Pole Determination From nodal equation for the circuit in frequency domain, m g m g P T o r A A P o r L L o r L L m g T π π π µ π 2 0 8/0/0 High-frequency repone i given by 2 pole, one finite zero and one zero at infinity. Finite right-half plane zero, Z g m / µ > T can be important in FET amplifier. For a polynomial 2 A A 0 with root a and b, a A and ba 0 /A. L L L P π µ π / ( 2 Smallet root that give firt pole limit frequency repone and determine H. Second pole i important in frequency compenation a it can degrade phae margin of feedback amplifier. hap 7-33

34 Direct High-Frequency Analyi: -E Amplifier (Overall Tranfer Function ( ( V 2 / ( / ( / ( ( ( th V V o ( 2 / ( / ( - ( ( th V V o ( r g P P o g L g Z o r L g m x r th P P o g L g m g x r th π π π π µ 8/0/0 ( / ( ( th V V o ( ( / ( ( th V - V o ( P mid A vth A P o r L m g x r th π π β r x r th L o mid A T o r P π Dominant pole model at high frequencie for -E amplifier i a hown. hap 7-34

35 Direct High-Frequency Analyi: -E Amplifier (Example Problem: Find midband gain, pole, zero and f L. Given data: Q-point (.60 ma, 3.00V, f T 500 MHz, β o 00, µ 0.5 pf, r x 250Ω, L 0 Analyi: g m 40I 40( ms, r π β o /g m.56 kω. g m π µ 9.9pF f.56mhz 2ππ f P 2 π r T πo T g f m 52 MHz P2 2π( π L r o r ( r x 656Ω g π π th f m 20.4GHz T π µ g m Z 2π L L r ( µ L 56pF µ πo A A A 0.52( vth i bc 8/0/0 hap 7-35

36 Spice Simulation of Example -E Amplifier 8/0/0 hap 7-36

37 Etimation of H uing the Open-ircuit Time ontant Method At high frequencie, impedance of coupling and bypa capacitor are mall enough to be conidered hort circuit. Open-circuit time contant aociated with impedance of device capacitance are conidered intead. H m io i i where io i reitance at terminal of ith capacitor i with all other capacitor open-circuited. For a -E amplifier, auming L 0 π o rπ o v x ( L µ o r g i πo m L x r πo H πo π µ o µ r πo T 8/0/0 hap 7-37

38 High-Frequency Analyi: -S Amplifier Analyi imilar to the -E cae yield the following equation: th I L D G 3 v v th i G I G T GS GD g m L ( L GD L th P th T g m P2 GS L Z g m GD 8/0/0 hap 7-38

39 -S Amplifier High Frequency epone with Source Degeneration eitance Firt, find the implifed mallignal model of the -A amp. ecall that we can define an effective g m to account for the unbypaed ource reitance. g m ' g m g m S 8/0/0 hap 7-39

40 -S Amplifier High Frequency epone with Source Degeneration eitance (cont. Input gain i found a A i v g v i G i G Terminal gain i 2 i 2 A gd v d g m '( id D 3 g m D 3 v g g m S Again, we ue the Miller effect to find the equivalent capacitance at the gate a: eqg GD ( A gd GS ( A g GD ( [ g m L ] g m S GS ( g m S g m S GD ( g m D L g m S GS g m 3 8/0/0 hap 7-40

41 -S Amplifier High Frequency epone with Source Degeneration eitance (cont. The total equivalent reitance at the gate i The total capacitance and reitance at the collector i eqg G I th eqd GD L Becaue of interaction through GD, the two time contant interact, giving rie to the dominant pole: And from previou analyi: p 2 p th [ GD ( eqd id D 3 D 3 L g m L g m S g m ' ( GS L g m ( g m S ( GS L GS L ( GD L ] g m S th z g m ' GD g m ( g m S ( GD 8/0/0 hap 7-4

42 -E Amplifier with Emitter Degeneration eitance Analyi imilar to the -S cae yield the following equation: r π 0 eqb ( th r x [r π (β E ] p r rπ 0 T r π 0 ([ µ ( L 3 g m L π ] L [ µ L ] g m E g m E r π 0 p 2 g m 2π( g m E ( π L z g m 2π[ g m E ][ µ ] 8/0/0 hap 7-42

