# ECE 546 Lecture 11 MOS Amplifiers

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1 ECE 546 Lecture MOS Amplifiers Spring 208 Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois ECE 546 Jose Schutt Aine

2 Amplifiers Definitions Used to increase the amplitude of an input signal to a desired level This is a fundamental signal processing function Must be linear (free of distortion) Shape of signal preserved v i (t) AMP v o (t) v () t Av (), t where A is the voltage gain o i Voltage Gain A v o : v vi Power Gain : A p Load Power ( PL ) Input Power ( P ) I ECE 546 Jose Schutt Aine 2

3 Amplifiers A p vi vi oo I I Current Gain A Note A : p AvA i i o : i ii Expressing gain in db (decibels) Voltage gain in db 20log A V Current gain in db 20log A I Power gain in db 0log A P ECE 546 Jose Schutt Aine 3

4 Amplifiers Since output associated with the signal is larger than the input signal, power must come from DC supply P VI VI DC 2 2 PDC PI PL Pdissipated PL 00 P DC Power Efficiency ECE 546 Jose Schutt Aine 4

5 Biasing of Amp Bias will provide quiescent points for input and output about which variations will take place. Bias maintain amplifier in active region. V () t V v () t I QI I V () t V v () t o QO o v () t Av () t o v I Amplifier characteristics are determined by bias point A v dv dv o I at Q ECE 546 Jose Schutt Aine 5

6 Small-Signal Model What is a small-signal incremental model? Equivalent circuit that only accounts for signal level fluctuations about the DC bias operating points Fluctuations are assumed to be small enough so as not to drive the devices out of the proper range of operation Assumed to be linear Derives from superposition principle ECE 546 Jose Schutt Aine 6

7 Biasing of MOS Transistors Bias Characteristics Operation in saturation region Stable and predictable drain current W I C V V 2 L 2 D n ox GS T ECE 546 Jose Schutt Aine 7

8 Single-Supply MOS Bias Choose R and R 2 to fix V G Choose R S and R 2 to fix V S V GS determines I D Choose R D to fix V D ECE 546 Jose Schutt Aine 8

9 Common Source MOSFET Amplifier Bias is to keep MOS in saturation region ECE 546 Jose Schutt Aine 9

10 Common Source MOSFET Amplifier Small-Signal Equivalent Circuit for MOS (device only) W I k V V 2 L 2 ' D n GS T Which leads to g m I V D GS V GS V GSQ 2I V D eff g k W L I ' m 2 n / D where VGS VT V g / eff m is proportional to W L ECE 546 Jose Schutt Aine 0

11 MOSFET Output Impedance To calculate r ds, account for r ds VDS I W D V 2 I GS VGSQ Cox VGS V T 2L DP W I k V V 2 L 2 ' DP n GS T r ds, accounts for channel width modulation resistance. ECE 546 Jose Schutt Aine

12 Midband Frequency Gain Incremental model for complete amplifier A MB v R r R g v R R r R out B ds D m in B g ds D ECE 546 Jose Schutt Aine 2

13 Example For the circuit shown, k=75 A/V 2, V T = V, =0 (a) Find V DQ, V SQ (b) Find the midband gain R 205 V V 4V GQ 2 DD R R2 25 V V V 42I GSQ GQ SQ DQ 2 2 IDQ K VGSQ V T IDQ I I I 2 DQ 0.075(9 2 DQ 4 DQ) 2 2 4IDQ 2IDQ 9 3.3IDQ IDQ 6.33IDQ ECE 546 Jose Schutt Aine 3

14 Example (Cont ) IDQ maor ma 2 IDQ V V R I V DQ DD D DQ V R I V SQ S DQ VDQ VSQ ma 6.22V 0.756V reject since voltage drop across R D will be too large ECE 546 Jose Schutt Aine 4

15 Example (Cont ) W g k I L ' m 2 n DQ A g R MB m D AMB 3.37 ECE 546 Jose Schutt Aine 5

16 Low-Pass Circuit V o In frequency domain: Vi Vo Av jrc V jrc A v jrc jf / f i 2 V o Vi R jc j C ECE 546 Jose Schutt Aine 6

17 Low-Pass Circuit f 2 2 RC 2 2 RC timeconstant ECE 546 Jose Schutt Aine 7

18 High-Pass Circuit V o VR i Vi Vo Av R V i 2 / jc jrc j jf f 2 frc f2 2 RC ECE 546 Jose Schutt Aine 8

19 Model for general Amplifying Element C c and C c2 are coupling capacitors (large) F C in and C out are parasitic capacitors (small) pf ECE 546 Jose Schutt Aine 9

20 Midband Frequencies - Coupling capacitors are short circuits - Parasitic capacitors are open circuits A MB vout Rin RL A v R R R R in g in out L ECE 546 Jose Schutt Aine 20

21 Low Frequency Model - Coupling capacitors are present - Parasitic capacitors are open circuits v vinrin vin jcc Rin R j Cc ( Rg Rin) g Rin jcc R jcc ( Rg Rin) in vab vin R g R in jcc ( Rg Rin) ab ECE 546 Jose Schutt Aine 2

22 MOSFET High-Frequency Model C sb C sbo V V SB o W W 2I gm ncox Veff ncox ID L L V 2 D g g g 2 2 V mb m m F sb eff r V / I ds A D I 2 C WLC WL C 3 gs ox ov ox C C db D C WL C V V gd ov ox dbo DB o ECE 546 Jose Schutt Aine 22

