# Chapter 5 :Optical Detectors and Receivers¶

## Example 5.1 , Page no:54¶

In [1]:
import math
from __future__ import division

#initialisation of variables
optical_power=10*10**-6;  #optical power in W
R=0.5;  #Responsivity in A/W
Is=optical_power*R;  #shot noise current in A
Id=2*10**-9;  #dark current in A
B=1e6;  #bandwidth in Hz
T=300;  #Temperature in K

#CALCULATIONS
K=1.38*10**-20;  #Boltzman constant in m2 g s-2 K-1
q=1.609*10**-19;  #charge of a electron in Coulombs
Ith=4*K*T*B/Rl;  #Mean Square Thermal noise current in A
SNR=(Is**2)/(2*q*(Is+Id)+Ith);  #Signal to noise ratio

#RESULTS
print"Thermal noise current=",Ith*10**18,"*10^-18A";
print"Shot noise current=",Is*10**6,"*10^-6A";
print"Signal to noise ratio=",round(10*math.log10(SNR),5),"dB";  #The answers vary due to round off error

Thermal noise current= 16.56 *10^-18A
Shot noise current= 5.0 *10^-6A
Signal to noise ratio= 61.7888 dB


## Example 5.2 , Page no:54¶

In [2]:
import math
from __future__ import division

#initialisation of variables
eta=0.6;  #quantum efficiency
Po=10*10**-6;  #optical power in W
q=1.6*10**-19;  #charge of an elctron in columb
lambda1=0.85*10**-6;  #wavelength in m
h=6.6*10**-34;  #planck's constant
c=3*10**8;  #velocity of light in m/s

#CALCULATIONS
R=(q*eta*lambda1)/(h*c);  #responsivity in A/W
I=R*Po;  #current in A
V=Rl*I;  #Voltage in V

#RESULTS
print"Responsivity=",round(R,5);
print"Current=",round(I*10**6,5),"uA";  #multiplication by 1e6 to convert unit from A to uA
print"Voltage=",round(V*10**3,5),"mV";  #multiplication by 1e6 to convert unit from V to mV

Responsivity= 0.41212
Current= 4.12121 uA
Voltage= 0.20606 mV


## Example 5.3 , Page no:54¶

In [3]:
import math
from __future__ import division

#initialisation of variables
tau_tr=2*1e-9;  #transit time in sec

#CALCULATIONS
tau=2*Rl*Cd;  #Circuit time constant in sec
f3dB=(0.35/tau_tr);  #3dB bandwidth in Hz

#RESULTS
print"Circuit time constant =",round(tau*1e9,5),"ns";  #multiplication by 1e9 to convert unit from s to ns
print"3dB bandwidth=",round(f3dB*1e-6,5),"MHz";  #multiplication by 1e-6 to convert unit from Hz to MHz

Circuit time constant = 0.3 ns
3dB bandwidth= 175.0 MHz


## Example 5.4 , Page no:54¶

In [4]:
import math
from __future__ import division

#initialisation of variables
I=100*1e-9;  #current in A
P=5*1e-9;  #Incident power in W
h=6.6*10**-34;  #planck's constant
c=3*10**8;  #velocity of light in m/s
q=1.6*10**-19;  #charge of an elctron in columb
eta=0.7;  #quantum efficiency

#CALCULATIONS
lambda1=1.5*10**-6;  #wavelength in m
R=I/P;  #APD responsivity in A/W
M= (R*h*c)/(q*eta*lambda1);  #Multiplication factor

#RESULTS
print"Responsivity=",round(R,5);
print"Multiplication factor=",round(M,5);

Responsivity= 20.0
Multiplication factor= 23.57143


## Example 5.5 , Page no:55¶

In [5]:
import math
from __future__ import division

#initialisation of variables
h=6.6*10**-34;  #planck's constant
c=3*10**8;  #velocity of light in m/s
q=1.6*10**-19;  #charge of an elctron in columb
lambda1=0.85*10**-6;  #//wavelength in m
I=0.1;  #incident light intensity in mW/mm2
Iph1=10*1e-6;  #photocurrent in pin in A
Iph2=500*1e-6;  #photocurrent in APD in A
A=0.2;  #detector area in mm2

#CALCULATIONS
P=I*A;  #Power seen by detector in mW
photons_generated=P*1e-3/(h*c/lambda1);  #photons Generated
Rate=Iph1/q;  #rate of carrier generation for pin
eta=Rate/photons_generated;  #Quantum efficiency for pin
M=Iph2/Iph1;  #Multiplication factor

#RESULTS
print"Quantum efficiency is=",round(eta,5);  #The answers vary due to round off error
print"Avalanche multiple factor=",round(M,5);

Quantum efficiency is= 0.72794
Avalanche multiple factor= 50.0