rf module design - [chapter 5] low noise amplifier

RF Transceiver Module DesignChapter 5

Low Noise Amplifier李健榮助理教授

Department of Electronic EngineeringNational Taipei University of Technology

Outline

• Basic Amplifier Configurations

• Cascode Low Noise Amplifier (LNA)

• Feedback Topologies

• Classical Two-port Noise Theory

• Input Matching for an LNA

• Noise Figure and Bias Current

• Effect of the Cascode on Noise Figure

• Summary

Department of Electronic Engineering, NTUT2/26

Simple Transistor Amplifier (I)

• Common-emitter (CE) configuration

• Common-base (CB) configuration

• Common-collector (CC) configuration

CE (driver)

CCV

inV

outV

EEV

CB (cascode)

CCV

inV

outV

EEV


CC (buffer)

CCV

inV

outV

EEV

• Bipolar Transistor Amplifier

• MOSFET Transistor Amplifier

Simple Transistor Amplifier (II)

CE CB CC

Current Gain High (β) Low (~1) High (1+β)

Voltage Gain High High Low (~1)

Power Gain High Medium High

Zin Medium Low High

Zout Medium High Low

I/O Phasing 180o In-phase In-phase

CS CG CD

Voltage Gain High High Low (~1)

Power Gain High Medium High

Zin High Low High

Zout High High Low

I/O Phasing 180o In-phase In-phase


Common-Emitter Configuration

• Gain

• Input Impedance

o Lvo m L

i b e

v r ZA g Z

v r r rπ

π

= = −+

≃

er : B-E diode resistance as seen from emitter

er rπ β= 1m eg r=

in bZ r rπ= +

For low frequencies, the parasitic capacitanceshave been ignored and rb has been assume to below compared to .rπ

CE (driver)

CCV

inV

outV

EEV

LZormg vπrπCπ

br

ivov

Cµ

vπ

+

−

+

−

+

−

and


Miller Effect (I)

• Impedance that connects from input to output

fZ

LZ

inv outv

inZ outZ

vA

( ) 1fin

inin out f v

ZvZ

v v Z A= =

− −

( ) ( ) for 11 1

foutout f v

out in f v

ZvZ Z A

v v Z A= = >>

− −≃

fC

LZ

inV outV

inZ outZ

vA

( )1 11 1

fin

v f v

sCZ

A sC A= =

+ +

( ) ( )1 1

1 1 1 1f

outv f v

sCZ

A sC A= =

+ +

Like larger cap

Slightly larger


Miller Effect (II)

• At radio frequencies:

• Miller’s theorem

Cπ : Low impedance

Cµ : Provides feedback

( )1 1oA m L m L

vC C C g Z C g Z

vµ µ µπ

= − = +

≃

11 1B

o m L

vC C C C

v g Zπ

µ µ µ

= − = +

≃

The dominant pole is usually the one formed byand AC Cπ

( ) ( )1

1

2 ||p

b s A

fr r R C Cπ ππ

=+ +

sR : source resistance

Note that as ZL decreases, CA is reducedand the dominant pole frequency isincreased.

Cµvπ ov

vπ ov

AC

BC


Simplified CE Small-signal Model

• Simplified model for transistor above the dominant pole:Ignore and just use in transistor model with little error.

• Knowing the pole frequency, we can estimate the gain athigher frequencies, assuming that there are no other polespresent, with

( )

1

1

vov

p

AA f

fj

f

=+

目前無法顯示此圖像。

rπ

br

iv vπ Cπ

Cµ

mg vπ or LZ ovsv

sR

+

−

+

−

+

−

+

−


Common-Base Configuration

• CB amplifier is often combined with the CE amplifier to froman LNA but it can be used by itself as well.

• Low Zin when driven from a current source, it can pass currentthrough it with near unity gain up to very high frequency.Therefore, with an appropriate choice of impedance levels, itcan also provide voltage gain.

ini

br

vπ

Cµ

Cπmg vπrπ LZ

outi

+

−

Ignoring output impedance


Cascode LNA (I)

• CB + CE to form a cascode LNA.

• Since the CB amplifier has a currentgain of approximately 1, then,

ic1 ≈ ic2 = gm1vi .

• The gain is the same as for the CEamplifier. However, the cascodetransistor reduces the feedback of ,resulting in increased high-frequency gain.

1Cµ

CR

CCV

CbiasV

outv

inv

EEV

Driver Q1

Cascode Q2

2ci

1ci

( ) ( )1

1 1

1

2 || 2p

b s

fr r R C Cπ π µπ

=+ +

21 mg≈


Cascode LNA (II)

• Advantages:

� Improves frequency response.