23 CS - Three Frequency Bands ECE 546 Jose Schutt Aine 23

24 Unity-Gain Frequency f T f T is defined as the frequency at which the short-circuit current gain of the common source configuration becomes unity Define: s j (neglect sc gd V gs since C gd is small) I g V sc V o m gs gd gs I g V o m gs V gs sc gs Cgd I i Io gm I s C C i gs gd ECE 546 Jose Schutt Aine 24

25 Calculating f T For s=j, magnitude of current gain becomes unity at T gm gm ft C C 2 C C gs gd gs gd f T ~ 00 MHz for 5-m CMOS, f T ~ several GHz for 0.3m CMOS ECE 546 Jose Schutt Aine 25

26 CS - High-Frequency Response ECE 546 Jose Schutt Aine 26

27 CS Miller Effect Exact Analysis G R G R G R i D g ds D g i ds ' RD R D rds GD gds ' GR i D gm scgd o ' ' 2 ' i i g gs gd gd D i g gd m D gd gs D v v G G sc C sc R G G sc g R s C C R g r ECE 546 Jose Schutt Aine 27

28 CS Miller Effect Exact Analysis We neglect the terms in s 2 since sc C R sc g R or sc g 2 ' ' gd gs D gd m D gs m ' ' ' v GR o i D gm scgd v G G s C C g R C R G G i i g gs gd m D gd D i g Miller If we multiply through by R i G i ECE 546 Jose Schutt Aine 28

29 CS Miller Effect Exact Analysis ' v RD g o m scgd v RG sr C C g R C R RG ' ' i i g i gs gd m D gd D s g From which we extract the 3-dB frequency point f H RG i g ' ' 2 R C C g R C R RG i gs gd m D gd D i g ECE 546 Jose Schutt Aine 29

30 CS Miller Effect Exact Analysis If G g is negligible f H 2 R C C g R C R ' ' i gs gd m D gd D If R i =0 f H 2 C R gd ' D ECE 546 Jose Schutt Aine 30

31 F () s a H Transfer Function Representation In general, the transfer function of an amplifier can be expressed as m sz sz... sz 2 sp sp... sp 2 m m Z, Z 2, Z m are the zeros of the transfer function P, P 2, P m are the poles of the transfer function s is a complex number s = + j ECE 546 Jose Schutt Aine 3

32 Designer is interested in midband operation However needs to know upper 3 db frequency In many cases some conditions are met: Zeros are infinity or at very high frequencies One of the poles ( P ) is at much lower frequency than other poles (dominant pole) If the conditions are met then F H (s) can be approximated by: F 3dB Frequency Determination A() s A F () s ( s) and we have M H H P s / P H ECE 546 Jose Schutt Aine 32

33 3dB Frequency Determination If the lowest frequency pole is at least 4 times away from the nearest pole or zero, it is a dominant pole If there is no dominant pole, the 3 db frequency H can be approximated by: H / P P2 Z Z2 ECE 546 Jose Schutt Aine 33

34 F Open-Circuit Time Constants H () s asas as n n bs bs... bs The coefficients a and b are related to the frequencies of the zeros and poles respectively. n n b... p p2 pn b can be obtained by summing the individual time constants of the circuit using the open-circuit time constant method ECE 546 Jose Schutt Aine 34

35 Open-Circuit Time Constant Method The time constant of each capacitor in the circuit is evaluated. It is the product of the capacitance and the resistance seen across its terminals with: All other internal capacitors open circuited All independent voltage sources short circuited All independent current sources opened The value of b is computed by summing the individual time constants b n CR i i io ECE 546 Jose Schutt Aine 35

36 Open-Circuit Time Constant Method An approximation can be made by using the value of b to determine the 3dB upper frequency point H If the zeros are not dominant and if one of the poles P is dominant, then b P Assuming that the 3 db frequency will be approximately equal to P CR H b i i io ECE 546 Jose Schutt Aine 36

37 Bandwidth of Multistage Amplifier The poles of a multistage amplifier are difficult to obtain analytically An approximate value for the 3dB upper frequency point 3dB can be obtained by assigning an open circuit time constant io to each capacitor C i ECE 546 Jose Schutt Aine 37

38 Bandwidth of Multistage Amplifier The time constant io is the product of the capacitance and the resistance seen across its terminals with: All other internal capacitors open circuited All independent voltage sources short circuited All independent current sources opened The upper 3dB frequency point 3dB is then found by using : 3dB io ECE 546 Jose Schutt Aine 38

39 MOSFET Amp Bandwidth MOSFET amplifier has R sig = 00 k, C gs =C gd = pf, g m = 4 ma/v and R L =3.33 k. Find midband voltage gain and 3-dB frequency. A Vo Rin ' 420 g R V R R M m L sig in sig

40 MOSFET Amp Analysis To determine the 3 db frequency, we first evaluate the time constant associated with C gs. First, we determine the resistance R gs seen by C gs. The capacitance C gd is removed and V sig is short circuited R R R 420 k 00 k80.8 k gs in sig The time constant associated with C gs is C R gs gs gs ns ECE 546 Jose Schutt Aine 40

41 MOSFET Amp Analysis The resistance R gd seen by C gd is found by setting C gs = 0 and short circuiting V sig I I x V R g V gs in x m gs V R gs sig V gs V R ' L x V gs I R x ' ' R Rin Rsig V R R R g RR x ' ' ' ' gd L m L I x ECE 546 Jose Schutt Aine 4

42 MOSFET Amp Analysis The open circuit time constant of C gd is C R gd gd gd ns The upper 3 db frequency H can now be determined from H 806 krad / gs gd 9 s fh H khz ECE 546 Jose Schutt Aine 42

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