**Review questions for HW 9**

1. What are disadvantages of surface emitting lasers?
How to compensate for these disadvantages?
**
Reduction in d and higher threshold current
Use multilayer mirror to increase R and special structure to enhance stimulated
emission
**

2. What other device is similar to a waveguide grating router
(WGR)?
**
MZ interferometer
**

3. What are advantages of WGR comparing to DFB laser array?
**
Frequency spacing is fixed and independent on temperature, low loss
**

4. What is the upper limit for direct modulation?
**
40 Gb/s
**

5. What is the difference between APD and PIN diode?
**
APD has a current gain region
**

6. An APD with responsivity=0.3A/W, M=30, `I_d = 2nA`,
`P_{"in"}= {10^{-5}} /3` (mW).
Find a) `I_{apd}`, b) mean square value of shot noise for the APD if
`Delta f = 20`MHz and `F_{apd} =1`,
and
c) mean square value of thermal noise if `Delta f`=20MHz and F=1,
T=300K and `R_L`= 500 Ohm.

**
a)
`I_{apd} = M times R times I_{ph} = 30 times 0.3 times 0.333 times 10^{-5}=30`(nA)
b)
`\bar {i_S^2} ` = `2q (R P_"in" + I_d) Delta f times M^2 times F
_{apd} = 1.728 times 10^{-17}(A^2)`
c)
`\bar {i_T^2} ` = `{4 kT Delta f times F}/{R_L} = 6.656 times 10
^{-16} (A^2)`
**

7. Under what condition, you will get shot noise (quantum)
limited detection.
**
Current gain tends to infinity
**

8. Why digital systems perform better than analog systems?
What is their trade-off?
**
The requirement on SNR is low for reasonable BER but it requires more
bandwidth.
**

9. For a thermal-noise limited digital system, we have SNR=17dB.
a) What is its BER?
b) What should be the minimum receiver power if the mean square
current of thermal noise is `10^{-15} (A^2)` for a detector with
responsivity=0.5A/W.
**
SNR = `10^{-17/10} = 50.12`
`x = 0.354 times sqrt{SNR} = 2.506`
BER = `0.5 times (1-erf(x)) = 0.5 times (1-0.99959) = 2.05 times 10^{-4}`
**
b) What should be the minimum receiver power if the mean square
current of thermal noise is `10^{-15} (A^2)` for a detector with
responsivity=0.5A/W.

`I_{ph}^2 = SNR times 10^{-15} = 5.012 times 10^{-14} (A^2)`

`P_{"in"} = I_{ph}/R = 2 I_{ph} = 4.48 times 10^{-7}` (W)

10. Name one factor that limits the maximum number of channels
in using a prism as a multiplexer/demultiplexer.
**
The beam divergence limits the max. number of channels.
**

Last Modified: April 18, 2018

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