Single State Transistor

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 19-1

Lecture 19 - Transistor Amplifiers (I)

Common-Source Amplifier

November 15, 2005

Contents: 1. Amplifier fundamentals 2. Common-source amplifier 3. Common-source amplifier with current-source supply

Reading assignment: Howe and Sodini, Ch. 8, §§8.1-8.6 Announcements: Quiz 2: 11/16, 7:30-9:30 PM,

open book, must bring calculator; lectures #10-18.

Quiz 2 TA Review Session: 11/15, 7:30-9:30 PM,

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 19-2

Key questions

• What are the key figures of merit of an amplifier?

• How can one make a voltage amplifier with a single MOSFET and a resistor? • How can this amplifier be improved?

Lecture 19-3

6.012 - Microelectronic Devices and Circuits - Fall 2005

1. Amplifier fundamentals Goal of amplifiers: signal amplification.

vOUT +V

+

output signal

+

vIN

RL

vOUT -

-

vIN

-V

input signal

Features of amplifier: • Output signal is faithful replica of input signal but amplified in magnitude. • Active device is at the heart of amplifier.

• Need linear transfer characteristics for distortion not to be introduced.

Lecture 19-4

6.012 - Microelectronic Devices and Circuits - Fall 2005

Signal could be represented by current or voltage

⇒ four broad types of amplifiers: RS

vs

voltage amplifier

+ −

is

+ −

transconductance amplifier

RS

transresistance amplifier

RL

RL

iout

is

+ vout −

iout

RS

vs

RL

RS

current amplifier

RL

+ vout −

Lecture 19-5

6.012 - Microelectronic Devices and Circuits - Fall 2005

More realistic transfer characteristics:

vOUT

output signal

Q

vIN

input signal

• Transfer characteristics linear over limited range of voltages: amplifier saturation. • Amplifier saturation limits signal swing.

• Signal swing also depends on choice of bias point, Q (also called quiescent point or operating point). Other features desired in amplifiers: • Low power consumption. • Wide frequency response [will discuss in a few days].

• Robust to process and temperature variations. • Inexpensive: must minimize use of unusual components, must be small (in Si area)

Lecture 19-6

6.012 - Microelectronic Devices and Circuits - Fall 2005

2. Common-Source Amplifier

Consider the following circuit: V+=VDD

RD

iR

signal source RS

iD

+ vOUT

vs VGG

signal load RL

V-=VSS

Consider it first unloaded by RL. How does it work? • VGG, RD and W/L of MOSFET selected to bias transistor in saturation and obtain desired output bias point (i.e. VOU T = 0). • vGS ↑ ⇒ iD ↑ ⇒ iR ↑ ⇒ vout ↓ • Av = vvout < 0; output out of phase from input, but if s amplifier well designed, |Av | > 1. [watch notation: vOU T (t) = VOU T + vout(t)]

Lecture 19-7

6.012 - Microelectronic Devices and Circuits - Fall 2005

Load line view of amplifier:

load line

IR=ID VDD-VSS

VGG-VSS=VDD-VSS

RD

VGG-VSS

VGG-VSS=VT 0 VSS

VDD

VOUT

Transfer characteristics of amplifier:

VOUT VDD

VSS

0

VT

VDD-VSS VGG-VSS

Want: • Bias point calculation; • small-signal gain; • limits to signal swing • frequency response [in a few days]

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 19-8

2 Bias point: choice of VGG, W/L, and RD to keep transistor in saturation and to get proper quiescent VOU T . Assume MOSFET is in saturation: ID =

W µnCox (VGG − VSS − VT )2 2L VDD − VOU T IR = RD

If we select VOU T = 0: VDD W 2 ID = IR = µnCox (VGG − VSS − VT ) = 2L RD Then: VGG =

� � � � � � �

2VDD + VSS + VT W RD L µnCox

Lecture 19-9

6.012 - Microelectronic Devices and Circuits - Fall 2005

2 Small-signal voltage gain: draw small-signal equivalent circuit model:

RD +

vin

vgs

-

D

G

+

+

gmvgs

ro

vout -

- S

+

+

vin

gmvin

-

ro//RD

vout -

vout = −gm vin(ro//RD ) unloaded Then unlo aded voltage gain: Avo =

vout = −gm (ro//RD ) vin

Lecture 19-10

6.012 - Microelectronic Devices and Circuits - Fall 2005

2 Signal swing: VDD

RD signal source +

RS

vOUT

vs VGG

-

VSS

• Upswing: limited by transistor going into cut-off: vout,max = VDD • Downswing: limited by MOSFET entering linear regime: VDS,sat = VGS − VT or vout,min − VSS = VGG − VSS − VT Then: vout,min = VGG − VT

