ECE 546 Lecture 11 MOS Amplifiers - University of Illinois ...

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ECE 546 – Jose Schutt‐Aine 1

ECE 546Lecture 11

MOS AmplifiersSpring 2020

Jose E. Schutt-AineElectrical & Computer Engineering

University of Illinoisjesa@illinois.edu

• 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

Amplifiers

( ) ( ),o iv t Av t where A is the voltage gain

vi(t) vo(t)AMP

vVoltage Gain Av

( ) :( )

Load Power PPower Gain AInput Power P

Amplifiers

: p v iNote A A A

iCurrent Gain Ai

v iAv i

20log VVoltage gain in dB A

20log ICurrent gain in dB A

10log PPower gain in dB A

Expressing gain in dB (decibels)

Amplifiers

1 1 2 2DCP V I V I

P Power EfficiencyP

Since output associated with the signal is larger than the input signal, power must come from DC supply

DC I L dissipatedP P P P

Biasing of Amp

( ) ( )I QI IV t V v t

Bias will provide quiescent points for input and output about which variations will take place. Bias maintain amplifier in active region.

( ) ( )o QO oV t V v t

( ) ( )o v Iv t A v to

vI at Q

Amplifier characteristics are determined by bias point

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

• Bias Characteristics– Operation in saturation region– Stable and predictable drain current

Biasing of MOS Transistors

212D n ox GS T

WI C V VL

Single-Supply MOS Bias

– Choose R1 and R2 to fix VG– Choose RS and R2 to fix VS– VGS determines ID– Choose RD to fix VD

Common Source MOSFET Amplifier

Bias is to keep MOS in saturation region

Small-Signal Equivalent Circuit for MOS (device only)

Common Source MOSFET Amplifier

2'12D n GS T

WI k V VL

GS GSQ

GS effV V

I IgV V

GS T effwhere V V V /mg is proportional to W L

'2 /m n Dg k W L I

Which leads to

To calculate rds, account for

2GS GSQ

D DPV V ox GS T

Vr WI IC V VL

2'12DP n GS T

WI k V VL

rds, accounts for channel width modulation resistance.

MOSFET Output Impedance

Midband Frequency Gain

out ds DBMB m

in B g ds D

v r RRA gv R R r R

Incremental model for complete amplifier

For the circuit shown, k=75 A/V2, VT=1 V, =0(a) Find VDQ, VSQ(b) Find the midband gain

20 5 425

GQ DDRV V V

Example

4 2 GSQ GQ SQ DQV V V I

20.075(9 12 4 )DQ DQ DQI I I

2 24 12 9 13.3 6.33 2.25 0DQ DQ DQ DQ DQI I I I I

2 20.075 4 2 1DQ GSQ T DQI K V V I

26.33 93.167 0.378 or 5.9532

DQI mA mA

20 10 0.378 16.22DQ DD D DQV V R I V

2 0.378 0.756SQ S DQV R I V

Example (Cont’)

16.22DQV V

0.756SQV V

reject since voltage drop across RD willbe too large0.378DQI mA

0.337 10 3.37MB m DA g R

Example (Cont’)

'2 4 0.075 0.378 0.337m n DQWg k IL

3.37MBA

Low-Pass Circuit

In frequency domain:1

j CRj C

i oo v

V VV Aj RC V j RC

1 11 1 /vA

j RC jf f

2 time constantRC

Low-Pass Circuit

High-Pass Circuit

1 11i i

oV R VV

Rj C j RC

1 11 1 /1

VAV jf fj

Model for general Amplifying Element

Cc1 and Cc2 are coupling capacitors (large) F

Cin and Cout are parasitic capacitors (small) pF

Midband Frequencies

- Coupling capacitors are short circuits

- Parasitic capacitors are open circuits

out in LMB

in g in out L

v R RA Av R R R R

Low Frequency Model- Coupling capacitors are present- Parasitic capacitors are open circuits

1 1 ( )in in in c in

abc g in

v R v j C Rvj C R RR R

( )1 ( )

c g ininab in

g in c g in

j C R RRv vR R j C R R

22 Dm n ox eff n ox D

W W Ig C V C IL L V

MOSFET High-Frequency Model

2 2mb m mF sb

g g gV

1/ds A DD

r V II

23gs ox ov oxC WLC WL C

gd ov oxC WL C

CS - Three Frequency Bands

o m gs gd gsI g V sC V

Unity-Gain Frequency fTfT is defined as the frequency at which the short-circuit current gain of the common source configuration becomes unity

