Chapter 4 Single-stage MOS amplifiers

Chapter 4 Single-stage MOS amplifiers ELEC-H402/CH4: Single-stage MOS amplifiers 1

Single-stage MOS amplifiers NMOS as an amplifier: example of common-source circuit NMOS amplifier example Introduction to biasing and small-signal operation Biasing in MOS amplifier circuits Fixing VGS Fixing VG and adding a source resistance Using DG Using a constant-current source Small-signal operation and models Introduction to small-signal operation: common-source circuit Small-signal models for NMOS transistors Other common single-stage MOS amplifiers Common-source circuit Common-source with source resistance Common-drain circuit Common-gate circuit Frequency response of MOSFET HF response of NMOS transistor HF response of common-source amplifier LF response of common-source amplifier Outline ELEC-H402/CH4: Single-stage MOS amplifiers 2

NMOS amplifier example common = grounded i D can be defined in two ways Common-source amplifier Kirchhoff s voltage law in V DD - D -v o loop: v V i o DD D D Output of transistor: i D = k n W L v GS V T v o 1 2 v o 2 if v DS v GS V T i D = 1 2 k n W L v GS V T 2 otherwise ELEC-H402/CH4: Single-stage MOS amplifiers 3

Small-signal operation Common-source amplifier V GS is the constant voltage used to bias the transistor v gs is the AC signal to be amplified v V v GS GS gs 1 W 2 id k n VGS vgs Vt 2 L 1 W W 1 W i k V V k V V v k v 2 L L 2 L 2 2 D n GS t n GS t gs n gs W i I i with i k V V v L D D d d n GS t gs v gs V GS ELEC-H402/CH4: Single-stage MOS amplifiers 4

MOSFET transconductance: Small-signal operation Common-source amplifier i W g k V V d m n GS t vgs L Equal to slope of id-vgs characteristic at bias point: g m i v D GS v GS V GS Biasing: setting the bias point Q Small-signal operation: signal variations around the point Q ELEC-H402/CH4: Single-stage MOS amplifiers 5

Output voltage: Small-signal operation Common-source amplifier v V i D DD D D v i g v d D d m D gs v A g d v m D vgs V I i D DD D D d V I i DD D D D d V v d ELEC-H402/CH4: Single-stage MOS amplifiers 6

NMOS amplifier example Common-source amplifier ELEC-H402/CH4: Single-stage MOS amplifiers 7

NMOS amplifier example Common-source amplifier ELEC-H402/CH4: Single-stage MOS amplifiers 8

NMOS amplifier example Biasing and small scale signals v I If input: small AC signal (no DC component) => Add a DC component so that vgs VIQ vi if small, transfer characteristic +/- linear and v V Av v I o oq I gain of circuit Biasing => setting the DC signals such that the transistor circuit operates in a linear region for small AC input Note: choosing the bias point Q appropriately allows for larger AC input signals ELEC-H402/CH4: Single-stage MOS amplifiers 9

Biasing MOS amplifier circuits eal voltages and currents in the transistor are noted with lowercase letters and uppercase indices E.g. v GS, i D, v DS DC voltages and currents for biasing a transistor are usually noted with uppercase letters and uppercase indices E.g. V GS, I D, V DS, Voltage and current variations (AC signals) are noted with lowercase letters and lowercase indices E.g. v gs, i d, v ds In the frequency analysis (LF and HF), AC signals are noted with uppercase letters and lowercase indices E.g. V gs, I d, V ds About notations ELEC-H402/CH4: Single-stage MOS amplifiers 11

Biasing MOS amplifier circuits Biasing by fixing V GS V GS fixed (e.g. by voltage divider with power supply V DD ) V V V V G2 GS G S DD G 1 G2 I D is fixed through transistor equation 1 W I C V V 2 L 2 D n ox GS t ELEC-H402/CH4: Single-stage MOS amplifiers 12

Biasing MOS amplifier circuits I Biasing by fixing V GS 1 C 2 W L V V 2 D n ox GS t can vary a lot between transistors, even for devices supposedly of the same size! For the same value of V GS, I D varies a lot between different transistors Fixing V GS not a good way to set I D! ELEC-H402/CH4: Single-stage MOS amplifiers 13

Biasing MOS amplifier circuits Fixing V G and adding a source resistance V S s D I D I V G V s GS If S is chosen large enough, I D becomes much more stable w.r.t. manufacturing tolerance V G again set with voltage divider ELEC-H402/CH4: Single-stage MOS amplifiers 14

Biasing MOS amplifier circuits Fixing V G and adding a source resistance Adding a source resistance makes the transistor biasing much more stable against transistor manufacturing tolerance I D does not change so much between transistors Key idea: set I D (and let V GS vary depending on transistor) Choosing large values for G1 and G2 ensures that the circuit has large input impedance ELEC-H402/CH4: Single-stage MOS amplifiers 15

