SATELLITE LINKS

BASIC LINK BUDGETS

ALLOCATING THE AVAILABLE SATELLITE RESOURCES TO

ACCOMODATE THE PARAMETERS OF THE TX & RX EARTH STATIONS ...

2

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

3

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

4

C/T (dBW/K)

CARRIER-TO-THERMAL NOISE

where,

C = EIRP - LOSSES + Grand,

C/T = EIRP - LOSSES + G/T

THIS IS THE HEART OF THE LINK BUDGET

5

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)

6

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

7

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.

8

E (dBuV/m)

ELECTRIC FIELD STRENGTH (POWER PER UNIT AREA)

W = 1/2[c(PERMITTIVITY)] x E^2 (W/m^2)

W = [1/2(E^2)] / Z (W/m^2)where,

Z = 1 / [c(PERMITTIVITY)]

W = 2E - 148.77 (dBW/m^2)

E = 1/2(W + 148.77) (dBuV/m)

9

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

10

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

11

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)

12

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

13

ANTENNA BEAMWIDTH

14

G/T (dBi/K)

FIGURE OF MERIT

G/T = Gr - 10logTswhere,

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.

15

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) = kTBwhere,

T = ABSOLUTE TEMPERATURE

B = BANDWIDTH OF INTEREST

16

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

17

W (dBW/m^2)

ILLUMINATION LEVEL

W = PGt / [4pi(S^2)]

W = EIRP - 20logS - 71where,

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

18

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)

19

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

20

LINK BUDGET (COMPONENTS)

TRANSMITTER POWER P (W) ANTENNA GAIN G (dBi) RADIATED EIRP (dBW) ILLUMINATION LEVEL @ RCVR (dBW/m^2) FREE SPACE LOSS (dB) SYSTEM NOISE TEMPERATURE Ts (K) RECEIVE FIGURE OF MERIT G/Ts (dBi/K) CXR-to-THERMAL NOISE RATIO C/T (dBW/K) CARRIER-to-NOISE DENSITY C/No (dBHz) CARRIER-to-NOISE RATIO C/N (dB)

21

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

22

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

23

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)