### INTRODUCTION

• • • • Cost to build and launch a GEO satellite is about 25,000 dollars per kg Weight is the most critical factor in any design Dimension of the satellite : dia must be less than 3.5m

Antennas are the limiting factor

### Factors influencing system design

Weight of the satellite is driven by two factors I. The number and the output power of he transponder on the satellite (requires large power from solar cells which in turn increases the weight ) II. Weight of the station keeping fuel

### Factors influencing system design

• • • The choice of frequency band Atmospheric propagation effects Multiple access techniques

### Performance objective

• • Bit error rate (BER) in a digital link Signal-to-noise ratio (S/N) in an analog link

Measured in base band channel

• BER or S/N is determined by Carrier - to- noise ration (C/N) at the input of the demodulator in the receiver • C/N > 6 dB

### Basic transmission theory

Objective : Calculation of the power received by an earth station from satellite transmitter Two approaches for calculating : i. Use of flux density ii. Link equation (Friis transmission equation )

• • • Consider an Isotropic Source radiating Pt Watts uniformly into free space.

At distance R, the area of the spherical shell with center at the source is 4 p

R 2

Flux density at distance R is given by

F

P t

4 p

R

2 W/m 2 Equ 4.1

Isotropic Source

Distance R Pt Watts

Surface Area of sphere =

4

p

R 2

encloses Pt.

Power Flux Density:

F

P t

4 p

R

2 W/m 2

### Antenna Gain

• • We need directive antennas to get power to go in wanted direction.

Defined as the ratio of power per unit solid angle radiated in a 

G

(  ) 

P

0

P

(  / ) 4 p • • P(  ) is variation of power with angle.

G(  ) is gain at the direction  .

• P 0 is total power transmitted.

• sphere = 4 p solid radians (Eqn 4.2)

### Antenna Gain

• • • • • Antenna has gain in every direction! Usually “Gain” denotes the maximum gain of the antenna.

The direction of maximum gain is called “boresight”.

Gain is a ratio: It is usually expressed in Decibels (dB) G [dB] = 10 log 10 (G ratio)

### Flux density

The flux density in the direction of the antenna boresight at distance R meter is

F

P t G t

4 p

R

2 W/m 2

### EIRP (Pt*Gt)

• • • • • An isotropic radiator is an antenna which radiates in all directions equally Antenna gain is relative to this standard Antennas are fundamentally passive – No additional power is generated – Gain is realized by focusing power – Similar to the difference between a lantern and a flashlight Effective Isotropic Radiated Power (EIRP) is the amount of power the transmitter would have to produce if it was radiating to all directions equally Note that EIRP may vary as a function of direction because of changes in the antenna gain vs. angle

### EIRP

Isotropic Source Pt Watts Incident flux disunity, F Receiver Received power P t Receiving antenna area , A gain G t R

For an ideal receiving antenna with an aperture area of Am 2 , P r = FA

### EIRP

• A antenna with physical aperture area of A r m 2 will not deliver the power • Thus the efficiency is reduced • It is descried by using effective aperture A e A e = ηA r (4.5) Where η – aperture efficiency of the antenna

t G t A e

P r = 4 p

R

2

### Fundamental of antenna theory

G r

 4 p

A

e  2 (4.7) Sub A e in (4.6) P r  

P t G t G r

  4 p

R

2

This expression is called as the Friis transmission equation

### Contd..

EIPR

 Re

ceiving antenna gain Path loss

(4.9)

In decibel term

Pr  (

EIRP

Gr

Lp

)

dBW

(4.10) Where, EIRP = 10 log 10 (P t G t )dBW Gr = 10 log 10 ( 4 p

A

e  2 ) dB Lp – path loss = 20 log 4 p

R

10 dB

### In general

Where

Pr = EIRP+G r -L p -L a -L ta -L ra dBW

(4.11) L a = attenuation in atmosphere L ta = losses associated with transmitting antenna L ra = losses associated with receiving antenna

Units

dBi dBW dBm dBHz dBK dBi/K dBW/m 2 dB\$

### Reference of dB

Reference

isotropic gain antenna 1 watt 1 milliwatt 1 Hertz 1 Kelvin isotropic gain antenna/1 Kelvin 1 watt/m 2 1 dollar

### Problem # 1

A satellite at a distance of 40,000km from a point on the earth’s surface radiates a power of 10W from an antenna with a gain of 17 dB in the direction of the observer, find the flux density at the receiving point, and the power received by an antenna at this point with an effective area 10m 2

### Problem # 2

• A satellite operates at a frequency of 11 GHz. The receiving antenna has a gain of 52.3 dB, Find the received power.