� Adding another transistor improves the isolation.

• Disadvantages:

� Additional poles can become a problem for a large load resistance.

� An additional bias voltage is required, and if this cascode bias node isnot properly decoupled, instability can occur.

� Reduce signal swing at a given supply voltage, compared to the simpleCE amplifier.


Common-Collector Configuration (I)

• The CC amplifier (emitter follower) is a very useful general-purpose amplifier.

• Voltage gain is close to 1 (buffer).

• High input impedance and low output impedance (goodbuffer/output stage).

ER

CCV

iv

EEV

ov

ivB s bR R r= +

vπ rπ Cπ

ER

mg vπ

Cµ

+

−


Common-Collector Configuration (II)

• Miller effect is not a problem, since the collector is grounded.

• Since is typically much less than , it can be left out of theanalysis with little impact on the gain.

• The input impedance:

• The output impedance:

CµCπ

ivB s bR R r= +

vπ rπ Cπ

ER

mg vπ

Cµ

+

−

( )1A E mZ Z R g Zπ π= + +

1

1B B

out em m

r R sC r RZ r

g r sC r gπ π π

π π π

+ += ≈ ≈+ +


CE with Series Feedback (I)

• CE with Series Feedback (Emitter Degeneration)

� Cascode:

Higher frequencies, superiorreverse isolation, but suffersfrom reduced linearity.

� Most CE and cascode LNAs:

Employing the degenerationtransforms the impedance realpart looking into the base to ahigher impedance formatching. De-generation alsotrades gain for linearity.

outRF

CCV

1L 1C LR

inRF 1Q

eL

CE tuned LNA

CCV

1L 1C LR

2Q

1Q

eL

inRF

biasVoutRF

Cascode tuned LNA


CE with Series Feedback (II)

• As the degeneration becomes larger, the gain becomes solelydependent on the ratio of the two impedances.

• If ZE is inductive, then it will become a real resistance whenreflected to base (raise Zin, useful for matching purposes).

• Conversely, if ZE is capacitive, it will tend to reduce Zin andcan even make it negative.

1

out m L L

in EEm E

v g R R

v ZZg Z

Zπ

−= ≈ −

+ +

sR rπ Cπ mg vπ

EL EREC

xiinv

vπ

Zπ

EZ

+

−

( )1in E mZ Z Z g Zπ π= + +


CE with Shunt Feedback (I)

• Matching over a broad bandwidth while having minimalimpact on the noise figure.

• Rf forms the feedback and Cf allow for independent biasing.

• Can be modified to become a cascode amplifier.

• Ignoring the Miller effect and assuming Cf is a short circuit(1/ωCf << Rf ), the gain is given by

1 1

Lm L

o m LFv

L Li

f f

Rg R

v g RRA

R RvR R

−−= = ≈

+ +

The gain without feedback (−gmRL) is reducedby the presence of feedback.

sRfC

fR LR

ov

sv

inZ

outZ


CE with Shunt Feedback (II)

• Input impedance

The last term, which is usually dominant, shows that the input impedance is equalto Rf +RL divided by the open loop gain. Input impedance for the shunt feedbackamplifier has less variation over frequency and process than open-loop amplifier.

• Output impedance

• Feedback results in the reduction of the role the transistorplays in determining the gain and therefore improves linearity,but the presence of Rf may degrade the noise depending on thechoice of value for this resistor.

( )( ) || ||1

f L f L f Lin f

f L m L m L m L

Z R R R R R RZ R Z

R R Z g R g R g Rπ

ππ

+ + += ≈ ≈

+ + +

( ) ( )1 || ||11 || ||

f fout

m s fs f m

f

R RZ

g R R ZR R Z g

Rπ

π

= ≈ +

+ −


Example

2.5 pF2 V

3 V

LR

sRfR

12-GHz fT transistorscurrents about 5 mA

ov

svInput matching

Sample plots using shunt feedback

22

20

18

16

14

12

10100 300 500 700 900 1100 1300 1500

Gain

Noise figure

OIP3

IIP3

2

0

2−

4−

6−

8−

10−

3

2.5

2

1.5

1.0

0.5

0

IIP3(dBm)

NF(dB)

RfG

ain

(dB

), O

IP3

(dB

m)


CE w/ Shunt Feedback and CC Output Buffer

• CE with an output tends to make for a better match.

