chapter 11

Chapter 11 - Click to edit Master subtitle style Dr Joseph C 11.1 11 THE FIBER FORUM Fiber Optic Dr JOSEPH C PALAIS PRESENTED BY Dr Joseph C 11.1

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Unformatted text preview: Click to edit Master subtitle style 5/13/10 Dr. Joseph C. 11.1 11 THE FIBER FORUM Fiber Optic Dr. JOSEPH C. PALAIS PRESENTED BY 5/13/10 Dr. Joseph C. 11.1 22 Chapter 11 Noise and Detection 5/13/10 Dr. Joseph C. 11.1 33 Noise degrades signals. Without noise, it would not matter how little optical power arrived at the receiver. Signal quality is measured in several ways. Analog systems: The signal-to-noise ratio (SNR) is the measure. Digital systems: The bit-error-rate (BER) is the measure. It this chapter we determine how to evaluate the SNR and BER. 5/13/10 Dr. Joseph C. 11.1 44 Section 11.1 Thermal and Shot Noise 5/13/10 Dr. Joseph C. 11.1 55 11.1.1 Thermal Noise Recall the simple receiver circuit: RL v P- + i Vb 5/13/10 Dr. Joseph C. 11.1 66 Even if P = 0 (and the photodiode dark current is zero), a current i = iNT will exist in resistor RL. It has zero average value, but it is random, like: iN T t 5/13/10 Dr. Joseph C. 11.1 77 The current arises from the random thermal motion of the electrons. The instantaneous noise power is RL i2NT The average thermal noise power is RL i2NT RLi2NT RLi2NT t 5/13/10 Dr. Joseph C. 11.1 88 i2NT = mean square thermal noise current. It is given by : i2NT = 4kT ∆ f /RL k = 1.38 x 10-23 J /K, Boltzmann constant T = temperature, K ∆ f = receiver’s bandwidth. Usually ∆ f is a bit larger than the information bandwidth. 5/13/10 Dr. Joseph C. 11.1 99 RL v i2NT = 4kT ∆ f /RL The load resistor’s equivalent circuit looks like: where RL is an ideal (noiseless) resistor. 5/13/10 Dr. Joseph C. 11.1 1010 11.1.2 Shot Noise It is caused by the discrete nature of charge carriers (electrons and holes). Consider a single emitted photoelectron, shown for a vacuum phototube: Vb - + RL i- electron Anode Cathode hf +- 5/13/10 Dr. Joseph C. 11.1 1111 A current exists in the circuit during the transit time ( τ ) of the emitted electron. τ = time for travel from cathode to anode. The electron recombines at the anode with a positive ion. The current caused by a single electron looks something like : h(t) τ t 5/13/10 Dr. Joseph C. 11.1 1212 Every electron produces the same current pulse shape. Consider constant optical power P incident on the detector. The expected current is : t i = ( η e/hf)P This current is made up of numerous pulses of the type shown by h(t). i 5/13/10 Dr. Joseph C. 11.1 1313 Example : t The pulses start at random times, tN. The total current is the sum of these pulses. i = Σ N h(t - tN) tN 5/13/10 Dr. Joseph C. 11.1 1414 i ( η e /hf)P t The average current is still: i = ( η e /hf)P but noise is superimposed onto this current. This is shot noise . Total current: 5/13/10 Dr. Joseph C. 11.1 1515 The shot noise current is: iNS = Σ N h(t - tN) - ( η e /hf)P i2NS = 2eI ∆ f (11-2) ∆ f = receiver’s bandwidth I = average current I = iS + ID where iS = average of the signal current ID = average dark current 5/13/10 Dr. Joseph C. 11.1 1616 The equivalent circuit for shot noise is just a noise current generator, as shown below....
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This note was uploaded on 05/11/2010 for the course EEE EEE-546 taught by Professor Palais during the Spring '10 term at ASU.

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Chapter 11 - Click to edit Master subtitle style Dr Joseph C 11.1 11 THE FIBER FORUM Fiber Optic Dr JOSEPH C PALAIS PRESENTED BY Dr Joseph C 11.1

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