Optical Receivers Theory and Operation

Optical ReceiversTheory and Operation Xavier Fernando Ryerson Communications Lab http://www.ee.ryerson.ca/~fernando

Part A Photodetectors

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.

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

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

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

Examples of Photon Absorption

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

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 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 and they gain enough energy to cause further impact ionization • This phenomena is called the avalanche effect

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 need high reverse bias voltage (Ex: 40 V) • Therefore costly and need additional circuitry

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

Responsivity When λ<< λc absorption is low When λ >λc; no absorption

Light Absorption Coefficient • The upper wavelength cutoff is determined by the bandgap energy Egof the material. • At the lower-wavelength end, the photo response cuts off as a result of the 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 .

Quantum (Shot Noise) 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

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

Thermal Noise The photodetector load resistor RLcontributes to thermal (Johnson) noise current 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 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

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 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.

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

SNR vs. Received Power

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 For a high speed Si PD, td = 0.1 ns

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

Junction Capacitance εo = 8.8542 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

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

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.

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.

Part B Optical receiver

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 amplifierboosts 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

Noise Sources in a Receiver The term noisedescribes 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).

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

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

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 Vththat is decided to minimize the Pe Question: Do you think Vth = ½ [Von + Voff] ?

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

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

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.

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. The inclusion of all possible signal distortion effects results in a stressed eye with only a small diamond-shaped opening

Optical Receivers Theory and Operation