Radio Links:

Antenna Gain:
g = (Power density on-axis at given distance) / (power density from isotropic source at
same distance)
g = 4π.a/λ2
Antenna Aperture:
a = η.π.r2
Power density from transmit antenna at receive aperture is:
pden = (pt.gt)/(4π.d2)
Power collected by receive antenna:
pr = ((pt.gt)/(4π.d2)).ar.α
= pt.gt.gr(λ/(4π.d))2.α
Path transmission loss ("free space loss"):
lp = ((4π.d)/λ)2
Thermal noise at output of receive antenna:
n = k.T.B
Carrier-to-noise ratio:
pr/nr = (pt.gt.gr.α)/(lp.k.T.B)
Hence "Link Budget Equation" expressed in dB:
C/N = Pt+Gt-Lp-La+(G/T)|r-k-10.log(B)
Note: |r means evaluated at r.
When calculating the link budget, we must take account of additional factors:
- Interferences from other radio systems
- Intermodulation noise
- Additional loss, interference and noise due to propagation events (e.g. rain,
rain-scatter, noise degradation, ducting, etc.)
Figure of merit (G/T) is a useful way of categorising the performance of a receiving
system.
In a constant RF field, different receiving systems (with the same receive bandwidth) will
yield a C/N proportional to the system G/T.
EIRP is the usual way of combining transmit power and gain:
EIRP = Pt+Gt
So, the link budget equation is normally expressed as:
C/N = EIRP - Lp - La - Lm + G/T - 10log(B) + 228.6
The satellite link:
Uplink and downlink are analysed seperately as individual radio links:

Overall Link Quality:
C/N = C/(Nup+Ndown+Iup+Idown+Nimod)
(c/ntot)-1=(c/nup)-1+(c/ndown)-1+(c/iup)-1+...
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