Satellite Communications
Link budget analysis
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Lect 05
Transmitted power
Transmitting antenna gain
Path loss
Receiving antenna gain
Receiver sensitivity
© 2012 Raymond P. Jefferis III
1
Tx Down-Link Budget Analysis
• Starting with transmitter link loss factors:
– Power is reduced by system loss factors
• detuning losses, cabling losses, coupling losses, etc.
– Power is reduced by antenna inefficiency, from beam
sidelobes, for instance
• Dynamic losses
– Backoff, beamwidth, and pointing losses
• Path loss factors
– Free space loss
– Atmospheric losses
– Precipitation losses
Lect 05
© 2012 Raymond P. Jefferis III
2
Rx Down-Link Budget Analysis
• Receiver factors:
– Receiver antenna gain – efficiency loss
– Coupling, cabling, and detuning losses
– Receiver sensitivity
• Noise factors
– Input noise (natural factors)
– Antenna, RF amplifier, and mixer noise
Lect 05
© 2012 Raymond P. Jefferis III
3
Transmitted Power
• Usually specified in Watts
• Can be converted to dBW by,
Pt dB
 Pt 
 10 log 

 1.0 
where,
Pt db = Transmitter power [dB-Watts]
Pt = Transmitter power [Watts]
Lect 05
© 2012 Raymond P. Jefferis III
4
Transmitted Power
• Usually specified in Watts
• Can be converted to dBm by,
Pt dBm
Pt


 10 log 

 1 * 10 3 
where,
Pt dbm = Transmitter power [dB-milliWatts]
Pt = Transmitter power [Watts]
Lect 05
© 2012 Raymond P. Jefferis III
5
Examples 05-01, 05-02
• Transmitter power = 20 Watts
• Pt db = 10 log(20) = 13 dBW
• Pt dbm = 10 log(20/10-3) = 43 dBm
• Transmitter power = 75 Watts
• Pt db = 10 log(75) = 18.75 dBW
• Pt dbm = 10 log(75/10-3) = 48.75 dBm
Lect 05
© 2012 Raymond P. Jefferis III
6
What does this specification mean?
Intelsat GALAXY-11 at 91W (NORAD 26038)
• 39.1 dBW on C-Band (20W, 24 ch, Bw: 36 MHz)
• 47.8 dBW on Ku-Band (75/140W, 40 ch, Bw: 36 MHz)
Two possible interpretations (CDMA vs. TDMA)
• Transmitter power, is simultaneously distributed across all
the available channels (CDMA)
• The satellite has four antennas, two for each band, and
sequential channels are transmitted on one antenna in a
band and received on the other. Shared channel (TDMA)
Lect 05
© 2012 Raymond P. Jefferis III
7
Transmitter Antenna Gain
For a circular antenna (parabolic dish),
A e   A  (d / 2 )
G 
4

