The received power will be 1.243 nW
We're given:
frequency [tex]f[/tex] = 150MHz
distance of the receiver [tex]d[/tex] = 32.2 km=32200m
Power of transmitter [tex]P_{t}[/tex] = 3W
Antenna gain = 8dB
To find :
Power received [tex]P_{r}[/tex]
[tex]P_{r}= \frac{P_{t} *G_{t}*G_{r}* \lambda^2 }{16*\pi^2*d^2}[/tex]
where [tex]G_{t[/tex] is transmit gain and [tex]G_{r[/tex] is receive gain as refrenced to isotropic source
⇒wavelength [tex]\lambda = \frac{c}{f}[/tex] where c is the speed of the light
⇒ [tex]\lambda = \frac{3*10^8}{150*10^6} =2m[/tex]
[tex]G_{t}= 1*1.64[/tex] ( value of [tex]dipole[/tex] = 1.64)
Now,
Antenna gain[tex]=8dB[/tex] ( in decibals)
⇒[tex]10log(x)=8[/tex]
⇒[tex]x=10^0^.^8=6.3095[/tex]
⇒ considering isotropic receiver
⇒[tex]G_{r}=6.3095*1.64=10.3477[/tex] ([tex]dipole[/tex] =1.64)
Now , using the formula
[tex]P_{r}= \frac{3 *1.64*10.3477 *2^2 }{16*\pi^2*32200^2}=1.2437*10^-^9[/tex]
Hence The received power will be 1.243 nW
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