SATELLITE LINKS
BASIC LINK BUDGETS
ALLOCATING THE AVAILABLE
SATELLITE RESOURCES TO
ACCOMODATE THE PARAMETERS OF
THE TX & RX EARTH STATIONS ...
C (dBW)

CARRIER POWER RECEIVED IS DEFINED BY :
C = PtAe / [4pi(radius^2)]
(WATTS)
where,
4pi(radius^2) = SURFACE AREA OF A SPHERE
Pt = ISOTROPICALLY SPREAD Tx POWER
Ae = EFFECTIVE AREA OF THE Rx ANTENNA

WHEN A DIRECTIONAL ANTENNA IS USED :
C = PtGtAe / [4pi(radius^2)]
where,
Gt = Tx GAIN
2
pi

A CONSTANT OF PROPORTIONALITY
(USEFUL IN SOLVING FOR THE AREA OF A CIRCLE)

THE EGYPTIAN RULE FOR FINDING THE AREA :
EQUALS 3.16 TIMES THE RADIUS SQUARED

WHICH WAS CLOSER TO THE TRUTH THAN
THE BABYLONIAN VALUE OF 3
(BASED ON THE BIBLE)

IN ACTUALITY, THE MATHEMATICAL VALUE
OF pi IS AN IRRATIONAL NUMBER
3
C/T (dBW/K)

CARRIER-TO-THERMAL NOISE
where,
C = EIRP - LOSSES + Gr
and,
C/T = EIRP - LOSSES + G/T
THIS IS THE HEART OF THE LINK
BUDGET
4
C/kT (dBHz)

CARRIER-TO-THERMAL NOISE DENSITY
(WITH BOLTZMANNS CONSTANT k)
C/kT = C/No = C/T + 228.6
where,
kT = No = N/B = N (dBW/Hz)
(IN A 1Hz BANDWIDTH)
5
C/N (dB)

CARRIER-TO-NOISE IN BANDWIDTH B
C/N = C/kTB
where,
C/kTB = C/kT - 10log(BW)
and,
C/kT = C/No
6
Eb/No (dB)

ENERGY PER BIT - NOISE DENSITY
Eb/No = C/No - 10log(R)
where,
R = BIT RATE (BITS/SECOND)
PERFORMANCE OF DIGITAL CIRCUITS IS OFTEN
MEASURED AS A SPECIFIC BER.
WHICH IS RELATIVE TO THE Eb/No.
7
E (dBuV/m)

ELECTRIC FIELD STRENGTH
(POWER PER UNIT AREA)
W = 1/2[c(PERMITTIVITY)] x E^2
W = [1/2(E^2)] / Z
(W/m^2)
(W/m^2)
where,
Z = 1 / [c(PERMITTIVITY)]
W = 2E - 148.77
E = 1/2(W + 148.77)
(dBW/m^2)
(dBuV/m)
8
EIRP (dBW)

EQUIVALENT ISOTROPICALLY RADIATED POWER
EIRP = PGt
(WATTS)
EIRP = 10log(P) + 10log(Gt)
(dBW)
TYPICAL VALUES OF EIRP RANGE FROM :
0-90 dBW FOR EARTH STATIONS
20-60 dBW FOR SATELLITES
9
G (dBi)

GAIN OF AN ANTENNA
(AS REFERENCED TO AN ISOTROPIC RADIATOR)
G = Tx PWR OF ANTENNA / ISOTROPIC Tx PWR
G (PARABOLIC) = (4pi x eff x A) / WAVELENGTH^2
G = eff{[(piD x FREQ)/C]^2}
G = 20logD + 20logFREQ + 10log(eff) + 20.4
TYPICAL E/S GAIN FIGURES ARE 1-60dBi
SATELLITE GAIN FIGURES RANGE FROM 14-40dBi
10
eff

Antenna efficiency (assumed 60-70%)
Actual values range from .2 to .75
 Conventially illuminated (large) Earth stations
typically are 65-75%
 Flat plate antennas are 75% efficient
(Superconductive surfaces on these may further
increase this value)
 Satellite spacecraft antennas are usually less
efficient.
(40-55%, or 20-30% for multi-beam)

11
BASICS OF ANTENNA GAIN

A Tx SHAPED ANTENNA FOCUSES THE Tx PWR

IF NO BEAM DIRECTIVITY IS APPLIED, THE
RESULT IS AN ISOTROPIC RADIATOR.
(THE SUN COULD BE USED AS AN EXAMPLE)

THEORETICAL GAIN OF A PARABOLIC IS INFINITE
(THUS, THE LIMITATION IS BASED ON WAVELENGTH)

GAIN CALCULATED BY VIRTUE OF THEORETICAL IS
USUALLY CONSIDERED PEAK (ON-AXIS) GAIN.

OFF-AXIS GAIN IS ALSO A SERIOUS CONSIDERATION
12
ANTENNA BEAMWIDTH
13
G/T (dBi/K)

FIGURE OF MERIT
G/T = Gr - 10logTs
where,
Gr = Rx ANTENNA GAIN (dBi)
Ts = Rx SYSTEM NOISE TEMP (DEGREES KELVIN)

Gr IS A FACTOR OF THE EFFICIENCY, OR SIZE OF THE
ANTENNA.