(neglect sCgdVgs since Cgd is small)

o m gsI g V i

gsgs gd

IVs C C

i gs gd

I gI s C C

s jDefine:

For s=j, magnitude of current gain becomes unity at

T Tgs gd gs gd

g gfC C C C

fT ~ 100 MHz for 5-m CMOS, fT ~ several GHz for 0.13m CMOS

Calculating fT

CS - High-Frequency Response

'i D m gdo

' ' 2 'i i g gs gd gd D i g gd m D gd gs D

G R g sCvv G G s C C sC R G G sC g R s C C R

CS – Miller Effect – Exact Analysis

'D D ds

1R R || rG g

2 ' 'gd gs D gd m D gs ms C C R sC g R or sC g

We neglect the terms in s2 since

i D m gdo' '

i i g gs gd m D gd D i g

G R g sCvv G G s C C 1 g R C R G G

If we multiply through by

Miller

'D m gdo

' 'i i g i gs gd m D gd D s g

R g sCvv 1 R G s R C C 1 g R C R 1 R G

H ' 'i gs gd m D gd D i g

1 R Gf

2 R C C 1 g R C R 1 R G

From which we extract the 3-dB frequency point

H ' 'i gs gd m D gd D

1f2 R C C 1 g R C R

H 'gd D

1f2 C R

If Gg is negligible

If Ri =0

...( )

s Z s Z s ZF s a

s P s P s P

Transfer Function Representation

Z1, Z2,…Zm are the zeros of the transfer function

P1, P2,…Pm are the poles of the transfer function

In general, the transfer function of an amplifier can be expressed as

s is a complex number s = + j

•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 frequenciesOne of the poles (P1) is at much lower frequency than other poles (dominant pole)

• If the conditions are met then FH(s) can be approximated by:

1( ) and we have1 /H H P

( ) ( )M HA s A F s3dB 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 Hcan be approximated by:

2 2 2 21 2 1 2

1 1 1 11/ ... 2 ...HP P Z Z

3dB Frequency Determination

1 ...( )1 ...

a s a s a sF sb s b s b s

The coefficients a and b are related to the frequencies of the zeros and poles respectively.

Open-Circuit Time Constants

b1 can be obtained by summing the individual time constants of the circuit using the open-circuit time constant method

1 1 1...p p pn

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 circuitedAll independent voltage sources short circuitedAll independent current sources opened

• The value of b1 is computed by summing the individual time constants

• An approximation can be made by using the value of b1 to determine the 3dB upper frequency point H

• If the zeros are not dominant and if one of the poles P1 is dominant, then

Assuming that the 3‐dB frequency will be approximately equal to P1

Open-Circuit Time Constant Method

• 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 Ci

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 circuitedAll independent voltage sources short circuitedAll independent current sources opened

• The upper 3dB frequency point 3dB is then found by using :

Bandwidth of Multistage Amplifier

MOSFET amplifier has Rsig= 100 k, Cgs=Cgd= 1 pF, gm = 4 mA/V and RL’ =3.33 k. Find midband voltage gain and 3-dB frequency.

MOSFET Amp Bandwidth

' 420 4 3.33 10.8420 100

o inM m L

sig in sig

V RA g RV R R

|| 420 ||100 80.8gs in sigR R R k k k

12 31 10 80.8 10 80.8gs gs gsC R ns

MOSFET Amp AnalysisTo determine the 3‐dB frequency, we first evaluate the time constant associated with Cgs. First, we determine the resistance Rgs seen by Cgs. The capacitance Cgd is removed and Vsig is short‐circuited

The time constant associated with Cgs is

gs gsx

in sig

gs xV I R

x m gsL

V VI g V

' ' ' 'x

gd L m Lx

VR R R g R RI

The resistance Rgd seen by Cgd is found by setting Cgs = 0 and short‐circuiting Vsig

MOSFET Amp Analysis

' ||in sigR R R

12 61 10 1.16 10 1160gd gd gdC R ns

1 1 806 /80.8 1160 10H

krad s

128.32

HHf kHz

MOSFET Amp Analysis

The open‐circuit time constant of Cgd is

The upper 3‐dB frequency H can now be determined from

ECE 546 Lecture 11 MOS Amplifiers - University of Illinois ...

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