Broadband LNA andSummary of a paper about gm-Boosted

Common-Gate LNA

Xiaoyoung Li, Member, IEEE,Sudip Shekhar, Student Member, IEEE,

David J. Allstot, Fellow, IEEE&

Summarized by Taeyoung Chung

2

Outline

• Broadband LNA Techniques

• Common-Gate LNA

• gm-Boosted Common-Gate LNA

– Principle of Operation

– Capacitor Cross-Coupled gm-Boosted CGLNA

– Transformer-Coupled gm-Boosted CGLNA

3

Broadband LNA Techniques

• To obtain broadband input matching, the input impedance of

the amplifier should be resistive and equal to 50Ω over the en-

tire bandwidth.

• Broadband input matching is difficult for common source type

amplifiers due to capacitive nature of the transistor input

• Types of broadband LNA

– Resistive Feedback

– LC Ladder Matching Network

– Common Gate Input Stage

– Distributed Amplifiers

4

Common Gate

• Gain and Input Matching

– The input matching is achieved by making the effective input re-

sistance(1/gm) equal to RS(50Ω)

1

m Lv

L

o

g ZA

Z

r

11 L

inm o

ZR

g r

5

Common Gate

(1 )

in gs m gs S

m S gs

V V g V R

g R V

,

1

d m gs

mg

m S

m eff g

i g V

gV

g R

g V

1

1gs gm S

V Vg R

, 1m

m effm S

gg

g R

Small signalequivalent circuit

• Noise Factor

–

– Source Degeneration

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( )

/ /

/ ( ) /

1

i i source i i source o totali

o o o total i o total i source

o total o source o added o added

o source o source o source

S N S N NSNRF

SNR S N S G N G N

N N N NF

N N N

6

Common Gate

• Noise Factor2

222

2 22

1

1 11 1

1

ndm S nd

m SnSm SnS

m S

ig R i

Fg Rig R

ig R

204nd di kT g f

2 14nS Si kTR f

2

01

02

1

4 11

4

1 1m

m S

d

S m S

d

g RS

kT g fF

kTR f g R

g

g R

• ins : the current noise of the source resistance

• ind : the drain current noise of the MOSFET

• Induced gate noise is usually negligible.

7

gm-Boosted CGLNA

• Noise Factor

2

01

02 2

(1 ) 1

4 11

4 (1 )

1 1(1 ) (1 )m

m S

d

S m S

d

S A g R

kT g fF

kTR f A g R

g

A g R A

(1 )m mG A g

=> Enhanced NF by the fraction (1+A)

8

Capacitor Cross-Coupled gm-Boosted CGLNA

1c

c gs

CA

C C

(1 ) 1

1(1 )

12

m SA g R

c gs

c gs

FA

C C

C C

In general, Cc>>Cgs

12

F

9

Capacitor Cross-Coupled gm-Boosted CGLNA

• Two drawbacks of Capacitor Cross-Coupled CGLNA

① It consumes twice the bias current and silicon area as its sin-

gle-ended counterpart

② A is always less than one due to the capacitor divider between

Cgs and coupling capacitance Cc.

1c

c gs

CA

C C

10

Transformer-Coupledgm-Boosted CGLNA

(a) Single-ended (b) Fully differential

(c) Small signal model

S xx m gs S

P P

Mi vi g v i

L sL ⓐ

g PS

S S

v Mii

sL L ⓑ

Sgs

gs

iv

sCⓒ

S xP

P P

Mi vi

L sL ⓓ

g x gsv v v ⓔ

/ P Sk M L L

/S Pn L L

From the small signal equivalent circuit,

coupling coefficient

turns ratio

11

Transformer-Coupledgm-Boosted CGLNA

• Solving (a)-(e) in the previous slide,

2 2

2 2 2 2

1 / 1 / 11 1

1 1 1 1m S S gs m S S gsx

inx P SS gs S gs

k n g sL k n s L C g sL nk s L CiY

v sL sLk s L C k s L C

11 (1 )S S

in m gs m gsP P P

L Lk kY g sC g nk sC

sL n L n L

211 (1 2 )in m gs

P

Y nk g nk n sCsL

2 21 1S gsk s L C

2 /S Pn L L

1(1 )

Fnk

(when induced gate noise is not considered)

12

Transformer-Coupledgm-Boosted CGLNA

• when induced gate noise is considered,

• To minimize F, choose k as a maximized value. (k=1)

• Setting results in

22 2

3

1 211

1 5 1T

nk nwF

nk w nk

2

11 1

1 5 T

wF n

n w

channel noise∝1/(1+n)

induced gate noise∝1+n

/ 0F n

2

51T

opt

wn

w

1 25opt

T

wF

w

(optimum noise factor)

13

Transformer-Coupledgm-Boosted CGLNA

• Result