43 Gain-Bandwidth Trade-off Uing Source/Emitter Degeneration eitor Adding ource reitance to the S amp caued gain to decreae and dominant pole frequency to increae. p However, decreaing the gain alo decreaed the frequency of the econd pole. Increaing the gain of the -E/-S tage caue pole-plitting, or increae of the difference in frequency between the firt and econd pole. A gd v d v g g m D 3 g m S th [ GD ( g m L GS L ( GD L ] g m S g m S th g p2 m ( g m S ( GS L 8/0/0 hap 7-43

44 High Frequency Pole for the -B Amplifier A i g m i A ec v c g m i L g m L v e i r o ( g m r π I Since µ doe not couple input and output, input and output pole can be found directly. eqe π eq µ L eqe g m E i p ( g m E i π g m π p2 eq i L L ( i L ( µ L L ( µ L 8/0/0 hap 7-44

45 High Frequency Pole for the -G Amplifier Similar to the -B, ince GD doe not couple the input and output, input and output pole can be found directly. p eqs GS eqs 4 I g m ( g m p 2 4 I GD GD g m eqd GD L eqd id L L ( id L ( GD L L ( GD L 8/0/0 hap 7-45

46 High Frequency Pole for the - Amplifier ( A ( A ( 0 ( g m L eqb µ bc π be µ π g m L π µ g m L A i v b v i A be v e v b in i in g m L g m L eqb i in [( i B r x ] [r π (β L ] ( th r x [r π (β L ] eqe π L eqe ie L [/g m ( th r x β ] L 8/0/0 hap 7-46

47 High Frequency Pole for the - Amplifier (cont. The low impedance at the output make the input and output time contant relatively well decoupled, leading to two pole. p ([ th r x ] [r π (β L ]( µ π g m L p2 [ ie L ][ π L ] [(/g m th r x β L ][ π L ] The feed-forward high-frequency path through p lead to a zero in the - repone. Both the zero and the econd pole are quite high frequency and are often neglected, although their effect can be ignificant with large load capacitance. z g m π 8/0/0 hap 7-47

48 High Frequency Pole for the -D Amplifier Similar the the - amplifier, the high frequency repone i dominated by the firt pole due to the low impedance at the output of the - amplifier. p p2 z g m GS th ( GD GS g m L [ is L ][ GS L ] [/g m L ][ GS L ] 8/0/0 hap 7-48

49 Summary of the Upper-utoff Frequencie of the Single-Stage Amplifier (pg.037 8/0/0 hap 7-49

50 Frequency epone: Differential Amplifier EE i total capacitance at emitter node of the differential pair. Differential mode half-circuit i imilar to a -E tage. Bandwidth i determined by the r πo T product. A emitter i a virtual ground, EE ha no effect on differential-mode ignal. For common-mode ignal, at very low frequencie, A ( 0 cc << 2 EE Tranmiion zero due to EE i Z EE EE 8/0/0 hap 7-50

51 Frequency epone: Differential Amplifier (contd. m g o x r r EE EEO 2 β π m g EE x r EE m g m g x r EE EE m g x r P µ π A i uually deigned to be large, 8/0/0 ommon-mode half-circuit i imilar to a -E tage with emitter reitor 2 EE. OT for π and µ i imilar to the -E tage. OT for EE /2 i: A EE i uually deigned to be large, ( ( 2 x r x r m g EE P µ µ π hap 7-5

52 Frequency epone: ommon- ollector/ ommon-bae acade pb EE i aumed to be large and neglected. r r x out π β o g m r r B 2 π 2 x2 in β o2 g m2 The intermediate node pole i neglected ince the impedance i quite low. We are left with the input pole for a -D and the output pole of a -B tage. ([ th r x ] [r π (β L ]( µ ([ th r x ] [2r π ]( µ π 2 2 p 2 ( µ L π g m L 8/0/0 hap 7-52

