Lecture 8. Comparison of modulaters sizeCapacitanceInsertion loss Chirping Electro- absorption smalllowerhighersome Electro-optic type (LiNbO3) largehigherlowernone.

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Presentation transcript:

Lecture 8

Comparison of modulaters sizeCapacitanceInsertion loss Chirping Electro- absorption smalllowerhighersome Electro-optic type (LiNbO3) largehigherlowernone

Optical Receiver Converts optical signals to electrical signals. Photons to electrons. Consider the noise at the receiving side using SNR or BER.

Optical Receiver

Photon Statistics Poisson Distribution P( ) = Probability that N photons will arrive during time interval T. N = number of photoelectrons produced in time interval T. = rT = the average number of photoelectrons in time T. r = average rate at which photoelectrons are produced.

Photon Statistics N/P(N) x x

Photon Statistics

The Poisson distribution has the interesting property that the variance and the mean are equal. Mean square deviation in N = average value of N.

Gaussian probability Gaussian probability distribution function is a good approximation to Poisson distribution function for sufficiently large, say.

Gaussian probability

Assume that the variance and the meal are equal as in Poisson distribution, we have

Probability of error in digital communication

Average number of electrons in time T for “0” transmitted = Average number of electrons in time T for “1” transmitted = Probability of error is the area of tail of Gaussian distribution.

Probability of error in digital communication If equal number of “1’s” and “0’s” transmitted, then the probability of error is equal to ‘bit error rate’ or BER.

Probability of error in digital communication The area under a curve to one side of a point  =  is given by a Q-function.

Probability of error in digital communication

Assume

Probability of error in digital communication

Relate BER to electrical signal-to-noise ratio (SNR) in receiver. n s = number of photoelectrons per time interval produced by turning light on.  = root mean square deviation in number of photoelect.rons per time interval

Probability of error in digital communication Assume

Probability of error in digital communication (SNR) 1/2 SNRSNR(dB)BER

Example In an optical communications experiment, an average of m1, photons is detected when a “1” is transmitted and m 0 when a “0” is transmitted. What is m 1 for error rates of and , if (a) m 0 = 0 and (b) m 0 = 1. Assume Poisson statistics.