The Friis Transmission Formulausers.cecs.anu.edu.au/~Gerard.Borg/anu/courses/... · The Friis Transmission Formula If we assume that the antennas are aligned for maximum transmission

The Friis Transmission Formula

If we assume that the antennas are aligned for maximum transmission and

reception, then in free space,

PRX =GTXAePTX

4πr2

where Ae is the receiving aperture of the receiving antenna.

Since Ae =GRXλ2

4π

PRX = GTXGRXPTX

[

λ

4πr

]2

1 ENGN6521 / ENGN4521: Embedded Wireless L#10

Antenna Noise

Random noise comes from both objects and the sky (from space): E.G. The cosmicradiation background at 3oK.

Black body radiation => it must be there at finite temperature even in a vacuum!

This noise can be picked up by antennas. In a receiver it adds to the noise of the receiverelectronics.

PSD = No = KT where K = 1.38× 10−23J/oK and T is the absolute temperatureo−Kelvin.

The noise power is

PN = kTB

Such noise picked up by the antenna leads to the definition of antenna temperature.


Link Budget: Friis transmission

Use the Friis transmission formula which applies to propagation between line of sightantennas:

PRX = GRXGTXPTXλ

(4πr)

2

where PTX and PRX are the transmit and received powers, GTX, GRX are the gains ofthe antennas at each end of the link.

Express in dBm (dB w.r.t 1 mW):

P (dBm) = 10 log10P (Watts)

.001

Express in dB with respect to 1 mW.. dBm

PRX(dBm) = PTX(dBm) + 10 log10GTX + 10 log10GRX +20 log10

(

λ

4πr

)


Link Budget: Example

Determine required parabolic dish diameter of a 4 GHz earth station antenna if

its system temperature is 100k for an S/N ratio (SNR) of 20 dB, Bw 30MHz and

satellite transponder power of 5 Watts, dish diameter 2m

Some data...

SNR = PRX − PN . Here PRX will eventually mean at the very end of the receive chain.

Radius of geosynch. orbit = 42164kms

Radius of earth = 6371kms

Elevation od Geosynch. satellite = 35793 ≈ 36000kms



Determine required parabolic dish diameter of a 4 GHz earth station antenna if

its system temperature is 100k for an SNR of 20 dB, Bw 30MHz and satellite

transponder power of 5 Watts, dish diameter 2m

Pearth(dBm) = Psat(dBm) +Gsat +Gearth +20 log10 [λ

4π(36× 106)]

SNR = Psat(dBm)− PN +Gsat +Gearth +20 log10 [λ

4π(36× 106)] = 20dB

Gearth = (−Psat + 20+ Pn)−Gsat − 20log10[λ

4π(36× 106)]

where Gsat =4πAsat

λ2 = 35.4dB and Asat = πD2sat/8 = 1.6m2 is the satellite antenna aperture

(assuming 50% aperture efficiency).



Using noise and transmitted powers (dBm)

PN = 10 log10(KTB/.001) = −104dBm

PTX = 10 log10(5/.001) = 37dBm

we obtain Gearth = 39.3dB and Aearth = Gλ2

4πewhere e = 0.5 is the aperture efficiency,

Aearth = (10Gearth/10)λ2

4πe=> Dearth =

√

4Aearth

π

and Dearth = 3.12m.


Satelllite Frequency Bands


General Satellite System Block Diagram.


Typical ground terminal


Satellite Communications Systems (cont.)

The most desired frequency band for satellite communications is 6GHz on

the uplink (Earth to satellite) and 4GHz on the downlink (satellite to earth).

Why? In this range: 1) equipment is relatively inexpensive, 2) cosmic

noise is small and 3) rainfall does not appreciably attenuate the signals

(worse for higher f ⇒ smaller wavelength of order of size of raindrops.)

Unfortunately, these bands are already allocated to terrestrial microwave

radio relay links so the power density on Earth from satellites operating in

these bands is restricted .


Satellite Communications Systems (cont.)

Also need to carefully place receivers for satellites in these bands so that

they do not receive interference signals from these microwave links.

In the 6GHz/4GHz band, satellites are assigned a spacing of 2.

Many satellite transponders do not demodulate the received signal before

retransmission. They simply amplify, down-convert (from say 6GHz to

4GHz) and then retransmit .

As technology allows, satellites will also process the incoming signals (e.g.

filter noise, reshape pulses) before retransmission. Will result in better

BER.


Noise in Electronics - Johnson / Nyquist / thermal

Exists everywhere - even in a vacuum - The noise produced by thermal

equilibrium (as in Physics)

Noise power

Power(Watts) = kB T(oK) B(Hz)

where kB = 1.38× 10−23J/oK (Boltzmann’s constant)

Convert to dBm

P(dBm) = 10 log10kBTB

0.001

At T = 300oK and B = 7MHz(TV), P = −105dBm

Thermal noise power increases with bandwidth


Noise in Electronics - Shot or Schottky noise

Arises from the discrete nature of charge carriers

Noise curremt (r.m.s.)

