Optical Receivers Theory and Operation

Photodetector Requirements

• High sensitivity (responsivity) at the desired wavelength and low responsivity elsewhere

• Low noise and reasonable cost

• Fast response time high bandwidth

• Insensitive to temperature variations

• Compatible physical dimensions

• Long operating life

Photodiodes• Due to above requirements, only photodiodes

are used as photo detectors in optical communication systems

• Positive-Intrinsic-Negative (pin) photodiode– No internal gain

• Avalanche Photo Diode (APD)– An internal gain of M due to self multiplication

• Photodiodes are reverse biased for normal operation

Basic pin photodiode circuit

• Incident photons trigger a photocurrent Ip in the external circuitry

Photocurrent Incident Optical Power

pin energy-band diagram

cg

hc

E Cut off wavelength depends on the

bandgap energy

Responsivity ()

Quantum Efficiency () = number of e-h pairs generated / number of incident photons

Avalanche PD’s have an internal gain M

0

/

/pI q

P h

0

pI q

P h

M

p

IM

I IM : average value of the total multiplied current

M = 1 for PIN diodes

mA/mW

APD PIN M

Responsivitycg

hc

E

Signal to Noise Ratio

Signal to noise Ratio (SNR) as a function of the average number of photo electrons per receiver resolution time for a photo diode receiver at two different values of the circuit noise

Signal to noise Ratio (SNR) as a function of the average number of photoelectrons per receiver resolution time for a photo diode receiver and an APD receiver with mean gain G=100 and an excess noise factor F=2

At low photon fluxes the APD receiver has a better SNR. At high fluxes the photodiode receiver has lower noise

Signal to Noise Ratio

For high SNR

• The Photodetector must have a large quantum efficiency (large responsivity or gain) to generate large signal current

• Detector and amplifier noise must be low

Signal power from photocurrent

Detector Noise + Amplifier NoiseSNR

SNR Can NOT be improved by amplification

Quantum (Shot Noise)

)(2 22 MFBMqIi pQ

F(M): APD Noise Figure F(M) ~= Mx (0 ≤ x ≤ 1) Ip: Mean Detected CurrentB = Bandwidth

Due optical power fluctuation because light is made up of discrete number of photons

Dark/Leakage Current Noise

)(2 22 MFBMqIi DDB

BqIi LDS 22

Bulk Dark Current Noise

Surface Leakage Current Noise

ID: Dark Current

IL: Leakage Current

There will be some (dark and leakage ) current without any incident light. This current generates two types of noise

(not multiplied by M)

Thermal Noise

The photodetector load resistor RL contributes a mean-squarethermal (Johnson) noise current

LBT RTBKi /42

KB: Boltzmann’s constant = 1.38054 X 10(-23) J/K T is the absolute Temperature

• Quantum and Thermal are the important noise mechanisms in all optical receivers • RIN (Relative Intensity Noise) will also appear in analog links

Signal to Noise Ratio

2 2

22 ( ) ( ) 2 4 /p

p D L B L

i MSNR

q I I M F M B qI B k TB R

Detected current = AC component (ip) + DC component (Ip)

Signal Power = <ip2>M2

Typically not all the noise terms will have equal weight

SNRDark current and surface leakage current

noise are typically negligible, If thermal noise is also negligible

For analog links, (RIN= Relative Intensity Noise)

2

2 ( ) ( )p

p

iSNR

q I F M B

2 2

2 22 ( ) ( ) 4 / ( )

p

p D B L p

i MSNR

q I I M F M k T R RIN I B

Response Time in pin photodiode

Transit time, td and carrier drift velocity vd are related by

/d dt w v For a high speed Si PD, td = 0.1 ns

Rise and fall times

Photodiode has uneven rise and fall times depending on:1. Absorption coefficient s() and2. Junction Capacitance Cj

o rj

AC w

Junction Capacitance

o rj

AC w

εo = 8.8542 x 10(-12) F/m; free space permittivity εr = the semiconductor dielectric constant A = the diffusion layer (photo sensitive) areaw = width of the depletion layer

Large area photo detectors have large junction capacitance hence small bandwidth (low speed) A concern in free space optical receivers

Various pulse responses

( )0( ) (1 )s xP x P e

Absorbed optical power at distance x exponentially decaysdepending on s

Digital Receiver Performance

0 ( ) ( / 0)th

th VP V p y dy

1( ) ( /1)thV

thP V p y dy

11 02 ( ) ( )e th thP P V P V Probability of error assuming

Equal ones and zeros

Where,

Depends on the noise variance at on/off levels and the Threshold voltage Vth that is decided to minimize the Pe

Question: Do you think Vth = ½ [Von + Voff] ?

Logic 0 and 1 probability distributions

1( ) ( /1)thV

thP V p y dy

0 ( ) ( / 0)th

th VP V p y dy

1

1 02 ( ) ( )e th thP P V P V

Select Vth to minimize Pe

Asymmetric distributions

Noise variances

12( ) 1

2 2th

e on off

VP erf

Probability of error depends on Vth and noise power

Bit Error Rate

BER is equal to number of errors divided by total number of pulses (ones and zeros). Total number of pulses is bit rate B times time interval. BER is thus not really a rate, but a unitless probability.

Q Factor and BER

on

thon

off

offth VVVVQ

21

2

1 QerfBER

BER vs. Q, continued

When off = on and Voff=0 so that Vth=V/2, then Q=V/2. In this case,

221

2

1

V

erfBER

Fig. 7-7: BER (Pe) versus

Q factor

BER vs SNR(equal standard deviations and boff = 0)

Sensitivity

The minimum optical power that still gives a bit error rate of 10-9 or below

Receiver Sensitivity

1/22

2 22

Sensitivity= Average detected optical power for a given bit error rate

For pin detectors

2 damplifier

hvP Q iq

i i qI I B

(Sm

ith a

nd P

erso

nick

198

2)

2 /2

-9

Probability of error vs. Q is to good approximation:

1 E 2

eg. for a SNR = Q = 6 Bit Error Rate= P(E)=10

QePQ