1. Optical Receivers Theory and Operation

2. 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

3. 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

4. Basic pin photodiode circuit
Incident photons trigger a photocurrent Ip in the external circuitry
Photocurrent  Incident Optical Power

5. pin energy-band diagram
Cut off wavelength depends on the
bandgap energy 2

6. Responsivity ()
Quantum Efficiency () = number of e-h pairs generated / number of incident photons
Avalanche PD’s have an internal gain M
mA/mW
IM : average value of the total multiplied current
M = 1 for PIN diodes

7. Responsivity 3

8. 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

9. 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
SNR Can NOT be improved by amplification

10. Quantum (Shot Noise) F(M): APD Noise Figure F(M) ~= Mx (0 ≤ x ≤ 1)
Due optical power fluctuation because light is made up of
discrete number of photons
F(M): APD Noise Figure
F(M) ~= Mx (0 ≤ x ≤ 1)
Ip: Mean Detected Current
B = Bandwidth

11. Dark/Leakage Current Noise
There will be some (dark and leakage ) current without any
incident light. This current generates two types of noise
Bulk Dark Current Noise
ID: Dark Current
Surface Leakage
Current Noise
(not multiplied by M)
IL: Leakage Current

12. Thermal Noise
The photodetector load resistor RL contributes a mean-square
thermal (Johnson) noise current
KB: Boltzmann’s constant = 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

13. Signal Power = <ip2>M2
Signal to Noise Ratio
Detected current = AC component (ip) + DC component (Ip)
Signal Power = <ip2>M2
Typically not all the noise terms will have equal weight

14. SNR
Dark current and surface leakage current noise are typically negligible, If thermal noise is also negligible
For analog links, (RIN= Relative Intensity Noise)

15. Response Time in pin photodiode
Transit time, td and carrier drift velocity vd are related by
For a high speed Si PD, td = 0.1 ns 4

16. Rise and fall times
Photodiode has uneven rise and fall times depending on:
Absorption coefficient s() and
Junction Capacitance Cj 5

17. Junction Capacitance
εo = x 10(-12) F/m; free space permittivity εr = the semiconductor dielectric constant
A = the diffusion layer (photo sensitive) area
w = 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

18. Various pulse responses
Absorbed optical power at
distance x exponentially decays
depending on s 7

19. Digital Receiver Performance
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] ?

20. Logic 0 and 1 probability distributions
Asymmetric distributions
Select Vth to minimize Pe 5

21. Noise variances
Probability of error depends on Vth and noise power 6

22. 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.

23. Q Factor and BER

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

25. Fig. 7-7: BER (Pe) versus Q factor

26. BER vs SNR (equal standard deviations and boff = 0)8

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

28. Receiver Sensitivity
(Smith and Personick 1982)