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ECE565_midterm_solutions

# ECE565_midterm_solutions - Solutions to ECE 565 Mid-Term...

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Solutions to ECE 565 Mid-Term Examination, 3/23/2005 Show all your work, show all assumptions, circle your answers Name______Key_______________________

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Problem 1. A receiver operating at 1.55 µ m and T =300 Kelvin uses a high-speed InGaAs-InP PIN detector with a quantum efficiency of 0.7. Assume that the receiver bandwidth is limited by the RC time constant, where R is the load resistor and C is the junction capacitance of the PIN diode, C = 0.8 pf. Moreover, assume that depending on the transmission speed, the load resistance is judiciously selected to that the receiver bandwidth exactly matches that of the transmitted digital signal. a. Calculate the responsivity of this PIN detector. The responsivity, R , is q η / h ν = ηλ /1.24, with λ expressed in µ m . For λ =1.55 µ m, R = 0.8739A/W. b. Write the expression for the receiver SNR and comment on the relative significance of Johnson noise and shot noise as a function of the load resistance. SNR = i p 2 / ( σ s 2 + σ T 2 ) = ( R P ) 2 /{(4 k B TB/R ) + 2 qi p B }. If the bit duration is T b s, then the bandwidth required to support the corresponding transmission is B = 1/2 T b . On the other hand, since the load resistance R is selected so that the receiver bandwidth exactly matches that of the transmitted digital signal, we have (2 π RC ) -1 = 1/2 T b , or R = T b / π C . Thus, we obtain SNR = (8.739 x 10 -7 ) 2 /{(4 k B T π C/ 2 T b 2 ) + 2 q x8.75 x 10 -7 x 1/2 T b } = 7.6372 x 10 -13 /{(2.0820x10 -32 / T b 2 ) + 1.3983 x 10 -25 / T b }. At high transmission speeds (when T b becomes small), Johnson noise will dominate shot noise because of the T b - 2 dependence in the Johnson-noise term as opposed to the T b - 1 dependence in the shot-noise term. c.
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ECE565_midterm_solutions - Solutions to ECE 565 Mid-Term...

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