53 Frequency epone: acode Amplifier pb p 2 There are two important pole, the input pole for the -E and the output pole for the -B tage. The intermediate node pole can uually be neglected becaue of the low impedance at the input of the -B tage. L i mall, o the econd term in the firt pole can be neglected. Alo note the L i equal to /g m2. r π 0 T L ( µ 2 L r π 0 ([ µ ( g m L π ] L [ µ L ] g m E r π 0 r π 0 ([ µ ( g m g m 2 π ] /g m 2 r π 0 [ µ π 2 ] r π 0 (2 µ π 8/0/0 hap 7-53

54 Frequency epone: MOS urrent Mirror Thi i very imilar to the -S tage implified model, o we will apply the -S equation with relevant change. P (/g m T /g ( g r m GS GS2 GD2 m2 o2 2 GS g m 2 GD2 r o2 ( r o2 r o2 /g GD2 m Aume matched tranitor. 8/0/0 hap 7-54

55 Frequency epone: Multitage Amplifier Problem:Ue open-circuit and hort-circuit time contant method to etimate upper and lower cutoff frequencie and bandwidth. Approach: oupling and bypa capacitor determine low-frequency repone, device capacitance affect high-frequency repone. At high frequencie, ac model for multi-tage amplifier i a hown. 8/0/0 hap 7-55

56 Frequency epone: Multitage Amplifier Parameter Parameter and operation point information for the example multitage amplifier. 8/0/0 hap 7-56

57 Frequency epone: Multitage Amplifier (ST Etimate of L ST for each of the ix independent coupling and bypa capacitor are calculated a follow: 2S 200Ω 66. 7Ω S g 0.0S m 57Ω th2 B2 D r o 4S r th2 π Ω E2 β o2 8/0/ k Ω th3 B3 2 r o2 r th3 π 3 3Ω 6S L E3 β o3 n L i 3330rad/ is i f L L 2π 530Hz hap 7-57

58 Frequency epone: Multitage Amplifier (High-Frequency Pole High-frequency pole at the gate of M: Uing our equation for the -S input pole: f p 2π th [ GD ( g m L GS L th ( GD L ] L π 2 µ 2 ( g m 2 L 2 8/0/0 hap 7-58

59 Frequency epone: Multitage Amplifier (High-Frequency Pole cont. High-frequency pole at the bae of Q2: From the detailed analyi of the -S amp, we find the following expreion for the pole at the output of the M -S tage: fp2 GSg L GD (g m g th g L L g th 2π[ GS ( GD L GD L ] For thi particular cae, L (Q2 input capacitance i much larger than the other capacitance, o f p2 implifie to: f p2 L g th 2π[ GS L GD L ] 2π th ( GS GD 8/0/0 hap 7-59

60 Frequency epone: Multitage Amplifier (High-Frequency Pole cont. High-frequency pole at the bae of Q3: Again, due to the pole-plitting behavior of the -E econd tage, we expect that the pole at the bae of Q3 will be et by equation 6.95: f p3 g m2 2π[ π 2 ( L 2 L 2 ] µ 2 µ 2 The load capacitance of Q2 i the input capacitance of the - tage. 8/0/0 hap 7-60

61 Frequency epone: Multitage Amplifier (f H etimate There i an additional pole at the output of Q3, but it i expected to be at a very high frequency due to the low output impedance of the - tage. We can etimate f H from eq uing the calculated pole frequencie. f H 2 2 f 2 p f p2 f p3 667 khz The SPIE imulation of the circuit on the next lide how an f H of 667 KHz and an f L of 530 Hz. The phae and gain characteritic of our calculated high frequency repone i quite cloe to that of the SPIE imulation. It wa quite important to take into account the pole-plitting behavior of the -S and -E tage. Not doing o would have reulted in a calculated f H of le than 550 KHz. 8/0/0 hap 7-6

62 Frequency epone: Multitage Amplifier (SPIE Simulation 8/0/0 hap 7-62

63 Intro to F Amplifier Amplifier with narrow bandwidth are often required in radio frequency (F application to be able to elect one ignal from a large number of ignal. Frequencie of interet > unity gain frequency of op amp, o active filter can t be ued. Thee amplifier have high Q (f H and f L cloe together relative to center frequency Thee application ue reonant L circuit to form frequency elective tuned amplifier. 8/0/0 hap 7-63