2
Ae
 d
G  A 

  
Lect 05
2
where,
Ae = Effective aperture [m2]
 A= aperture efficiency
d = aperture diameter [m]
G = aperture antenna gain
 = operating wavelength [m]
2
© 2012 Raymond P. Jefferis III
8
Circular Aperture Antenna
• The electric field of a circular aperture
antenna can be calculated from:
E [ ] 
2  J 1 [( D /  ) sin  ]
D
sin 
where, D/ gives the aperture diameter in
wavelengths and ϕ is the angle relative to the
normal to the plane of the aperture.
LECT 04
© 2012 Raymond P. Jefferis III
9
Example 05-03 - Ku-Band antenna
• 3dB beamwidth = 3˚
• D/ = 25
  = 0.63
• G = 3886
• GdBi = 36
Lect 05
© 2012 Raymond P. Jefferis III
10
Beamwidth – Circular Aperture
Show demo.
Lect 05
© 2012 Raymond P. Jefferis III
Lect 00 - 11
E-Field of a Circular Aperture Antenna
eps = 0.001;
Diam = 20;
Manipulate[e2 = (2.0/p*Diam)*
(BesselJ[1, p*Diam*Sin[theta]])/Sin[theta];
Plot[Abs[e2], {theta, -p/6, p/6},
PlotRange -> {{-0.5, 0.5}, {0, 600}},
PlotStyle -> {Directive[Thick, Black]}],
{Diam, 1, 25}
]
Lect 05
© 2012 Raymond P. Jefferis III
Lect 00 - 12
Antenna Gain vs Beamwidth Calculation
eff = 0.63;
beamw = 1;
f = 12*10^9;
c = 2.99792458*10^8;
lam = c/f;
Plot[app = 75.0/beamw;
diam = app*lam;
G = eff*p^2*app^2;
lG = 10*Log[10, G];
lG, {beamw, 1, 5}, AxesLabel -> {Beamwidth [deg], Gain}]
Lect 05
© 2012 Raymond P. Jefferis III
13
Antenna Gain vs Beamwidth Result
Lect 05
© 2012 Raymond P. Jefferis III
Lect 00 - 14
Link Budget – General Information
• The accounting of gains and losses over a link
• Other effects that can be considered
– Fading
– Reflections (multipath interference)
– Ground absorption
• Excessive power losses can reduce a transmitted
signal to levels below the receiver sensitivity in
the presence of noise
Lect 05
© 2012 Raymond P. Jefferis III
Lect 00 - 15
Link Budget Calculation (Downlink)
• Calculate power density of isotropic antenna
• Calculate effective radiated power (EIRP)
using transmitter antenna gain and efficiency
• Calculate path loss
• Calculate receiving antenna aperture and gain
• Calculate received power at the earth station
Lect 05
© 2012 Raymond P. Jefferis III
16
Link Budget Calculation (continued)
• Compare receiver input specifications with the
calculated power levels at the receiver
• Add noise factors
• Calculate receiver input Signal/Noise ratio
• If this is inadequate, change accessible link factors
Lect 05
© 2012 Raymond P. Jefferis III
Lect 00 - 17
The Isotropic (Ideal) Antenna
• The gains of antennas can be stated relative to an
isotropic ideal antenna as G [dBi], where G > 0.
• This antenna is a (theoretical) point source of EM
energy
• It radiates uniformly in all directions
• A sphere centered on this antenna would exhibit
constant energy per unit area over its surface
• The gain of an isotropic antenna is 0 dBi
Lect 05
© 2012 Raymond P. Jefferis III
Lect 00 - 18
EIRP
• Equivalent Isotropic Radiated Power
• – the equivalent power input that would be
needed for an isotropic antenna to radiate
the same power over the angles of interest
LECT 04
© 2012 Raymond P. Jefferis III
Lect 00 - 19
Equivalent Isotropic Radiated Power - EIRP
EIRP  G t Pt
Where: (in the far-field only),
EIRP = Equiv. isotropic rad. power [W]
Pt = Transmitted power [W]
Gt = Gain of lossless transmitting antenna
(Gt = 1 for lossless isotropic antenna)
or, in dB units,
EIRPdBW = Pt dBW + Gt dBi
Lect 05
© 2012 Raymond P. Jefferis III
20
Isotropic Radiated Flux Density
 1 
 
E IR P
2 
 4 r 
where (in the far-field only),
ψ = Transmitted power flux density (W/m2)
EIRP = Equiv. isotropic rad. power [W]
r = Distance from transmitter
Note: This is the EIRP per unit area of a sphere at
radius r from an isotropic antenna.
Lect 05
© 2012 Raymond P. Jefferis III
21
Actual Transmitting Antenna Gain
G te   t G t
EIRPeff   t G t Pt
where (in the far-field only),
EIRPeff = Effective EIRP [W]
Pt = Transmitted power [W]
Gt = Gain of a lossless (ideal) transmitting antenna
 t = Transmitting antenna efficiency
Gte = Effective gain of transmitting antenna
Lect 05
© 2012 Raymond P. Jefferis III
22
Example 05-04: Ku-Band Satellite
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Lect 05
Pt: 75 [W]
Antenna diam:
Frequency:
Wavelength:
Antenna Eff.:
Antenna Gain:
EIRPeff
=>
18.75 [dBW]
1.8 [m]
12 [GHz]
0.025 [m]
0.62 [-2.1 dBW]
45.02 [dBi]
63.77 [dBW]
© 2012 Raymond P. Jefferis III
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EIRP Calculation for Ku-band Example
c = 2.99792458*10^8; (* m/sec *)
freq = 12.0*10^9; (* Hz *)
pt = 75.0;(* Watts *)
ptdbW = 10*Log[10, pt]; (* dBW *)
eff = 0.62; (* efficiency *)
lam = c/freq; (* m *)
diam = 1.8; (* m *)
dl = diam/lam;
gain = eff*(p*diam/lam)^2;
loggain = 10*Log[10, gain];(* dB *)
eirp = gain*pt;(* W *)
dBW = 10*Log[10, eirp];(* dBW *)
Print["EIRP = ", dBW, "
[dBW]"]
Lect 05
© 2012 Raymond P. Jefferis III
Lect 00 - 24
Free Space Path Loss Calculation
• Due to the spreading of transmitted energy
• Other losses will be accounted separately
  
