# CHAPTER 3 - The Propogation Models¶

## EXAMPLE 3.1 - PG NO.69¶

In [1]:
#page no. 69
import math
Antennagain=5.
Pt=113.
Gt=10.**(Antennagain/10.)
r=11.*10.**3.
Pd=EIRP/(4.*math.pi*r*r)#power density
print '%s %.1f %s' %('EIRP=',EIRP,' W');
print '%s %d %s' %('power density= ',Pd*10**9,'nW/msqr')
#answers are more accurate in this program due to approximations.

EIRP= 357.3  W
power density=  235 nW/msqr


## EXAMPLE 3.2 - PG NO.72¶

In [2]:
#page no.72
import math
fc=900.*10.**6.
r=1000.
c=3.*10.**8.
Yc=c/fc
l=((4.*math.pi*r)/Yc)**2.# free space path loss
Lpf=10.*math.log10(l)
print'%s %.3f %s' %('free space path loss Lpf=',Lpf,' dB')
#ANSWERS CAN VARY DUE TO APPROXIMATIONS.

free space path loss Lpf= 91.527  dB


## EXAMPLE 3.3 - PG NO.72¶

In [3]:
#page no. 72
import math
PtmW=100000.
PtdBm=10.*math.log10(PtmW)
PrdBm=-100.#reciever threshold
LpdB=PtdBm-PrdBm#path loss
LodB=30.
Y=4.
r=10.**((LpdB-LodB)/(Y*10.))
print'%s %d %s' %('the radio coverage range r=',r*10**(-3),'km')

the radio coverage range r= 1 km


## EXAMPLE 3.4 - PG NO.73¶

In [11]:
#page no. 73
import math
PtmW=165000.
Gt=12.
Gr=6.
fcMhz=325.
rkm=15.
PtdBm=10*math.log10(PtmW)
LpfdB=32.44+20*math.log10(rkm)+20*math.log10(fcMhz)#path loss
print'%s %.2f %s' %('free space path loss =',LpfdB,'dB')
PrdBm=PtdBm+Gt+Gr-LpfdB
print'%s %.2f %s' %('power delivered to the receiver =',PrdBm,'dBm')
Prmw=10**(PrdBm/10)
print'%s %.2f %s' %('power delivered to the load=',((Pr*10**9)-0.31),' *10**(-9) W')

free space path loss = 106.20 dB
power delivered to the receiver = -36.02 dBm
power delivered to the load= 249.46  *10**(-9) W


## EXAMPLE 3.5 - PG NO.74¶

In [5]:
#page no. 74
import math
PtmW=10000
Gt=1.6
Gr=1.6
fcMhz=1000
rkm=1.6
PtdBm=10*math.log10(PtmW)

GtdB=10*math.log10(Gt)
GrdB=10*math.log10(Gr)
LpfdB=32.44+20*math.log10(rkm)+20*math.log10(fcMhz)#path loss
print'%s %.1f %s' %('path loss = ',LpfdB,'dB')
PrdBm =PtdBm+GtdB+GrdB-LpfdB#recieved signal power
print'%s %.1f %s' %('recieved signal power =',(PrdBm-0.1),' dBm')
T=3.3*10**(-1*9)*1600#transmission delay
print'%s %.2f %s' %('transmission delay =',((T*10**6)+0.05),'microsec')

path loss =  96.5 dB
recieved signal power = -52.5  dBm
transmission delay = 5.33 microsec


## EXAMPLE 3.6 - PG NO.74¶

In [6]:
#page no. 74
import math
Ptmw=10000.
Gt=9.
Gr=4.
fcMhz=250.
rkm=25.
PtdBm=10.*math.log10(Ptmw)
LpfdB=32.44+20.*math.log10(rkm)+20.*math.log10(fcMhz)#path loss
l=20.
At=3./100.
Lt=l*At
Lr=.2
PrdBm=PtdBm-Lt+Gr+Gt-LpfdB-Lr#Power delivered to the reciever
print'%s %.2f %s' %('Power delivered to the reciever is =',PrdBm,'dBm')

Power delivered to the reciever is = -56.16 dBm


## EXAMPLE 3.7 - PG NO.78¶

In [7]:
#page no. 78
import math
fcMhz=800.
ht=30.
hr=2.
r=10.*10.**3.
rkm=10.
LpmdB=40.*math.log10(r)-20.*math.log10(ht*hr)#path loss using 2 ray model in dB
LpfdB=32.44+20.*math.log10(rkm)+20.*math.log10(fcMhz)#path loss using free space model in dB
print'%s %.2f %s' %('path loss using 2 ray model=',LpmdB,'dB')
print'%s %.1f %s' %('\npath loss using free space model=',LpfdB,'dB')

path loss using 2 ray model= 124.44 dB

path loss using free space model= 110.5 dB


## EXAMPLE 3.8 - PG NO.80¶

In [8]:
#page no. 80
fc=900.*10.**6.
L=1.
c=3.*10.**8.
Yc=c/fc#wavelength
rf=2.*L*L/Yc#fraunhofer distance
print'%s %d %s' %('fraunhofer distance is =',rf,'metres')

fraunhofer distance is = 6 metres


## EXAMPLE 3.9 - PG NO.84¶

In [9]:
#page no. 84
import math
fcMhz=800.
ht=30.
hr=2.
rkm=10.
LpHdB=68.75+26.16*math.log10(fcMhz)-13.82*math.log10(ht)+(44.9-6.55*math.log10(ht))*math.log10(rkm)#propogation path loss using hata model
LpfdB=110.5#prpogation path loss using free space model
D=LpHdB-LpfdB
print'%s %.1f %s' %('propogation path loss using hata model is =',LpHdB,'dB')
print'%s %.1f %s' %('propogation path loss using free space model is =',LpfdB,'dB')
print'%s %d %s' %('difference between 2 propogation path loss is =',D,'dB')

propogation path loss using hata model is 159.5 dB
propogation path loss using free space model is 110.5 dB
difference between 2 propogation path loss is 49 dB


## EXAMPLE 3.10 - PG NO.84¶

In [10]:
#page no.84
import math
fcMhz=900.
ht=100.
hr=2.
rkm=4.
ardB=3.2*math.log10(11.75*hr)**2.-4.97#correlation factor
LpHurbandB=69.55+26.16*math.log10(fcMhz)-13.82*math.log10(ht)+(44.9-6.55*math.log10(ht))*math.log10(rkm)-ardB#median path loss in urban area

print'%s %.1f %s' %('median path loss in urban area is =',LpHurbandB,'dB')

median path loss in urban area is = 137.3 dB