I2shot = 2qIdcB

where q = 1.6022× 10−19Coulomb (electronic charge)

Convert to power

Pshot = 10 log102RqIdcB

0.001

R = 50Ω, Idc = 1mA, Pshot = −100dBm.


Man Made Noise


Noise Performance of Amplifiers

When a signal of SNR, SNRi, with noise power Ni enters an amplifier

(any electronic device with gain) and exits with a new SNR, SNRo with

noise power No then we define the Noise Factor (F) of the network as,

F =SNRi

SNRo

Notice that SNRi is always > SNRo.

The Noise Figure is defined as,

NF = 10log10(F)

If the noise is only amplified then the NF is 0. In practice of course

amplifiers make things worse.


The Noise Performance of Cascaded Amplifiers

The noise factor of cascaded amplifiers is given by,

FTOT = F1 +F2 − 1

G1+

F3 − 1

G1G2+ ...

where Gk are the power gains of the various amplifiers and Fk are the

noise factors

............

F1,G1 F2,G2 F3,G3 Fk,Gk

Provided that the amplifier gains are much larger than unity, the noise

factor (and therefore the noise figure) of a receiver chain is dominated by

that of the first amplifier.


Noise Performance of Lossy Networks

If noise enters a lossy circuit then the NF is equal to the insertion loss (IL)

of the circuit.

NF = IL(dB)

Insertion Loss (IL) refers to that fraction of the signal power which is

dissipated in the network.

Insertion Loss (IL) is another name for the (power) transfer function


Example Noise Power Calculation.

Consider the following receiver chain which is typical of that in a wireless

receiver.

The noise figure of the mixer and filter (both passive devices with the given

insertion losses) is 11dB.

Find the overall noise figure of the receiver


Example Noise Power Calculation. (Contd)

The noise factor of the amplifier is 2 (=103/10).

The noise figure of the mixer and filter is 11 dB and so the noise factor is

12.6 (=1011/10). Thus,

FTOT = F1 +F2 − 1

G1= 2+ (12.6− 1)/10 = 3.16.

Finally we obtain

NF = 10log10(3.16) = 5dB.


Receiver Noise Calculations

The thermal noise added to a signal when passing through a system is

given by,

No = kBTB

In dBm

No = 10log10kBTB

1× 10−3

If No and the NF are known, then the required input signal level for a given

output SNR can be calculated,

Si = NF +No + SNRo


Receiver Noise Calculations (Example)

In the above example compute the required input signal level for a 10 dB

output SNR and a 1.25 MHz bandwidth.

No = 10log10(1.38× 10−23)(293)(1.25 × 106)

1.× 10−3= −113dBm

Therefore

Si = NF +No + SNRo = 5dB − 113dBm+10dBm = −98dBm

Notice that Johnson noise was assumed as the baseline input noise to the

receiver. This is rarely the case in practice





Dealing with Noise

In telecommunications the effects of noise are mitigated by the choice of receivercomponents that have a low NF. That is: NF is the parameter to look for in activecomponent datasheets. Because it is that first amplifier in the receiver chain whichdetermines the noise figure, it is usually chosen to be a Low Noise Amplifier (LNA)(≪ 10dB NF).

To determine the sensitivity of a receiver in a particular application, one needs tomeasure the input noise from the antenna in situ and this will depend on thequietness of the site where the receiver is located. Site test .


How to Measure Noise in Radio Receivers: SINAD (Signal to Noise And Distortion)

The method of measuring noise in arbitrary loads (e.g. antennas) and FM

receivers

Load

under

test

Coupler

1 kHz FM Modulated

carrier at RF frequency

FM Detector

I Khz

Notch filter

N(t) N(t) + W(t)

W(t)Audio amp

with AGC

RMS Volta meter

Galvanometer

set for 12 dB SINAD


Spectrum Analyser Revision

LO Sweep generator is mixed with incoming signal

IF signal is passed through two filters.

IF filter : Resolution Bandwidth.

DC filter : Video Bandwidth.

Thus be wary when measuring the phase noise with a spectrum analyser.


Transfer Function, Insertion Loss (Conversion Loss) and Attenuation.

The Transfer function of a four port network is the ratio of its output voltage Vo whenterminated (in Zo) to that when the network is replace by Zo.

Transfer function must be unity if the network is lossless.

Insertion loss is the same as the transfer function.

Attenuation only includes the loss from input to the output in terms of the voltage.

Transfer Function =2Vo

Zo

Attenuation =Vo

Vi

Transfer Function = Attenuation× (1 + ρ)

ρ =Zi − Zo

Zi + Zo


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The Friis Transmission Formulausers.cecs.anu.edu.au/~Gerard.Borg/anu/courses/... · The Friis Transmission Formula If we assume that the antennas are aligned for maximum transmission