Chapter04: Optical Detectors and Receivers

Ex4.1.1:Pg-4.5

In [3]:
#Given
Eg= 1.1 
lamda_c = 1.24/Eg 
print "The cut off wavelength in um= ",round(lamda_c,2) 

Eg_ger =0.67 
lamda_ger= 1.24/Eg_ger 
print " \nThe cut off wavelength for Germanium in um= ",round(lamda_ger,2) 

The cut off wavelength in um=  1.13
 
The cut off wavelength for Germanium in um=  1.85

Ex4.1.2:Pg-4.5

In [6]:
#Given 
Eg = 1.43 
lamda = 1.24/Eg 
lamda=lamda*1000   # converting in nm
print "The cut off wavelength in nm =",round(lamda,2) 

The cut off wavelength in nm = 867.13

Ex4.1.3:Pg-4.5

In [8]:
#Given
P = 6*10**6 
Eh_pair= 5.4*10**6 
n= Eh_pair/P*100 
print " The quantum efficiency in % = ",n 

 The quantum efficiency in % =  90.0

Ex4.1.4:Pg-4.6

In [9]:
#Given
R= 0.65 
P0= 10*10**-6 
Ip= R*P0 
Ip=Ip*10**6   # convertinf in uA...
print " The generated photocurrent in uA = ",Ip 

 The generated photocurrent in uA =  6.5

Ex4.1.5:Pg-4.6

In [12]:
#Given

Ec= 1.2*10**11 
P= 3*10**11 
lamda = 0.85*10**-6 
n= Ec/P*100 
print "The efficiency in % =",n 

q= 1.602*10**-19 
h= 6.625*10**-34 
c= 3*10**8 
n= n/100 
R= n*q*lamda/(h*c) 
print " \n\nThe Responsivity of the photodiode in A/W=",round(R ,4)

The efficiency in % = 40.0
 

The Responsivity of the photodiode in A/W= 0.2741

Ex4.1.6:Pg-4.7

In [5]:
#Given

n= 0.65 
E= 1.5*10**-19 
Ip= 2.5*10**-6 
h= 6.625*10**-34 
c= 3*10**8 
lamda= h*c/E 
lamda=lamda*10**6   # converting in um for displaying...
print "The wavelength in um =",lamda 
lamda=lamda*10**-6 
q= 1.602*10**-19 
R= n*q*lamda/(h*c) 
print "\nThe Responsivity in A/W =",R 
Pin= Ip/R 
Pin=Pin*10**6  #  converting in uW for displaying/..
print " \nThe incidnt power in uW= ",round(Pin,1) 

The wavelength in um = 1.325

The Responsivity in A/W = 0.6942
 
The incidnt power in uW=  3.6

Ex4.1.7:Pg-4.8

In [7]:
#Given
Iin= 1 
lamda= 1550*10**-9 
q= 1.602*10**-19 
h= 6.625*10**-34 
c= 3*10**8 
n=0.65 
Ip=n*q*lamda*Iin/(h*c) 
Ip=Ip*1000   # converting in mA for displaying...
print " The average photon current in mA= ",int(Ip)

 The average photon current in mA=  812

Ex4.1.8:Pg-4.9

In [14]:
#Given

n= 0.70 
Ip= 4*10**-6 
e= 1.602*10**-19 
h= 6.625*10**-34 
c= 3*10**8 
E= 1.5*10**-19
lamda = h*c/E 
lamda=lamda*10**6   # converting um for displaying...
print "The wavelength in um =",round(lamda,3) 
R= n*e/E 
Po= Ip/R 
Po=Po*10**6   # converting um for displaying...
print " \nIncident optical Power in uW =",round(Po,2) 

The wavelength in um = 1.325
 
Incident optical Power in uW = 5.35

Ex4.2.1:Pg-4.14

In [43]:
#Given
import math
Ct= 7*10.0**-12
Rt= 50*1*10.0**6/(50+(1*10**6))
B= 1/(2*math.pi*Rt*Ct)
B=B*10**-6  #converting in mHz for displaying...
print "The bandwidth of photodetector in MHz =",round(B,2)

The bandwidth of photodetector in MHz = 454.75

Ex4.2.2:Pg-4.15

In [45]:
#Given
import math
W= 25*10**-6 
Vd= 3*10**4 
Bm= Vd/(2*math.pi*W) 
RT= 1/Bm 
RT=RT*10**9    # converting ns for displaying...
print " The maximum response time in ns =",round(RT,2) 