Biasing MOS amplifier circuits Using a drain-to-gate feedback resistor V V I G DD D D I D V DD V D GS 1/ D Similar to previous biasing scheme G chosen large (usually MΩ range) to force I G =0 V DD ELEC-H402/CH4: Single-stage MOS amplifiers 16

Biasing MOS amplifier circuits Using a constant-current source Set I D with a constant-current source V G = 0 in this circuit V S is such that V GS matches I D I D fixed V GS = V t + 2I D /(k n W/L) Saturation region iif V DS V GS V t iif V D V t ELEC-H402/CH4: Single-stage MOS amplifiers 17

Biasing MOS amplifier circuits making a current source with 2 NMOS transistors Current mirror Drain Q1 connected to gate Q1: V I EF fixed by, V DD, V SS and NMOS: V D, Q1 G, Q1 V V V DS, Q1 GS, Q1 t saturation region VDD VSS VGS, Q1 IEF 1 W I k V V V Q1 EF n GS, Q1 t 2 LQ 1 V GS, Q1 GS, Q2 1 W I k V V I Q2 D2 n GS, Q2 t 2 LQ 2 D2 I EF W W / L Q2 Q2 / L Q1 Q1 2 2 I D1 I D1 V GS, Q 1 V V V DD SS GS, Q1 ELEC-H402/CH4: Single-stage MOS amplifiers 18

Small-signal operation Example of the common-source circuit V GS is the constant voltage used to bias the transistor v gs is the AC signal to be amplified v V v GS GS gs 1 W 2 id k n VGS vgs Vt 2 L 1 W W 1 W i k V V k V V v k v 2 L L 2 L 2 2 D n GS t n GS t gs n gs W i I i with i k V V v L D D d d n GS t gs v gs V GS ELEC-H402/CH4: Single-stage MOS amplifiers 20

MOSFET transconductance: Small-signal operation Example of the common-source circuit i W g k V V d m n GS t vgs L Equal to slope of id-vgs characteristic at bias point: g m i v D GS v GS V GS Biasing: setting the bias point Q Small-signal operation: signal variations around the point Q ELEC-H402/CH4: Single-stage MOS amplifiers 21

Output voltage: Small-signal operation Example of the common-source circuit v V i D DD D D v i g v d D d m D gs v A g d v m D vgs V I i D DD D D d V I i DD D D D d V v d ELEC-H402/CH4: Single-stage MOS amplifiers 22

Small signal equivalent-circuit models For small- signal operation, MOSFET transistor behaves like a voltage-controlled current source Input voltage v gs between gate and source Input resistance is very high (+/- infinite) Ouptut current g m v gs at drain terminal when analyzing (small) AC signal component, NMOS can be replaced with small-signal equivalent ELEC-H402/CH4: Single-stage MOS amplifiers 23

due to channel pinching NMOS small-signal model taking into account output resistance Variations in v DS result in different i D Imperfect current source r o V A gm k n W / LVGS Vt I D g m and r o depend on biasing point!!! ELEC-H402/CH4: Single-stage MOS amplifiers 24

NMOS small-signal model g m can be expressed several ways i W g k V V d m n GS t vgs L 1 W 2 L 1 I k V V V V 2 I 2 L W k D n GS t GS t D n W g 2k I L m n D g m 1 W 2 W 2ID ID k n VGS Vt k n 2 L L V V V 2I D GS V t GS t 2 ELEC-H402/CH4: Single-stage MOS amplifiers 25

DC voltage sources => short-circuits Small-signal models Converting a circuit to its small-signal equivalent DC current sources => open-circuits Capacitors => shortcircuits Transistors => equivalent mode ELEC-H402/CH4: Single-stage MOS amplifiers 26

Small-signal models T equivalent-circuit model for NMOS transistor ELEC-H402/CH4: Single-stage MOS amplifiers 27

Small-signal models T model with output resistance i r g o 0 r V I A D / g k W L V V in m n GS t ELEC-H402/CH4: Single-stage MOS amplifiers 28

Open-circuit voltage gain: Voltage gain: Input resistance: Amplifiers Definitions and general characteristics A v v v o i i vi i i A vo v v o i L Output resistance: o v i x x v sig 0 ELEC-H402/CH4: Single-stage MOS amplifiers 30

Common-source amplifier Biased with constant-current source Bypass capacitor C S for connecting source to ground (in AC) Coupling capacitors C C1 and C C2 in order not to disturb the DC bias voltage ELEC-H402/CH4: Single-stage MOS amplifiers 31

Common-source amplifier eplace circuit with small-signal equivalent i v v G g 0 i sig G sig v v v r g v gs i o o D m i L A r g vo o D m A r g v o D L m ELEC-H402/CH4: Single-stage MOS amplifiers 32

Common-source amplifier eplace circuit with small-signal equivalent i v i i i i G o v x o ro D i x v sig 0 ELEC-H402/CH4: Single-stage MOS amplifiers 33