2
Lp  

 4 r 
where,
 = wavelength [m]
r = transmission-reception distance [m]
Lect 05
© 2012 Raymond P. Jefferis III
25
Received Power (Gain & Losses)
Pr  EIRP  L p  G r
  dr 
2
Gr  r 

  
where,
EIRP = Effective Isotropic Radiated Power
 r = Antenna efficiency
Gr = Antenna gain (G = 1 for isotropic)
dr = Antenna diameter [m]
Lp = Path loss
 = wavelength [m]
Lect 05
© 2012 Raymond P. Jefferis III
26
Net Received Power Calculation
Pr  E IR P  L p  G r _ eff
E IR P  G t _ eff Pt
G t _ eff
  dt 
 t 

  
  
2
2
Lp  

 4 r 
G r _ eff
Lect 05
  dr 
 r 

  
EIRP = Eff. Isotropic Radiated Power
 t/r = Antenna efficiency
Gt/r = Antenna gain
Dt/r = Antenna diameter [m]
Lp = Path loss
λ = wavelength [m]
R = transmitter-receiver distance [m]
2
© 2012 Raymond P. Jefferis III
27
Another Received Power Interpretation
Pr   r  A eff
Where,
Pr = Received power [W]
ψr = Received flux density [W/m2]
Aeff = Effective receiving antenna aperture [m2]
Lect 05
© 2012 Raymond P. Jefferis III
28
Path Loss Summary Diagram
Lect 05
© 2012 Raymond P. Jefferis III
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Power Ratio over Path Calculation
Pr
Pt

tGt  rG r
(4 d /  )
2
where,
 t = Efficiency of receiving antenna [-]
 r = Efficiency of receiving antenna [-]
Gt = Antenna gain (G=1 for isotropic antenna)
Gr = Antenna gain (G=1 for isotropic antenna)
λ = wavelength [m]
d = distance between antennas [m]
Lect 05
© 2012 Raymond P. Jefferis III
30
Path Loss [dB]
2
Pr
Lect 05
dB
 Pt
dB
  