 The maximum response time in ns = 5.24

Ex4.2.3:Pg-4.15

In [48]:
#Given
e= 1.602*10**-19 
h= 6.625*10**-34 
v= 3*10**8 
n=0.65 
I= 10*10**-6 
lamda= 900*10**-9 
R= n*e*lamda/(h*v) 
Po= 0.5*10**-6 
Ip= Po*R 
M= I/Ip 
print " The multiplication factor =",round(M,2) 

 The multiplication factor = 42.41

Ex4.3.1:Pg-4.18

In [51]:
#Given
n=0.65 
lamda = 900*10**-9 
Pin= 0.5*10**-6 
Im= 10*10**-6 
q= 1.602*10**-19 
h= 6.625*10**-34 
c= 3*10**8 
R= n*q*lamda/(h*c) 
Ip= R*Pin 
M= Im/Ip 
print " The multiplication factor =",round(M,2)
print "\n***NOTE-Answer wrong in textbook..."

 The multiplication factor = 42.41

***NOTE-Answer wrong in textbook...

Ex4.6.1:Pg-4.34

In [61]:
#Given
import math
lamda = 1300*10**-9 
Id= 4*10**-9 
n=0.9 
Rl= 1000 
Pincident= 300*10**-9 
BW= 20*10**6 
q= 1.602*10**-19 
h= 6.625*10**-34 
v= 3*10**8 
Iq= math.sqrt((q*Pincident*n*lamda)/(h*v)) 
Iq= math.sqrt(Iq) 
Iq=Iq*100   # converting in proper format for displaying...
print "Mean square quantum noise current in Amp*10^11 =",round(Iq,2)
I_dark= 2*q*BW*Id 
I_dark=I_dark*10**19  # converting in proper format for displaying...
print " \nMean square dark current in Amp*10^-19 =",round(I_dark,3) 
k= 1.38*10**-23 
T= 25+273 
It= 4*k*T*BW/Rl 
It=It*10**16  # converting in proper format for displaying...
print " \nMean square thermal nise current in Amp*10^-16 =",round(It,2)

Mean square quantum noise current in Amp*10^11 = 2.31
 
Mean square dark current in Amp*10^-19 = 0.256
 
Mean square thermal nise current in Amp*10^-16 = 3.29

Ex4.8.1:Pg-4.39

In [64]:
#Given

lamda = 850*10**-9 # meters
BER= 1*10**-9 
N_bar = 9*log(10) 
h= 6.625*10**-34 # joules-sec
v= 3*10**8 # meters/sec
n= 0.65 #  assumption
E=N_bar*h*v/(n*lamda) 
E=E*10**18 # /converting in proper format for displaying...
print " The Energy received in Joules*10^-18 =",round(E,2)

 The Energy received in Joules*10^-18 = 7.45

Ex4.8.2:Pg-4.39

In [67]:
#Given
lamda = 850*10**-9 
BER = 1*10**-9 
BT=10*10**6 
h= 6.625*10**-34 
c= 3*10**8 
Ps= 36*h*c*BT/lamda 
Ps=Ps*10**12  # /converting in proper format for displaying...
print "The minimum incidental optical power required id in pW =",round(Ps,2) 

The minimum incidental optical power required id in pW = 84.18

Ex4.8.3:Pg-4.40

In [70]:
#Given
import math
C= 5*10**-12 
B =50*10**6 
Ip= 1*10**-7 
e= 1.602*10**-19 
k= 1.38*10**-23 
T= 18+273 
M= 1 
Rl= 1/(2*math.pi*C*B) 
S_N= Ip**2/((2*e*B*Ip)+(4*k*T*B/Rl)) 
S_N = 10*math.log10(S_N)   # in db
print " The S/N ratio in dB =",round(S_N,2) 
M=41.54 
S_N_new= (M**2*Ip**2)/((2*e*B*Ip*M**2.3)+(4*k*T*B/Rl)) 
S_N_new = 10*math.log10(S_N_new)   # in db
print " \n\nThe new S/N ratio in dB =",round(S_N_new,2)
print " \n\nImprovement over M=1 in dB =",round(S_N_new-S_N,1) 

 The S/N ratio in dB = 8.99
 

The new S/N ratio in dB = 32.49
 

Improvement over M=1 in dB = 23.5