Common-source amplifier Summary A r g vo o D m A r g v o D L m i G r o o D D large or small?? Moderately high voltage gain High input resistance elatively high output resistance ELEC-H402/CH4: Single-stage MOS amplifiers 34

CS amplifier with source resistance S at source terminal, biased with current source ELEC-H402/CH4: Single-stage MOS amplifiers 35

CS amplifier with source resistance Use T model for small-signal equivalent (neglect r o ) ELEC-H402/CH4: Single-stage MOS amplifiers 36

CS amplifier with source resistance Use T model for small-signal equivalent gmd Avo 1 gms gm D L Av 1 gms i 1/ gm vgs vi 1/ gm S 1 i g v v 1/ g G m gs i m S o v i x x v sig 0 o D ELEC-H402/CH4: Single-stage MOS amplifiers 37

CS amplifier with source resistance Compared to CS amplifier Summary Decreases gain by factor 1 gms But remember adding a resistance at the source makes the biasing much more stable w.r.t. transistor variations Input and output resistance identical to CS amplifier ELEC-H402/CH4: Single-stage MOS amplifiers 38

Common-gate amplifier Input signal applied to source terminal ELEC-H402/CH4: Single-stage MOS amplifiers 39

CG amplifier Small-signal equivalent (neglecting r o ) v gs v i g v i m v g v i o D L m i A g vo m D A g v m D L i o 1/ g D m ELEC-H402/CH4: Single-stage MOS amplifiers 40

Common-drain amplifier also called source-follower amplifier Drain is not connected to ground, but to VDD Small-signal equivalent is connected to ground ELEC-H402/CH4: Single-stage MOS amplifiers 41

CD amplifier Small-signal equivalent Use either small-signal model for transistor (do not neglect r o ) ELEC-H402/CH4: Single-stage MOS amplifiers 42

Open-circuit gain =? CD amplifier CD circuit characteristics Gain =? Input resistance =? Output resistance =? Why is it called source-follower amplifier? What is it used for? ELEC-H402/CH4: Single-stage MOS amplifiers 43

High-frequency models for MOSFET Several internal capacitances C gs C gd C gs 2 / 3 WLC ox C db 1/ 2 v DB C db These parasitic capacitances will affect the high-frequency response of the transistor (and transistor circuit)! ELEC-H402/CH4: Single-stage MOS amplifiers 45

High-frequency models for MOSFET Small-signal HF model C gd small but plays significant role C db often neglected to simplify analysis ELEC-H402/CH4: Single-stage MOS amplifiers 46

HF response of common-source amplifier eplace NMOS with HF small-signal model Group r o, D and L, and replace source and G with Thevenin equivalent, and sig and G ELEC-H402/CH4: Single-stage MOS amplifiers 47

HF response of common-source amplifier HF analysis Consider I gd small w.r.t. g m V gs I gd jcgd Vgs Vo V jc V g V gd gs m L gs jc 1g V gd m L gs g V o m L gs ELEC-H402/CH4: Single-stage MOS amplifiers 48

HF response of common-source amplifier HF analysis (cont d) eq gd 1 m L 1 1/ jcin Vgs V sig 1/ jc C C g C C C C C g in gs eq gs gd m L in sig 1 G V 1 jcin sig G sig sig C 0 1/ in sig ELEC-H402/CH4: Single-stage MOS amplifiers 49

HF response of common-source amplifier V o G gml V sig G sig 1 j 0 At high frequencies, gain tends to zero Cut-off frequency: HF analysis (cont d) f H 1 0 1 2 2C in sig ELEC-H402/CH4: Single-stage MOS amplifiers 50

LF response of common-source amplifier each coupling capacitor creates a high-pass filter Effect of C C1 V g G G G sig sig G 1 1 jc C1 V sig 1 1 jc C1 G sig V sig High-pass with cut-off frequency: 1 fp 1 2C C1 G sig ELEC-H402/CH4: Single-stage MOS amplifiers 51

LF response of common-source amplifier each coupling capacitor creates a high-pass filter Effect of C S (use T-model) I d Vg 1 1 g jc m 1 1 1 1 j g m S C S gv m g High-pass with cut-off frequency: 1 fp2 2C 1/ g S m ELEC-H402/CH4: Single-stage MOS amplifiers 52

LF response of common-source amplifier each coupling capacitor creates a high-pass filter Effect of C C2 (current divider) I o I I d d D D D D 1 jc L C 2 1 L 1 1 jc C 2 D L High-pass with cut-off frequency: 1 fp2 2C C2 D L ELEC-H402/CH4: Single-stage MOS amplifiers 53

V o L o LF response of common-source amplifier I Total low-frequency response V o D G j j j L gm Vsig D L G sig j P 1 j P2 j P3 Usually, one cut-off frequency is higher than the two others ELEC-H402/CH4: Single-stage MOS amplifiers 54

Frequency response of common-source amplifier Total LF and HF response ELEC-H402/CH4: Single-stage MOS amplifiers 55