• With an output buffer, the voltage gain isno longer affected by the feedback, so it is approximately thatof a CE amplifier given by [RL /(RE + 1/gm )] minus the loss inthe buffer.

fC fR

LR

CCV CCV

biasI

ER

inV

outVC


Classical Two-port Noise Theory (I)

• Use these equivalences, the expression for noise factor can bewritten purely in terms of impedances and admittances:

NoisyTwo-portsY

si sYsi

ne

niNoiselessTwo-port

22

2s n s n

s

i i Y eF

i

+ += n c ui i i= + c c ni Y e=

( ) 2 22 2 2

2 21s u c s n u c s n

s s

i i Y Y e i Y Y eF

i i

+ + + + += = +

where

2

4n

n

eR

kTB≡

2

4u

u

iG

kTB≡

2

4s

s

iG

kTB≡

( ) ( )2 22

1 1u c s c s nu c s n

s s

G G G B B RG Y Y RF

G G

+ + + ++ + = + = +

, ,and


Classical Two-port Noise Theory (II)

• Optimum source admittance:

s c optB B B= − = 2us c opt

n

GG G G

R= + =and

2min 1 2 1 2 u

n opt c n c cn

GF R G G R G G

R

= + + = + + +

( ) ( )2 2

minn

s opt s opts

RF F G G B B

G = + − + −

GA circles

NF circles

Inputmatching

OutputmatchingAmplifier

sΓ LΓ0Z

0Z

inΓ outΓoutZ

inZ

Department of Electronic Engineering, NTUT

Min. noise figure, min ,, s optNF Γ

Max. available power gain, s in∗Γ = Γ

21/26

Input Matching of LNAs for Low Noise

• Many methods for matching the input using passive circuitelements are with varying bandwidth and complexity.

• Use two inductors to provide the power and noise match forthe LNA, the input impedance is (assume Miller effect is not importantand that r

πis not significant at the frequency of interest)

• To be matched:

, therefore

If Miller effect is considered, the capacitancewill be larger than C

π, and a larger inductor

will be required to perform the match. Also, theimaginary part of the input impedance mustequal zero. Therefore,

inRFbL

1Q

eLC

m es

g LR

Cπ

= se

m

R CL

gπ=

2

1 sb

m

R CL

C gπ

πω= −

m ein e b

g LjZ j L j L

C Cπ π

ω ωω−= + + +


NF and Bias Current (I)

• Noise due to the base resistance is in series with the inputvoltage, so it sees the full amplifier gain. The output noise dueto base resistance is given by

Note that this noise voltage is proportional to the collector current, as is the signal,so the SNR is independent of bias current.

• Collector shot noise is in parallel with collector signal currentand is directly sent to the output load resistor:

Note that this output voltage is proportional to the square root of the collectorcurrent, and therefore, to improve the noise figure due to collector shot noise, weincrease the current.

, 14bno r b m Lv kTr g R≈ ⋅

, 2Cno I C Lv qI R≈ ⋅


NF and Bias Current (II)

• Base shot noise can be converted to input voltage. If Zeq is theimpedance on the base (formed by a combination of matching,base resistance, source resistance, and transistor inputimpedance), then

Note that this output voltage is proportional to the collector current raised to thepower of 3/2. Therefore, to improve the noise figure due to base shot noise, wedecrease the current.

• At low currents, collector shot noise will dominate and noisefigure will improve with increasing current. However, theeffect of base shot noise also increases and will eventuallydominate. Thus, there will be some optimum level to whichthe collector current can be increased, beyond which the noisefigure will start to degrade again.

,

2B

Cno I eq m L

qIv Z g R

β≈ ⋅


Effect of the Cascode on NF

• The cascode transistor is a CBamplifier with current gain close to 1.The cascode transistor is forced to passthe current of the driver on to theoutput. This includes signal and noisecurrent. Thus, to a first order, thecascode can have no effect on the noisefigure of the amplifier. In reality it willadd some noise, the cascode LNA cannever be as low noise as a CE amplifier.

CCV

EEV

1br

iv

1cv2ei

2ci outv

2br

CR

cbiasv


Summary

• For three transistor amplifier configurations, the CE amplifierhas higher gain but poor frequency response than CB and CCamplifiers due to miller effects.

• Cascode configuration of CE and CB has the advantages ofimproving frequency response and a little impact on noisefigure.

• Feedback topologies are usually used to improve linearity withsacrificing some power gain and noise performance.

• Using two inductors (one at emitter and the other at base) toprovide the power and noise match is a common andconvenient matching strategy for the LNA design.
