EE 232: Lightwave Devices

Lecture #22 – Photodetector noise

Instructor: Seth A. Fortuna

Dept. of Electrical Engineering and Computer Sciences

University of California, Berkeley

4/25/2019

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Optical link budget example

Sensitivity also specified in photons per bit:1

data rate

opt

b

PN

hv=

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Noise

( ) ( )ph ph nI t iI t= +photocurrent

average photocurrent noise

2

2

( )

( )

avg n

n

t R

t R

p i

i=

=

Noise power dissipated into resistive load

noise power

2 2

0

1( ) ( )

T

n ni i tT

t dt= (RMS squared value of the noise)

(bar denotes average)

( )phI t

t

phI

( )ph niI t+

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Shot noise

Most fundamental noise source. Sets sensitivity limit for conventionaloptical receivers. Consequence of particle-like nature of photon.

4 5 3 4 4Numberof detectedphotons

time

time

ph

oto

ns

ph

oto

curr

ent

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Poisson statistics

The probability of detecting N photons is governed by the Poisson distribution

( )!

NNN

P NN

e−= N : average number of photons duringobservation period

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Shot noise power

2 2 ( ) 2s tshot phhoi Bi t qI== (amps2)

average valueof photocurrent

bandwidth of measurement

Shot noise power increases with higher average photocurrent.This is a consequence of Poisson statistics.

The observation time is reduced as the bandwidth increases. This increases the likelihood that the photocurrent measured within the observation time is different than the average photocurrent and thusincreases the noise power.

2shot phq Bi I=phI

Photodetector equivalent circuit

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Thermal noise

All physical resistances have fluctuating voltage as a result of thermal motionof charged carriers.

The photodetector may have resistance which can contribute to thermal noise (series resistance or junction shunt resistance) but often the largestcontribution to thermal noise comes from the amplifier connected to thephotodetector.

2 14thermali kTBR−=

2 ( ) 4thermalv Rt kTB=thermali

thermalv

RR

Resistance equivalent circuit

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p-i-n photodiode noise2

2 2

2 2 112 4

2 4

optph ph

shot thermal phopt

h

i i q B kTBS

Rq

qB k

qP

I INR

ITBR

hP

−−

=+ +

+

= =

shotiphI thermaliR

Simplified equivalent circuitof photoreceiver with p-i-n photodiode

Resistance includes junction resistanceand resistance of amplifier stage

50R =

20 GHzB =

2~

ph

qB

ISNR

2

4~

phR

kTB

ISNR

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Excess noise in APDs

Multiplication factor (M) is a random variable and can fluctuate aboutsome average value. The shot noise power for an APD can be written

2 2 2 2

, 2shot APD shot ph Bi i M F qI M F= =

Averagemultiplicationfactor

Excess noise factor

2

(1

21 )n

n

MF k

MMMk

= += −−

We desire k to be small forsmall excess noise factor

shoti FMphMI thermaliR

Simplified equivalent circuitof photoreceiver with APD

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Comparing p-i-n and APD noise

2 2 2 2

2 2 2 2 142

ph ph

APD

shot thermal ph

M I M ISNR

M F qIi i B TM F k BR−=

+=

+

2 2

2 2 12 4

ph ph

shot ther

p i n

mal ph

I IS

i i q B RNR

kTBI −− − =+ +

=

2

2

11 h

p i

t ermalAPD

shon t

S

S

iR

F

N

N iR − −

+

APD has better SNR when thermal noise dominates APD

p-i-n

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Direct detection

( )optP t

0 ( )V t

( )phI t

photodetector amplifier

2

0

2 2

0

( ) ( ) ( )

)

1

1cos (

ph opt opt

opt opt

I

q

Eh h Z

q qt P

t

t t

Eh Z

=

= +

=

Define average power as

Photocurrent can be written as

2

0

( )1

2opt opt optP

ZEP t ==

Then,2c( ) 2 )

)]

os (

[1 cos 2(

ph opt opt

opt opt

I P th

t

qt

h

q

P

= +

= + + The photodetector is too slow to respond to the time-varying field

( )ph optIq

ht P

=

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Direct detection

0 ( )V t

( )phI t

photodetector amplifier

( )ph optIq

ht P

= Direct detection receivers respond only to changes

in the intensity of the incident field.

2

2 2

2 2 112 4

2 4

optph ph

dd

shot thermal phopt

I I hSNR

i i qI B kT

q

BRq B kTBR

h

q

P

P

−−

+

= ==

++

( )optP t

(assuming p-i-n photodiode)

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Coherent detection

( )optP t

( )loP t

( )incP t

photodetector amplifier

localoscillator

beam splitter

Photocurrent can be written as

if opt lo = −

Intermediate frequency (IF)

2

0

2

0

1

1

2

( ) ( )

( ) ( )

( ) cos ( )

ph inc

opt lo

ph lo lo opt opt lo

I Eh Z

E Eh Z

I

qt t

qt t

P Pt P th

q

=

+

=

+ − +

0 ( )V t

( )phI t

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Coherent detection

( )optP t

( )loP t

( )incP t

photodetector amplifier

localoscillator

beam splitter

( ) c s2 oph lo lo opt ifI P P P tth

q

+ +

Coherent detection receivers respond to changes in frequency, phase, and intensity

This scheme where the IF is non-zero is known as heterodyne detection.

2

2

,

11,

2

2 42 4

lo optph rms

ph lolo

P PI h

SNRqI B kTBR

q B kTBRh

q

qP

−−

=

+

+=

0 ( )V t

( )phI t

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Coherent vs. direct detection

2

1

2

2 4

lo opt

lo

cd

P Ph

SNR

q B kTBRh

q

qP

−

=

+

2

12 4

opt

dd

opt

hS R

qP

qP

N

q B kTBRh

−

=

+

Coherent detection allows you to achieve shot-noise limit even if thermal noiseis large. You simply need to increase the local oscillator power (Plo).

In the limit of small thermal noise, heterodyne coherent detection increasesthe SNR by a factor of two compared with direct direction.

Despite benefits, coherent detection is not always used due to increasedcost, power and complexity.