 10 log( t G t )  10 log 
  10 log( r G r )
 4 r 
© 2012 Raymond P. Jefferis III
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Example 05-05: Ku-Band Satellite
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Lect 05
Receiving antenna diameter:
Frequency:
Wavelength:
Path length:
Antenna Eff.:
Receiving Antenna Gain:
EIRPeff
Path gain (-loss):
Received power:
© 2012 Raymond P. Jefferis III
0.9 [m]
12 [GHz]
0.025 [m]
42000 [km]
0.62
39 [dBi]
63.8 [dBW]
-206.5 [dBW]
-103.7 [dBW]
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Class Activity
• Compute the path loss of the previous
example in dBW.
• Compute the received power of the previous
example in dBW.
Lect 05
© 2012 Raymond P. Jefferis III
Lect 00 - 33
Activity Results
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f = 12 GHz [12000 MHz]
λ= 0.025 [m] => (-32 dBW)
Pt = 18.75 dBW
ηtGt = 45.02 dBW
ηrGr = 39.0 dBW
r = 42,000 km => (-206.5 dBW)
Pr = 18.75 + 45.02 - 206.5 + 39 = -103.7 [dBW]
Lect 05
© 2012 Raymond P. Jefferis III
Lect 00 - 34
Activity Calculation
c = 2.99792458*10^8; f = 12.0*10^9; lam = c/f;
r = 42.0*10^6;
pwrTx = 75.0; dAntTx = 1.8; effAntTx = 0.62;
gAntTxEff = effAntTx*(p*dAntTx/lam)^2;
gAntTxEffdB = 10 Log[10, gAntTxEff];
EIRPdB = 10 Log[10, pwrTx] + gAntTxEffdB;
Lp = (lam/(4*p*r))^2;
LpdB = 10 Log[10, Lp];
dAntRx = 0.9; effAntRx = 0.62;
gAntRxEff = effAntRx*(p*dAntRx/lam)^2;
GAntRxEffdB = 10 Log[10, gAntRxEff];
PrdB = EIRPdB + LpdB + GAntRxEffdB;
Print["Path Loss ", LpdB, " [dB]"];
Print["Rcv pwr = ", PrdB, " [dBW]"];
Lect 05
© 2012 Raymond P. Jefferis III
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Example: Ku-Band Link
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Lect 05
Tx power:
10 [Watts]
Rx and Tx antenna diameters:3.0 [m]
Frequency:
12 [GHz]
Path length:
35,900 [km]
Antenna Efficiencies
0.55
Antenna Gains:
48.93[dBi]
EIRPeff
58.93 [dBW]
Path gain (-loss):
-205.1 [dBW]
Received power:
-97.24 [dBW]
© 2012 Raymond P. Jefferis III
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Example Ku-Band Calculation
f = 12.0*10^9; Bw = 36.0*10^6; c = 2.99792458*10^8;
lam = c/f;
r = 35.9*10^6;
(* Tx EIRP CALC. *) pwrTx = 10.0;
pwrTxdB = 10 Log[10, pwrTx];
dAntTx = 3.0; effAntTx = 0.55;
gAntTxEff = effAntTx*(p dAntTx/lam)^2;
gAntTxEffdB = 10 Log[10, gAntTxEff];
EIRPdB = 10 Log[10, pwrTx] + gAntTxEffdB;
(* Path Loss *) Lp = (3.0*10^8/(4*p*f*r))^2;
(* Path Loss [DB] *) LpdB = 10 Log[10, Lp];
(* Rx Antenna CALC. *) dAntRx = 3.0; effAntRx = 0.55;
gAntRxEff = effAntRx*(p dAntRx/lam)^2;
GAntRxEffdB = 10 Log[10, gAntRxEff];
(* Received Power [DB] *) PrdB = EIRPdB + LpdB +
GAntRxEffdB;
(* Received Power [W] *) PrWatts = 10^(PrdB/10);
Lect 05
© 2012 Raymond P. Jefferis III
37
Conversion to Frequency Base
  c/ f
where,
2
 3 * 10 8 
Pr  Pt 
GtG r

 4  fR 
 c 
Lp  

 4  fR 
Pr d B
2
 Pt d B  (G t ) d B  ( L p ) d B  (G r ) d B
Lect 05
(Pt)dB = Transmitted power [dBW]
(Pr)dB = Received power [dBW]
(Lp)dB = Path loss power [dBW]
(Gt/r)dB = Transmitting or receiving
antenna gain
f = frequency [Hz]
R = distance [m]
© 2012 Raymond P. Jefferis III
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Example Calculation: Ku-Band
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f = 12 GHz [12000 MHz]
Pt = 18.7 dBW
Gt = 45 dBi
Gr = 39 dBi
R = 42, 000 km
Pr = 18.7 + 45 - 206.49 + 39 = - 103.8 dBW
Note:
Considering free space loss only
Lect 05
© 2012 Raymond P. Jefferis III
39
Workshop 05
• Please do all work indicated on the
Workshop 05 handout.
• You may use a spreadsheet or a
mathematics package (Mathematica®is
recommended) for your calculations
• Document ALL work and calculations
• Submit as a written Workshop report.
Lect 05
© 2012 Raymond P. Jefferis III
40
Workshop 05 Calculations
c = 2.99792458*10^8; f = 12.0*10^9;
lam = c/f; r = 42.0*10^6;
pwrTx = 75.0; pwrTxdB = 10 Log[10, pwrTx];
dAntTx = 1.8; effAntTx = 0.62;
gAntTxEff = effAntTx*(p dAntTx/lam)^2;
gAntTxEffdB = 10 Log[10, gAntTxEff];
EIRPdB = 10 Log[10, pwrTx] + gAntTxEffdB;
Lp =(3.0*10^8/(4*p*f*r))^2; LpdB =10 Log[10, Lp];
dAntRx = 0.9; effAntRx = 0.62;
gAntRxEff = effAntRx*(p dAntRx/lam)^2;
GAntRxEffdB = 10 Log[10, gAntRxEff];
PrdB = EIRPdB + LpdB + GAntRxEffdB;
Lect 05
© 2012 Raymond P. Jefferis III
41
End
Lect 05
© 2012 Raymond P. Jefferis III
42