1. Modulation and Demodulation
EECS 233
Fall, 2002
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2. Modulation Conversion of digital electrical data into optical format
On-off keying (OOK) is the most commonly used scheme
NRZ format  most commonly used
RZ format (requiring 2X NRZ bandwidth)
Pulse format (not commercially deployed)
bit interval
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3. DC Balance Typical problem for all OOK formats
Average transmitted power is not constant  decision threshold varies with ratio of 1s to 0s
Use line coding or scrambling to solve the problem
Binary block line code  encodes a block of k bits into n bits i.e. (k,n) code
Fiber Channel standard  (8, 10)
Fiber distributed data interface (FDDI)  (4,5)
Most data links
Scrambling
1-to-1 mapping of data stream and coded data streme
Minimize prob. of long 1s and 0s
Does not require more BW
Does not guarantee DC balance
Most telecom links
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4. Demodulation: Receiver
Recovering the transmitted data
Recovering the bit clock
Determining the bit value within each bit interval
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5. Binomial Random Variable
Suppose n independent trials are performed
each results in a success with probability p and in a failure with probability 1-p.
X represents the number of successes that occur in n trials, then X is said to be a binomial RV with parameter (n,p).
The probability mass function (pmf)
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6. Poisson Random Variable
First introduced by S.D. Poisson in 1837 regarding probability theory applied to lawsuits, criminal trials and the like.
Approximates a binomial random variable with parameters (n, p) when n is large and p is small and l=np is moderate.
X is a Poisson random variable, taking the values 0, 1, 2, …, with parameter l
Prove to yourself that this comes from the Binomial pmf
l is in a sense the average success (occurrence rate)
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7. Normal or Gaussian?
Normal distribution was introduced by French mathematician A. De Moivre in 1733.
Used to approximate probabilities of coin tossing
Called it exponential bell-shaped curve
1809, K.F. Gauss, a German mathematician, applied it to predict astronomical entities… it became known as Gaussian distribution.
Late 1800s, most believe majority data would follow the distribution  called normal distribution
DeMoivre-Laplace limit theorem
When n is large, a binomial RV will have approx. the same distribution as a normal RV with the same mean and variance.
Central limit theorem
The sum of a large number of independent RVs has a distribution that is approx. normal.
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8. Bit Error Rate: Ideal Receiver
Light signal with power P and B is bit rate
#Photons/sec=P/hn
Ave # Photons/bit interval = P/(hnB)
P[0|1]=
BER=p(1)P[0|1]+p(0)P[1|0] =
For BER, we need an average of 27 photons per bit
Where
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9. Normal Distribution = variance = (STD)2 = mean 11/27/2018
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10. Receiver Design
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11. Front End Configuration
High-impedance amplifier
Transimpedance front-end can achieve high bandwidth (small RC constant), high sensitivity and low thermal noise (high load resistance)
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12. PIN Basis Increase width of i-region Gain-Bandwidth trade-off
Increase RC constant
Increase Responsivity
Gain-Bandwidth trade-off
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13. Materials for PIN diodes
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14. Noise in PIN Diodes Shot noise (Poisson process ~ Gaussian)
R is responsivity of detector
Be elec. BW of detector (typically between bit rate and ½ bit rate)
Thermal noise (Gaussian process)
Fn is the noise figure of front-end amplifier, typically 3-5 dB.
Total noise power
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15. Signal to Noise Ratio Thermal-noise limit (practical cases)
Shot-noise limit
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16. Some terminology Noise-equivalent power (NEP) Detectivity
Minimum optical power per unit bandwidth required to produce SNR = 1
Detectivity
The inverse of NEP
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17. Avalanche Photodiodes
Electron multiplication was first observed in p-n junctions in Silicon and Germanium, by McKay, K. G. and K. B. McAfee in 1953 (Phys Rev. 91:1079)
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18. Electron Multiplication Effect
A high E-field in the depletion region causes carriers to have enough kinetic energy to “kick” new electrons from valence band up to conduction band – Avalanche Multiplication
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19. Positive Feedback
When both electrons and holes can ionize, both will contribute to gain. However, because they move in opposite directions, a positive feedback loop arises.
Positive feedback degrades both response bandwidth and noise, by a factor equal to loop-gain plus one. (from general feedback theory)
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20. Ionization Cofficient
Ionization coefficient is the number of new e-h pairs generated per unit length by one photo-carrier.
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21. APD Structures
Advanced APD structures have two regions: one for photon absorption, and the other for carrier multiplication. This is so that both absorption length and multiplicative gain can be optimized separately.
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22. APD Gain
One can derive the gain of an APD. Derivation is similar to gain/loss in lasers, fibers etc., except now carriers move in both directions, complicating things.
For the case where >>, the gain is as expected: Gm=exp (L).
For , gain is:
For =,
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23. Noise in APD Shot noise Where FA is the excess noise factor
InGaAs detectors typically have / =0.7
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24. Optical Preamp G RX Optical Preamp Receiver Spontaneous noise power
Photocurrent at the input side of receiver a optical power
= population inversion factor
Optical bandwdith
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25. Noise of Optical Preamp
Optical power is proportional to square of electric field
Includes beating noise of signal-spontaneous and spontaneous-spontaneous
When G is large, signal-spontaneous beat noise dominates over shot and thermal noise
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26. Noise Figure SNRo SNRi G RX Optical Preamp Receiver
No thermal noise, since the signal has not hit the detection circuit. Ignore dark current.
Noise Figure
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27. Bit Error Rates = Optical SNR
Typically we like to know what is the minimum receiver power for a given BER
Receiver sensitivity definition= minimum average optical power for a given BER (typical 1e-12)
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28. Receiver Sensitivity : Min. average power to achieve 1e-12 BER
For BER=1e-12, Q=7
Assuming I0=0
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29. Sensitivity Improvement in APD
APD gain reduces the effective thermal noise, but increases effective shot noise.
Assume l=1.55 mm, R=1.25 A/W, h=1, T=300 K, Be=B/2 and B=109 bits/sec, Fn=3dB (front end amplifier), RL=100W
For pin with front end amplifier, Gm=1,
For APD with Gm=10 and FA=1.3 (from kA=0.7)
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30. Receiver Sensitivity: Optical Preamp
: Min. average power to achieve 1e-12 BER
For BER=1e-12, Q=7
For large G,
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31. Improvement w. Optical Preamp
For nsp=1, l=1.55 mm, R=1.25 A/W, h=1, T=300 K, Be=B/2 and B=109 bits/sec
Or number of photons per bit = 2Q2 = 98
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32. PIN and APD Sensitivity
An APD typically has 10 dB better sensitivity than a PIN.
-36 dBm sensitivity at 2.5 GB/s is possible.
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33. Typical Spec-sheet of a 10Gb pin
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35. References B.E.A. Saleh and M.C. Teich, “Fundamentals of Photonics”
G. P. Agrawal, “Fiber-Optic Communication Systems”
A. Yariv, “Optical Electronics in Modern Communications”
Silvano Donati, “Photodetectors : devices, circuits, and applications”
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