1. Optical Receivers Theory and Operation
Xavier Fernando
Ryerson Communications Lab

2. Part A
Photodetectors

3. Photo Detectors
Optical receivers convert optical signal (light) to electrical signal (current/voltage)
Hence referred ‘O/E Converter’
Photodetector is the fundamental element of optical receiver, followed by amplifiers and signal conditioning circuitry
There are several photodetector types:
Photodiodes, Phototransistors, Photon multipliers, Photo-resistors etc.

4. Photodetector Requirements
High sensitivity (responsivity) at the desired wavelength and low responsivity elsewhere  high wavelength selectivity
Low noise and reasonable cost
Fast response time  high bandwidth
Insensitive to temperature variations
Compatible physical dimensions
Long operating life

5. 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 sufficiently reverse biased during normal operation  no current flow, the intrinsic region is fully depleted of carriers

6. Avalanche Photodiode (APD)
The internal gain of the APD is obtained by having a high electric field that energizes photo-generated electrons and holes
These electrons and holes ionize bound electrons in the valence band upon colliding with them
This mechanism is known as impact ionization
The newly generated electrons and holes are also accelerated by the high electric field
They gain enough energy to cause further impact ionization
This phenomena is the avalanche effect

7. APD Vs PIN
APD has high gain due to self multiplying mechanism, used in high end systems
The tradeoff is the ‘excess noise’ due to random nature of the self multiplying process.
APD’s are costly and need high reverse bias voltage (Ex: 40 V)
APD’s have the same excess noise at longer wavelengths, but they have an order of magnitude lower avalanche gain.

8. Physical Principles of Photodiodes
As a photon flux Φ penetrates into a semiconductor, it will be absorbed as it progresses through the material.
If αs(λ) is the photon absorption coefficient at a wavelength λ, the power level at a distance x into the material is
Absorbed photons trigger photocurrent Ip in the external circuitry
Photocurrent  Incident Light Power

9. Examples of Photon Absorption

10. pin energy-band diagram
Cut off wavelength depends on the
band gap energy 2

11. Quantum Efficiency
The quantum efficiency η is the number of the electron–hole carrier pairs generated per incident–absorbed photon of energy hν and is given by
Ip is the photocurrent generated by a steady-state optical power Pin incident on the photodetector.

12. 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

13. Responsivity When λ<< λc absorption is low
When λ > λc; no absorption 3

14. Light Absorption Coefficient
The upper wavelength cutoff is determined by the bandgap energy Eg of the material.
At the lower-wavelength end, the photo response cuts off as a result of the very large values of αs.

15. Photodetector Noise
In fiber optic communication systems, the photodiode is generally required to detect very weak optical signals.
Detection of weak optical signals requires that the photodetector and its amplification circuitry be optimized to maintain a given signal-to-noise ratio.
The power signal-to-noise ratio S/N (also designated by SNR) at the output of an optical receiver is defined by

16. 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

17. Notation: Detector Current
The direct current value is denoted by, IP ; capitol main entry and capital suffix.
The time varying (either randomly or periodically) current with a zero mean is denoted by, ip small main entry and small suffix.
Therefore, the total current Ip is the sum of the DC component IP and the AC component ip .

18. 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

19. 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

20. Thermal Noise The photodetector load resistor RL contributes to
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

21. Signal Power = <ip2>M2
Signal to Noise Ratio
Detected current = AC (ip) + DC (Ip)
Signal Power = <ip2>M2
Typically not all the noise terms will have equal weight.
Often the average signal current is much larger than the
leakage and dark currents

22. Noise Calculation Example

23. Limiting Cases for SNR
When the optical signal power is relatively high, then the shot noise power is much greater than the thermal noise power. In this case the SNR is called shot-noise limited or quantum noise limited.
When the optical signal power is low, then thermal noise usually dominates over the shot noise. In this case the SNR is referred to as being thermal-noise limited.

24. Limiting Cases of SNR In the shot current limited case the SNR is:
For analog links, there will be RIN (Relative Intensity Noise) as well

25. SNR vs. Received Power 10

26. Noise-Equivalent Power
The sensitivity of a photodetector is describable in terms of the minimum detectable optical power to have SNR = 1.
This optical power is the noise equivalent power or NEP.
Example: Consider the thermal-noise limited case for a pin photodiode. Then
To find the NEP, set the SNR = 1 and solve for P:

27. 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

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

29. 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

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

31. Comparisons of pin Photodiodes
NOTE: The values were derived from various vendor data sheets and from performance numbers reported in the literature. They are guidelines for comparison purposes. Detailed values on specific devices for particular applications can be obtained from photodetector and receiver module suppliers.

32. Comparisons of APDs
NOTE: The values were derived from various vendor data sheets and from performance numbers reported in the literature. They are guidelines for comparison purposes. Detailed values on specific devices for particular applications can be obtained from photodetector and receiver module suppliers.

