Limiting Amplifiers

Professor Jri Lee台大電子所 李致毅教授

Electrical Engineering DepartmentNational Taiwan University

Outline

IntroductionDesign ChallengesLoss of Signal DetectionBroadband TechniquesCase Study

General Considerations

Requirement

Broad Bandwidth ( 0.7 Data Rate)Low Noise (300 ~ 400 µVrms)Small Offset VoltageWell-Behaved Response to Large Signals

High Gain (40~60dB)≥ ×

Challenges of Noise

Example: OC-192 Receiver (Data Rate 10Gb/s)≈

For TIA output noise = 1 mVrms and LA contributes 10% of noise ⇒ LA input noise = 330 µVrmsFor a bandwidth of 10 GHz ⇒ Vn,LA < 3 nV/ Hz

Offset Due to Mismatches

Random asymmetries (e.g., device mismatches) in LA result in finite offset.Offset degrades sensitivity and causes pulse-width distortion, necessitating cancellation technique.Offset may totally destroy the output in high-gain systems (Why?).

Offset Cancellation Technique

outos,1mFoutos,inos, ][ VARGVV =−

1mF

inos,

inos,1mF

outos, 1

RGV

VRAG

AV

≈

+=

FF1mF

FF1m

in

out1

)(1RsCRAG

RsCRAGVV

+++

=

Offset cancellation introduces one zero and one pole.Lower corner defined by standards, usually very low.

First Order Realization of Gain Stages

12BW

1

1/n0tot

Lout0

−=

=

ω

ωCR

Cascading identical amplifying stages.Trade bandwidth with gain since the latter increases in a way faster than the former decreases.

Optimization of Stage Numbers

For a given technology, the gain-bandwidth product is relatively constant.

totopt

1/n1/ntot

tot

ln2

12GBWBW

AnA

=⇒

−=⇒

For Atot = 50 dB, nopt = 11

However, noise and power issues limit the number of stage to 5.

Large Swing Effect

Small-signal gain-bandwidth analysis is pessimistic!

The last few stages switch with large input.The speed of a cascade of stages is limited by only that of one stage.

⇒

AM/PM Conversion

3in3in1out VVI αα +=

)sin(343))sin(

43()( 2

3m331

3m3m11out θθ ωαωαα +−++= tVAtVVAtV

Noise on input signal amplitudes translates to variations of output zero crossings, i.e., jitter.

Broadband Technique (I): Inductive Peaking

ζω

ωζωζω

222 n

2nn

2n

Dmin

out

+++

−=ss

sRgVV

LD3dB 2

1.79CR

fπ

=− 21/=ζLD

3dB 21

CRf

π=−

for

Most Efficient method; no extra power consumption.Area consuming (although has been moderated in advanced technology).

Broadband Technique (II): Miller Capacitor Cancellation

1Dmeff1,

GDDmeffGD,

)(1)(1CRgCCRgC

−=

+=

GDGDDm

Dm1 1

1 CCRgRgC ≈

−+

=⇒

Mismatch or process variation matters.Efficient only for high gain.Button-plate parasitics degrade the performance.

Broadband Technique (III): Cherry-Hooper Amplifiers

Increase the bandwidth significantly in a cost of minor gain loss.Voltage headroom might be an issue in low supply technologies.

m2

m1Fm1

in

outggRg

VV

−=

Y

m2Yp,

X

m2Xp,

CgCg

≈

≈

ω

ω

Broadband Techniques (IV): Voltage-Current Feedback

Voltage-current (shunt-shunt) feedback can be further applied to multiple stages.Watch level shifting in BJT.

Double Triple

Broadband Techniques (V): f DoublerT

Din2in1mout )( RVVgV −=

Double IR drop, voltage headroom issue.Parasitics on tail current sources degrade the performance.Still quite useful in output buffer designs.

Broadband Technique (VI): Capacitive Degeneration

DL

D

smss

ssm

in

out1

21

)(1RsC

RRgsCR

sCRgVV

+++

+=

If RSCS = RDCL, bandwidth increases by a factor of (1+gmRS/2) whereas gain decreases by the same amount.

Broadband Technique (VII): Distributed Amplification

vlfnZgA T0Lmv 2

π≈=

Voltage gain is proportional to physical length l.With ideal T-lines, distributed amplifiers would achieve infinite gain with infinite bandwidth!

Modified Distributed Amplifiers

Cascade and segmented structure helps to improve the performance.

Realization of Monolithic Transmission Lines

mm-wave techniques become practical in deep-submicron CMOS.T-lines are lossy but still useful.

Challenges of Distributed Amplifiers

Transmission Line Loss.Output resistance of transistors. Miller capacitance.Propagation velocity mismatches.Routing difficulties in differential realization.PVT variations.

⇒ Nevertheless, T-line based distributed amplifiers still provide promising applications.

Case Study

[Galal et al., 2003]