Lecture 19-11

6.012 - Microelectronic Devices and Circuits - Fall 2005

2 Effect of input/output loading: VDD

RD

iR iL

signal source iD

RS

+ vOUT

vs VGG

RL

-

VSS

• Bias point not affected because selected VOU T = 0. • Signal swing: – Upswing limited by resistive divider: RL vout,max = VDD RL + RD – Downswing not affected by loading • Voltage gain: – input loading (RS ): no effect because gate does not draw current; – output loading (RL ): RL detracts from voltage gain because it draws current. |Av | = gm(ro //RD //RL) < gm (ro //RD )

Lecture 19-12

6.012 - Microelectronic Devices and Circuits - Fall 2005

2 Generic view of loading effect on small-signal operation:

Two-port network view of small-signal equivalent circuit model of voltage amplifier: Rin is input resistance

Rout is output resistance

Avo is unloaded voltage gain

RS

Rout +

+

vs

+

+

vin

-

Rin

-

input loading

-

Avovin

RL

vout -

unloaded circuit

output loading

Voltage divider at input:

s vin = Rin Rinv+R S

Voltage divider at output:

vin vout = RL RAoutvo+R L

Loaded voltage gain: vout Rin RL = Avo Av = vs Rin + RS RL + Rout

Lecture 19-13

6.012 - Microelectronic Devices and Circuits - Fall 2005

• Calculation of input resistance, Rin: - load amplifier with RL - apply test voltage (or current) at input, measure test current (or voltage) For common-source amplifier:

it

+ +

vt -

vgs

gmvgs

ro//RD

-

vt it = 0 ⇒ Rin = = ∞ it No effect of loading at input.

RL

Lecture 19-14

6.012 - Microelectronic Devices and Circuits - Fall 2005

• Calculation of output resistance, Rout : - load amplifier at input with RS - apply test voltage (or current) at output, measure test current (or voltage) For common-source amplifier:

it +

RS

+

vgs

gmvgs

ro//RD

-

vgs = 0 ⇒ gm vgs = 0 ⇒ vt = it(ro //RD ) Rout

vt = = ro//RD it

-

vt

Lecture 19-15

6.012 - Microelectronic Devices and Circuits - Fall 2005

Two-port network view of common-source amplifier:

RS

Rout +

+

vs

+

vin

-

-

input loading

+

Rin

-

Avovin

unloaded circuit

RL

vout -

output loading

vout vs Rin RL RL = Avo = −gm(ro //RD ) Rin + RS RL + Rout RL + ro //RD

Av =

Or: Av = −gm (ro //RD //RL )

Lecture 19-16

6.012 - Microelectronic Devices and Circuits - Fall 2005

2 Design issues of common-source amplifier (unloaded): Examine bias dependence: |Avo | = gm(ro //RD )  gm RD Rewrite |Avo | in the following way: � � � � � �

W VDD VDD √ ∝ |Avo |  gmRD = 2 µnCox ID L ID ID Then, to get high |Avo |: ⇒ VDD ↑ ⇒ ID ↓ Both approaches imply ⇒ RD =

VDD ID

↑

Consequences of high RD : • large RD consumes a lot of Si real state • large RD eventually compromises frequency response Also, it would be nice not to use any resistors at all! ⇒ Need better circuit.

Lecture 19-17

6.012 - Microelectronic Devices and Circuits - Fall 2005

3. Common-source amplifier with current-source supply VDD

iSUP signal source iD

RS

signal load

+

RL

vOUT

vs VGG

-

VSS

Loadline view: load line

iSUP=ID

VGG-VSS=VDD-VSS

ISUP

VGG-VSS

VGG-VSS=VT 0 VSS

VDD

VOUT

Lecture 19-18

6.012 - Microelectronic Devices and Circuits - Fall 2005

Current source characterized by high output resistance: roc. Then, unloaded voltage gain of common-source stage:

|Avo | = gm (ro //roc )

significantly higher than amplifier with resistive supply.

Can implement current source supply by means of pchannel MOSFET: VDD

VB

iSUP

signal source iD

RS

+ vOUT

vs VGG

VSS

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 19-19

• Relationship between circuit figures of merit and device parameters Remember: � � � � � �

gm = 2

W µnCox ID L

1 L ro  ∝ λnID ID Then: Circuit Parameters Device ∗ |Avo | Rin Rout Parameters gm (ro//roc ) ∞ ro//roc ISU P ↑ ↓ ↓

W ↑ -

↑ µnCox ↑ -

↑ L↑ ↑ ↑ ∗

adjustments are made to VGG so none of the other parameters change CS amp with current supply source is good voltage amplifier (Rin high and |Av | high), but Rout high too ⇒ voltage gain degraded if RL ro//roc .

6.012 - Microelectronic Devices and Circuits - Fall 2005

Lecture 19-20

Key conclusions

• Figures of merit of an amplifier: – gain – signal swing – power consumption – frequency response – robustness to process and temperature variations • Common-source amplifier with resistive supply: trade-

off between gain and cost and frequency response.

• Trade-off resolved by using common-source amplifier with current source supply. • Two-port network computation of voltage gain, input resistance and output resistance of amplifier.