33. Part B
Optical receiver

34. Signal Path through an Optical Link1

35. Fundamental Receiver Operation
The first receiver element is a pin or an avalanche photodiode, which produces an electric current proportional to the received power level.
Since this electric current typically is very weak, a front-end amplifier boosts it to a level that can be used by the following electronics.
After being amplified, the signal passes through a low-pass filter to reduce the noise that is outside of the signal bandwidth.
The also filter can reshape (equalize) the pulses that have become distorted as they traveled through the fiber.
Together with a clock (timing) recovery circuit, a decision circuit decides whether a 1 or 0 pulse was received,

36. Optical receiver schematic
Bandwidth of the front end:
CT: Total Capacitance = Cd+Ca
RT: Total Resistance = Rb // Ra
Try Example 6.7 in Keiser 4

37. Noise Sources in a Receiver
The term noise describes unwanted components of an electric signal that tend to disturb the transmission and processing of the signal
The random arrival rate of signal photons produces quantum (shot) noise
Dark current comes from thermally generated eh pairs in the pn junction
Additional shot noise arises from the statistical nature of the APD process
Thermal noises arise from the random motion of electrons in the detector load resistor and in the amplifier electronics

38. Probability of Error (BER)
BER is the ratio of erroneous bits to correct bits
A simple way to measure the error rate in a digital data stream is to divide the number Ne of errors occurring over a certain time interval t by the number Nt of pulses (ones and zeros) transmitted during this interval.
This is the bit-error rate (BER)
Here B is the bit rate.
Typical error rates for optical fiber telecom systems range from 10–9 to 10–12 (compared to 10-6 for wireless systems)
The error rate depends on the signal-to-noise ratio at the receiver (the ratio of signal power to noise power).

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

40. Deciding Threshold Voltage
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] ?

41. Derived BER Expression
A simple estimation of the BER can be calculated by assuming the equalizer output is a gaussian random variable.
Let the mean and variance of the gaussian output for a 1 pulse be bon and σ2on, respectively, and boff and σ2off for a 0 pulse.
If the probabilities of 0 and 1 pulses are equally likely, the bit error rate or the error probability Pe becomes

42. Probability of Error Calculation
The factor Q is widely used to specify receiver performance, since it is related to the SNR required to achieve a specific BER.
There exists a narrow range of SNR above which the error rate is tolerable and below which a highly unacceptable number of errors occur. The SNR at which this transition occurs is called the threshold level.

43. BER as a Function of SNR
BER as a function of SNR when the standard deviations are equal (σon = σoff) and when boff = 0

44. Receiver Sensitivity
To achieve a desired BER at a given data rate, a specific minimum average optical power level must arrive at the photodetector. The value of this minimum power level is called the receiver sensitivity.
Assuming there is no optical power in a received zero pulse, then the receiver sensitivity is
Where, including an amplifier noise figure Fn, the thermal noise current variance is

45. Receiver Sensitivity Calculation
The receiver sensitivity as a function of bit rate will change for a given photodiode depending on values of parameters such as wavelength, APD gain, and noise figure.

46. The Quantum Limit
The minimum received optical power required for a specific bit-error rate performance in a digital system.
This power level is called the quantum limit, since all system parameters are assumed ideal and the performance is limited only by the detection statistics.

47. Eye Diagrams
Eye pattern measurements are made in the time domain and immediately show the effects of waveform distortion on the display screen of standard BER test equipment.
The eye opening width defines the time interval over which signals can be sampled without interference from adjacent pulses (ISI).
The best sampling time is at the height of the largest eye opening.
The eye opening height shows the noise margin or immunity to noise.
The rate at which the eye closes gives the sensitivity to timing errors.
The rise time is the interval between the 10 and 90% rising-edge points

48. Stressed Eye Tests
The IEEE 802.3ae spec for testing 10-Gigabit Ethernet (10-GbE) devices describes performance measures using a degraded signal.
This stressed eye test examines the worst-case condition of a poor extinction ratio plus multiple stresses, ISI or vertical eye closure, sinusoidal interference, and sinusoidal jitter.
The test assumes that all different possible signal impairments will close the eye down to a diamond shaped area (0.10 and 0.25 of the full pattern height).
If the eye opening is greater than this area, the receiver being tested is expected to operate properly in an actual fielded system.
The inclusion of all possible signal
distortion effects results in a
stressed eye with only a small
diamond-shaped opening

49. Architecture of a Typical PON
A passive optical network (PON) connects switching equipment in a central office (CO) with N service subscribers
Digitized voice and data are sent downstream from the CO to customers over an optical link by using a 1490-nm wavelength.
The upstream (customer to central office) return path for the data and voice uses a 1310-nm wavelength.

50. Burst-Mode Receivers
The amplitude and phase of packets received in successive time slots from different user locations can vary widely from packet to packet.
If the fiber attenuation is 0.5 dB/km, there is a 10-dB difference in the signal amplitudes from the closest and farthest users.
If there are additional optical components in one of the transmission paths, then the signal levels arriving at the OLT could vary up to 20 dB.
A fast-responding burst-mode receiver with high sensitivity is needed
The guard time provides a sufficient delay time to prevent collisions between
successive packets that may come from different ONTs.