Ts IS THE SUM OF ANTENNA NOISE TEMP, LNA TEMP &
NOISE CONTRIBUTED BY RESISTIVE COMPONENTS
BETWEEN THE ANTENNA AND LNA.
14
k (dBW/Hz-K)

BOLTZMANNS
CONSTANT (OF PROPORTIONALITY)
k = 1.3806 x 10^-23 (W/Hz-K)
k = -228.6 (dBW/Hz-K)
Pn (MAX NOISE OUTPUT) = kTB
where,
T = ABSOLUTE TEMPERATURE
B = BANDWIDTH OF INTEREST
15
L (dB)

FREESPACE LOSS
C = (EIRP x eff x AREA) / (4pi x S^2)
G = (4pi x eff x AREA) / WAVELENGTH^2
C = EIRP x [(WAVELENGTH^2) / (4piS)^2] x Gr
L = (4piS)^2 / (WAVELENGTH^2)
C = EIRP - L + Gr
L = 20logS(km) + 20logFREQ(GHz) + 92.45
16
W (dBW/m^2)

ILLUMINATION LEVEL
W = PGt / [4pi(S^2)]
W = EIRP - 20logS - 71
where,
THE CONSTANT 71 = 10log{4pi[(1000m/km)^2]
THE MAXIMUM DISTANCE (S) = 41,679km
THIS CORRESPONDS TO A SATELLITE ON THE HORIZON @
0 DEGREES ELEVATION & MAXIMUM CENTRAL ANGLE
WITH THIS VALUE USED, THE WORST-CASE LEVEL IS :
W = EIRP - 163.4
17
PFD (dBW/m^2)

POWER FLUX DENSITY
(USUALLY DEFINED WITHIN A SPECIFIED BW)
PFD = W - 10log(B/Bccir)
where,
W = EIRP - 163.4
(dBW/m^2)
PFD = EIRP - 163.4 - 10log(B/Bccir)
THE STANDARD CCIR BANDWIDTH = 4kHz
(FOR C & Ku BAND SYSTEMS)
18
DEFINITION OF SIGNAL QUALITY
(C/T)
CXR-to-THERMAL NOISE RATIO
(C/No)
CXR-to-NOISE DENSITY
(C/N)
CXR-to-NOISE POWER
(S/N)
SIGNAL-to-NOISE POWER
19
LINK BUDGET (COMPONENTS)










TRANSMITTER POWER
ANTENNA GAIN
RADIATED EIRP
ILLUMINATION LEVEL @ RCVR
FREE SPACE LOSS
SYSTEM NOISE TEMPERATURE
RECEIVE FIGURE OF MERIT
CXR-to-THERMAL NOISE RATIO
CARRIER-to-NOISE DENSITY
CARRIER-to-NOISE RATIO
P (W)
G (dBi)
(dBW)
(dBW/m^2)
(dB)
Ts (K)
G/Ts (dBi/K)
C/T (dBW/K)
C/No (dBHz)
C/N (dB)
20
BASIC LINK BUDGETS

COME IN VARIOUS LENGTHS & STYLES

(THERE IS NO STANDARD FORMAT)
3 KEY EQUATIONS FORM THE BASIS :

FOR MOST UPLINK BUDGETS :
EIRP = 10logP + Gt
C/T = EIRP - L + G/T
C/kT = C/T + 228.6

FOR MOST DOWNLINK BUDGETS :
C/T = EIRP - L + G/T
C/kT = C/T + 228.6
C/N = C/kT - 10logB
21
THE TRANSPONDER
CHARACTERISTIC PARAMETERS







THE TX/RX FREQUENCY BANDS & POLARISATIONS
THE TX/RX COVERAGE (SFD & GAIN CONTOURS)
THE TX EIRP & CORRESPONDING PFD ACHIEVED
THE RX PFD REQUIRED TO ACHIEVE THE REQ’D TX EIRP
THE G/T BASED ON THE SFD CONTOUR
NON-LINEAR CHARACTERISTICS
RELIABILITY AFTER x YEARS FOR y PERCENTAGE OR
NUMBER OF CHANNELS TO REMAIN IN WORKING ORDER
22
TRANSMITTER POWER (P)


USUALLY SPECIFIED IN WATTS
THE 1st NUMBER OF THE LINK BUDGET
(OFTEN ADJUSTED TO OBTAIN THE DESIRED PERFORMANCE)

FOR SATELLITES, Tx POWER IS LIMITED BY THE DC
POWER AVAILABLE VIA THE SOLAR ARRAY. (10-200W)

EARTH STATION TRANSMITTERS RANGE FROM 1-10KW

IF LOSSES ARE SIGNIFICANT, THE Tx POWER IS
MEASURED @ THE ANTENNA INPUT FLANGE.
(LOSSES BEFORE THIS POINT MAY BE DEDUCTED FROM THE Tx PWR)
23