Optical Receivers Theory and Operation

Xavier Fernando

Ryerson Communications Lab

http://www.ee.ryerson.ca/~fernando

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.

Requirements

• Compatible physical dimensions (small size)

• Low sensitivity (high responsivity) at the desired wavelength and low responsivity elsewhere wavelength selectivity

• Low noise and high gain

• Fast response time high bandwidth

• Insensitive to temperature variations

• Long operating life and low cost

Photodiodes• Photodiodes meet most the requirements, hence

widely used as photo detectors.• Positive-Intrinsic-Negative (pin) photodiode

– No internal gain, robust detector

• Avalanche Photo Diode (APD)– Advanced version with internal gain M due to self

multiplication process• Photodiodes are sufficiently reverse biased during

normal operation no current flow without illumination, the intrinsic region is fully depleted of carriers

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

Examples of Photon Absorption

pin energy-band diagram

Cut off wavelength depends on the band gap energy

μm )(

24.1

eVEE

hc

ggc

Cut off wavelength:

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.

Avalanche Photodiode (APD)• APD has an internal gain M, which is obtained by

having a high electric field that energizes photo-generated electrons.

• These electrons ionize bound electrons in the valence band upon colliding with them which is known as impact ionization

• The newly generated electrons and holes are also accelerated by the high electric field and gain energy to cause further impact ionization

• This phenomena is the avalanche effect

APD Vs PIN

Responsivity ()Quantum Efficiency () = number of e-h pairs

generated / number of incident photons

APD’s have an internal gain M, hence

where, M = IM/Ip

IM : Mean multiplied current

0

/

/pI q

P h

0

pI q

P h

mA/mW

APD PIN M

M = 1 for PIN diodes

Responsivity

cg

hc

E When λ<< λc absorption is low

When λ > λc; no absorption

Light Absorption Coefficient

• The upper cutoff wavelength is determined by the bandgap energy Eg of the material.

• At lower-wavelength end, the photo response diminishes due to low absorption (very large values of αs).

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

SNR Can NOT be improved by amplification

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 .

ppP iII

2/

2/

22 )(1

LimT

T

pTp dttiT

i

Quantum (Shot Noise)

)(2 22 MFBMqIi pQ

F(M): APD Noise Figure F(M) ~= Mx (0 ≤ x ≤ 1) Ip: Mean Detected CurrentB = Bandwidthq: Charge of an electron

Quantum noise arises 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 tothermal (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 significant 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 (ip) + DC (Ip) Signal Power = <ip

2>M2

Typically not all the noise terms will have equal weight. Often thermal and quantum noise are the most significant.

Noise Calculation Example

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 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.

Limiting Cases of SNRIn the shot current limited case the SNR is:

For analog links, there will be RIN (Relative Intensity Noise) as well

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

Typical SNR vs. Received Power

• Note, APD has an advantage only at low received power levels

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:

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

Pulse response is a complex function of absorption coefficient and junction capacitance

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.

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 only.

OPTICAL RECEIVERPart B

Signal Path through an Optical Link

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,

Optical receiver schematic

Bandwidth of the front end:

CT: Total Capacitance = Cd+Ca

RT: Total Resistance = Rb // Ra

Try Example 6.7 in Keiser

1 2 T TB R C

Noise Sources in a ReceiverThe 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

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).

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

Deciding Threshold Voltage

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] ?

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 σ2

off 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

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.

BER as a Function of SNRBER as a function of SNR when the standard deviations are

equal (σon = σoff) and when boff = 0

Receiver Sensitivity• A specific minimum average optical power level must arrive at

the photodetector to achieve a desired BER at a given data rate. 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

Receiver Sensitivity CalculationThe 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.

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.

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

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.

46

The inclusion of all possible signaldistortion effects results in astressed eye with only a smalldiamond-shaped opening

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.

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 betweensuccessive packets that may come from different ONTs.