Sam Palermo Analog & Mixed-Signal Center

Texas A&M University

ECEN620: Network Theory Broadband Circuit Design

Fall 2012

Lecture 21: Transimpedance Amplifiers (TIAs)

Announcements & Agenda

• Exam 3 is postponed to Dec. 11 during scheduled final time

• Project presentation will still need to be prepared and turned in by 5PM on Dec 11, but will not be presented

• Optical Receiver Overview • Transimpedance Amplifiers

• Common-Gate TIAs • Feedback TIAs • Common-Gate & Feedback TIA Combinations

2

Optical Receiver Technology

• Photodetectors convert optical power into current • p-i-n photodiodes • Integrated metal-semiconductor-

metal photodetector

• Electrical amplifiers then

convert the photocurrent into a voltage signal • Transimpedance amplifiers • Limiting amplifiers • Integrating optical receiver

3

RF

M1

M2

RD

VDD

VA

TIA

LA stages

TIA Output

LA Output

• Key design objectives • High transimpedance gain • Low input resistance for high bandwidth and

efficient gain

Transimpedance Amplifier (TIA)

4

( )

( )T

in

outT

Zi

vZ

log20by dB of unitsin expressed Also

anceTransimped

Ω

Ω=

ZT

TIAiin vout

Resistive Front-End

• Direct trade-offs between transimpedance, bandwidth, and noise performance

5

DLDinpdB

LinT

CRCRBW

RRR11

3 ===

==

ω

L

Drmsinn

DLL

outninn

DLTnoutn

RCKT

I

CRkT

RV

I

CkTdf

fRCjR

RkTdfZIV

=

==

=

+

== ∫∫∞∞

,,

22

2,2

,

0

2

0

222, 21

4π

CDiin

RL

vout

RL CD

V2n,out

I2n,R

[Razavi]

Common-Gate TIA

• Input resistance (input bandwidth) and transimpedance are decoupled

6

( ) mombm

Doin

DT

grggRrR

RR1

1≈

+++

=

=

IBiin Rin

VB

VDD

RD

vout gm(-vi) ro gmb(-vi) RD

vout

vi

Riniin

[Razavi]

Common-Gate TIA Frequency Response

• Often the input pole may dominate due to large photodiode capacitance (100 – 500fF)

7

( )outDmbm

in

D

in

out

CsRgg

Cs

Riv

+

+

+=

11:

11

r transistor Neglecting o

IBiin

VB

VDD

RD

vout

Cin

Cout

[Razavi]

Common-Gate TIA Noise

• Both the bias current source and RD contribute to the input noise current

• RD can be increased to reduce noise, but voltage headroom can limit this

• Common-gate TIAs are generally not for low-noise applications

• However, they are relatively simple to design with high stability

8

( )

+=

+=+=

HzA

HzV

r transistor Neglecting

2

2

o

Dminn

DD

mDRDnMnoutn

RgkTI

RR

gkTRIIV

1324

1324

:

22,

22

22,

22,

2,

[Razavi]

Regulated Cascode (RGC) TIA

9

[Park ESSCIRC 2000] • Input transistor gm is boosted by common-source amplifier gain, resulting in reduced input resistance

• Requires additional voltage headroom

• Increased input-referred noise from the common-source stage

CMOS 20GHz TIA

10 333222 RgARgA mm −==

• An additional common-gate stage in the feedback provides further gm-boosting and even lower input resistance

• Shunt-peaking inductors provide bandwidth extension at zero power cost, but very large area cost

[Kromer JSSC 2004]

Feedback TIA w/ Ideal Amplifier

• Input bandwidth is extended by the factor A+1 • Transimpedance is approximately RF • Can make RF large without worrying about voltage

headroom considerations 11

( )

( )IDFTinp

Fin

FT

pTT

CCRA

CR

ARR

RA

AR

sRsZ

++

==

+=

+=

+−=

111

1

11

ω

ω

: AmplifierBandwidth Infinite With

-A

CDiin

RF

vout

CIRin

Feedback TIA w/ Finite Bandwidth Amplifier

12

( )

( ) ( )

( )

1

1

11

11

11

22

+=

++

=

+=

+=

++

−=

+=

+=

ARR

TCRTCRA

Q

TCRA

RA

AR

sQsRsZ

sTA

sAsA

Fin

ATF

ATF

ATFo

FT

ooTT

A

A

ω

ωω

ω

: AmplifierBandwidth Finite With

-A(s)

CDiin

RF

vout

CIRin

• Finite bandwidth amplifier modifies the transimpedance transfer function to a second-order low-pass function

Feedback TIA w/ Finite Bandwidth Amplifier

13

• Non-zero amplifier time constant can actually increase TIA bandwidth!!

• However, can result in peaking in frequency domain and overshoot/ringing in time domain

• Often either a Butterworth (Q=1/sqrt(2)) or Bessel response (Q=1/sqrt(3)) is used • Butterworth gives maximally flat

frequency response • Bessel gives maximally flat group-

delay Butterworth

Bessel

[Sackinger]

-A(s)

CDiin

RF

vout

CI1

RFCT

1TA

ω

Aopen

ADC

Feedback TIA Transimpedance Limit

14

• Maximum RT proportional to amp gain-bandwidth product • If amp GBW is limited by technology fT, then in order to

increase bandwidth, RT must decrease quadratically!

( ) ( )

( )3dB

3dB

bandwidth given afor possible maximum the yields expression above into Plugging

of case thanlarger times

:response hButterwort aFor

:response frequencyflat mazimallyfor response hButterwort a assume we If

ωω

ωωω

ω

≥

+

++

=

+=≈

+=

+==

===

TT

A

TFT

TFA

TFTF

A

TFAA

CRA

AA

RRA

AR

CRAT

CRAA

CRA

CRA

TQ

11

1

102211

212

1

0

23dBT

AT C

ARωω

≤ Maximum[Mohan JSSC 2000]

Feedback TIA

15

( )Dmmout

Dm

Fin

FDm

DmT

Dm

RggR

RgRR

RRg

RgR

RgA

12

1

1

1

1

11

1

1

+=

+=

+=

=1 of gain ideal an hasfollower source thethat Assuming

RF

M1

M2

RD

VDD

VA

iinCD

vout

• CMOS inverter-based TIAs allow for reduced voltage headroom operation

• Multiple inverter stages in feedback provide higher gain at the cost of reduced stability

• Diode-connected transistor loads allow for high-frequency internal poles

CMOS Inverter-Based Feedback TIA

16

[Ingels JSSC 1994]

Common-Gate & Feedback TIA

17

• Common-gate input stage isolates CD from input amplifier capacitance, allowing for a stable response with a variety of different photodetectors

• Transimpedance is still approximately RFA/(1+A)

Common-Gate

Feedback TIA

[Mohan JSSC 2000]

RF RF

BJT Common-Base & Feedback TIA

18

• Transformer-based negative feedback boosts gm with low power and noise overhead

• Input series peaking inductor isolates the photodetector capacitance from the TIA input capacitance

• High frequency techniques allow for 26GHz bandwidth with group delay variation less than 19ps

[Li BCTM 2011]

Next Time

• Broadband amplifiers • Limiting amplifiers • Transimpedance amplifiers

• CML gate design

19