Question

Consider a typical optical receiver that contains a InGaAs pin photodiode, a load resistor, and an amplifier. The receiver has the following parameters at the wavelength 1.15e-5 m:

The dark current is 5.0 nA, the quantum efficiency is 0.85, and the surface leakage current is negligible. The incident optical power is 3 mW, load resistance is 50 ohm, and the effective noise bandwidth of the receiver is 1 GHz.

(1)   Determine the photocurrent Iph .              
(2)   Calculate the total shot noise in the receiver.
(3)   Calculate the thermal noise in the receiver at the room temperature.
(4)   Calculate the signal to noise ratio (SNR) in dB at the input of the amplifier in the receiver.

Answer 1

Answer :

Given data :

Incident optical power = 3mW

Wavelength = $1.15\times 10^{-5} m$

Dark current = 5 nA

Quantum efficiency = 0.85

Load resistance = 50 ohm

Using the formula for photocurrent,

$\bf I_p_h = \frac{e\eta P}{h\nu }$  

For shot noise :

$\bf I_s = (2eI_dB)^{1/2}$

For thermal noise :

[4kTB 1/2 Is R

Total noise = shot noise + thermal noise

and

S/N ratio in decibal :

$\bf \left(\frac{S}{N}\right)_d_B = 10log_1_0 \left[\frac{I_p_h^2}{I_N^2} \right ]$  

I am putting some handwritten notes for calculations,

please go through them and please rate my answer positive when you find them useful.

Notes :

Date Notes Page 1 1 smod Girena + Incident optical power (P) 3 mW rul Wavelength aa 1.15 x 10 mo Dark current Id & 5 mA Quandem efficiency in 0.85 0 Load desistance R = 50 2. Elige cine mise bandwidth (B) = 1 GHz Photo current Iph enP en Pa A nc where -19 e = 1.6810 C h = 6.636x10 -34 & Iph= (1-0710-19) x ( 0185) x( 3x10 %) x 1:45 xlos (6.636 x 1080) x (3 x 108) Ion 0.2357 x 10 Ipn 23.57 mA Teacher's Signature

Notes | Page 2 PA Date (B). 118 So -putting Shot noise :- Is = [ge Id B values, oix de de Is = 2 x (116 X70169) x (5x1009) Is 16 x 10-49) Is a 1.96 x 10 1/2 x 1x10 112 (0) Thermal noise (also called Johnson noise) 1/2 Ij = 4KT B R where -23 JK So, putting K= Boltzmann constant = 1.38×10 values, for Room temperatore = 27°C = 300 K 4X (1.38% 1023 300 X (109) 50 112 Is Х 209) ] -14 33.12 x 10 15 50755 x10 = 5.755*10* A. Teachers

Page 3 Signal to noise ratio (in dB. Total noue . In = Is t Is 576.76 x 0-9 A Il In decibal to logo ş N. = 10 logo Ion KA de dezco [G7] 10 lozio 10 [ Elogio + I lage to 23.57 576.76 D (23.57 576.76 S १२.२२ dB

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