64 The Shunt-Peaked Amplifier A the frequency goe up, the gain i enhanced by the increaing impedance of the inductor. A v ( ( gm(l/ 2 where L L GD The gain improvement can be plotted a a function of parameter, m, defined below: A vn ( m m 2 where L m 2 8/0/0 hap 7-64

65 The Shunt-Peaked Amplifier 8/0/0 hap 7-65

66 Single-Tuned Amplifier L network elect the frequency, parallel combination of D, 3 and r o et the Q and bandwidth. V o ( g A ( GD m v V ( G ( (/ L i P GD G g o G G P D 3 Neglecting right-half plane zero, o A ( Q v A mid 2 o 2 Q o o L( Q P o GD ( P GD o L 8/0/0 hap 7-66

67 Single-Tuned Amplifier (contd. At center frequency, j o, A v A mid. A mid g m g m ( r o P D 3 BW o Q P 2 L o ( GD P 8/0/0 hap 7-67

68 Ue of tapped Inductor- Auto Tranformer GD and r o can often be mall enough to degrade characteritic of the tuned amplifier. Inductor can be made to work a an auto tranformer to olve thi problem. V o ( nv ( 2 V ( n Z 2 I 2 ( I ( / n I ( ( n Z p ( Thee reult can be ued to tranform the reonant circuit and higher Q can be obtained and center frequency doen t hift ignificantly due to change in GD. Similar olution can be ued if tuned circuit i placed at amplifier input intead of output 8/0/0 hap 7-68

69 Multiple Tuned ircuit Tuned circuit can be placed at both input and output to tailor frequency repone. adio-frequency choke(an open circuit at operating frequency i ued for biaing. Synchronou tuning ue two circuit tuned to ame center frequency for high Q. BW / n BW 2 n Stagger tuning ue two circuit tuned to lightly different center frequencie to realize broader band amplifier. acode tage i ued to provide iolation between the two tuned circuit and eliminate feedback path between them due to Miller multiplication. 8/0/0 hap 7-69

70 S Amp with Inductive Degeneration Typically need to match input reitance to antenna impedance at center frequency, uually 50 ohm. Uing our follower analye, the input impedance i found a: Z ( Z g Z (g m Z g Z in Z in (/ GS L eq where eq g m L S / GS The following lide how a complete low noie S amp where a erie inductor reonate with the input capacitance to leave only the r eitance at the center frequency. 8/0/0 hap 7-70

71 omplete acode LNA 8/0/0 hap 7-7

72 Mixer Introduction A mixer i a circuit that multiplie two ignal to produce um and difference frequencie: S0 S 2 S in 2 t in t co( 2 t co( 2 t 2 A filter i uually ued to reject either the um or difference frequency to implement upconverion or down-converion. 8/0/0 hap 7-72

73 Single-Balanced Mixer Thi baic mixer form i eentially a witched circuit that 'chop' the ine wave input with a quare wave function v (t Ain t (t 2 2 π n odd inn t n 2 8/0/0 hap 7-73

74 Single-Balanced Mixer Output Spectra v o (t A 2 in t A π n odd co(n t co(n t 2 2 n 8/0/0 hap 7-74

75 Differential Pair a Single-Balanced Mixer v o (t n odd 4 nπ I EE inn 2 t I co(n t co(n t /0/0 hap 7-75

76 Gilbert Multiplier a a Double-Balanced Mixer The Gilbert Multiplier i an extenion of the differential ingle-balanced mixer. The input polarity i revered on the econd diff pair and the ignal v elect between the two diff pair. The current are ummed in the load reitor and the D component i zero. Only um and difference frequencie are preent at the output. 8/0/0 hap 7-76

77 Gilbert Multiplier Mixer Spectra v o (tv 2 m nπ co(n c m t co(n c m t n odd 8/0/0 hap 7-77

78 End of hapter 7 8/0/0 hap 7-78