ECE 4710: Lecture #37 1

Link Budget Analysis

BER baseband performance determined by signal to noise ratio (S/N) at input to detector (product, envelope, etc.)

How do we predict the received signal and noise power? Link Budget Analysis

Predict received signal power at input to Rx» Depends on Tx output power, channel attenuation (path loss), antenna

gains (wireless), etc.

Predict received noise power at input to Rx» Depends on frequency, antenna field of view, etc.

Predict signal + noise power at detector input in Rx» Depends on Rx gain, noise characteristics, etc.

» S/N (or Eb/No) at detector input determines BER of digital system

ECE 4710: Lecture #37 2

Thermal Noise

Noise is present in all communication systems What is thermal noise?

Time-varying EM field (just like signal)» Must be time-varying to propagate

» Source for all time-varying EM fields is motion of charged particles (e.g. electrons)

Channel noise» Wireless: caused by random motion/vibration of electrons in

atmosphere and/or outer space (sun, stars, etc).

OR» Wired: caused by random motion of free electrons in conducting

cable

ECE 4710: Lecture #37 3

Thermal Noise

What is thermal noise? (continued) System Noise

» High gain Rx’s amplify signal AND input channel noise» Rx components add additional thermal noise because of random

motion of electrons in conducting and resistive (lossy) circuit components

» Noise output at baseband is function of: Input channel noise Rx amplification of input noise Additional system noise

Thermal?» Motion of free electrons (and therefore noise power) physical

temperature

ECE 4710: Lecture #37 4

Thermal Noise

Conductive (lossy) element with resistance R Free electrons have random motion if T > 0° K (absolute

zero!) Noise voltage will appear at output terminals across R Noise equivalent circuit

for physical resistor:» Noisy resistor =

Noise Free Resistor

+ Equivalent Noise Source

ECE 4710: Lecture #37 5

Thermal Noise

PSD for thermal noise source is

At room temperature and for f < 500 GHz the exponential argument is small and ex 1 + x so

(Kelvin)resistor of re temperatuabsolute )273(

constant) s(Boltzman'J/K 1038.1

constant) s(Planck' sec-J102.6

(Ohms) resistance physical of value

1

||

2

||2)(

23

34

)(/||

CT

k

h

R

e

fhfhRf

kTfhv

P

TkRfTkfh

Tkfh

Rf vv 2 )( so 2

|| and

2

||2)(

PP

ECE 4710: Lecture #37 6

Thermal Noise

For f < 500 GHz then thermal noise is white noise No frequency dependence Equal power at all frequencies white White noise approximation applicable for ALL non-

lightwave communication systems» RF & microwave frequencies << 500 GHz» Largest practical wireless communication frequency is 37 GHz

Atmospheric attenuation is too large to make practical wireless communication systems higher than 40 GHz

Open circuit noise voltage across physical resistor is

TkRfv 2 )( P

RBTkdfRTkdffvVBB

vRMS 422)(200

2 P

ECE 4710: Lecture #37 7

Noise Power

How much noise power is transferred from noise source to noise load?

RBTkVRMS 4

RRL

LV

RBTkRBTkV

VRR

RV

RR

RV

RMS

RMSRMSL

LL

42

1

2

1

BTkR

RBTk

R

VP

L

LL

2

RRL for matched load

condition, e.g .

ECE 4710: Lecture #37 8

Noise Power

Noise Power for Matched Load Pa is power available at load Does NOT depend on R Does depend on:

» System bandwidth : B Must restrict system BW to minimize noise power!!

» Noise temperature : T Thermal source then T = physical temperature in °K

resistor, cable, etc. Non-thermal source then T is NOT directly related to physical

temperature atmosphere, amplifier, etc.

aL PBTkP

ECE 4710: Lecture #37 9

Noise Power

Convenient specification for non-thermal noise source is noise temperature

Noise Characterization for Linear Devices Amplifiers, mixers, cables, etc. All practical devices will have internal noise sources that must be

accounted for Goal is to characterize output noise power for each device Two figures of merit describe noise performance

» Noise Figure F

» Effective Input Noise Temperature Te

Bk

PTBTkP a

a so

ECE 4710: Lecture #37 10

Device Noise Model #1

Noise free linear device with power gain Ga + excess noise source at output port

BTkN ii Dio NGNN

DN

Thermal Noise

Source

ECE 4710: Lecture #37 11

Noise Figure

Noise Figure F : measure of the degradation in the S/N ratio caused by the device Device will always add its internal noise to input signal +

noise Output S/N ratio will always be worse than input S/N ratio

Formal definition

F must be > 1 since» Ideal noise-free device has F = 1

Standard input thermal noise temperature To = 290 K (62.3°F) adopted since F varies with Ti

K290

oi TTo

i

NS

NSF

oi NSNS

ECE 4710: Lecture #37 12

Noise Figure

Noise Figure Measurement

Must specify input noise temperature Ti = To = 290 K» IEEE Standard

Measure output noise power No for standard To

In decibels

i

o

i

o

oi

ii

oo

ii

o

i

NG

N

BTkG

N

NGS

BTkS

NS

NS

NS

NSF

i

o

NG

NF Output Noise = Amplified Input Noise + Device Noise

Amplified Input Noise Power @ Device Output

BTkG

NFF

o

odB log10)(log10

ECE 4710: Lecture #37 13

Device Noise Model #2

Noise free linear device with power gain Ga + excess noise source at input port

BTkN ii )( ei

To

TTBkG

GNN

BTkN eD

)( eiT TTBkN

ECE 4710: Lecture #37 14

Effective Temperature

Effective Input Noise Temperature : Te

Device specification Additional temperature required at device input to

produce observed output noise» Temperature in addition to input noise temperature

From device model

For real device then so Te > 0

» Ideal noise-free device has Te = 0

BkG

TBkGNT

TTBkGGNN

ioe

eiTo

so

)(

iio NGTBkGN

ECE 4710: Lecture #37 15

Noise F and Te

Two figures of merit for noisy devices Noise Figure F

Effective Noise Temperature Te

Relationship to each other

Relationship between output/input S/N’s for any Ti

(not necessarily Ti = To) Very useful formula

that is not in the book

29011 e

o

e T

T

TF )1(290)1( FFTT oe&

i

o

io

TTF

NSNS

)1(1

ECE 4710: Lecture #37 16

Noise F and Te

Typical F, Te, and G Values for Various Amplifiers

Device Te (°K) F F (dB) G (dB)

Cooled LNA 30 1.1 0.5 10-20

RF LNA 170-435 1.6-2.5 2-4 10-20

IF AMP 870-1500 4-6.3 6-8 30-40

IC OP AMP 1500-4400 6-16 8-12 10-15

ECE 4710: Lecture #37 17

Example

An RF LNA with F = 3 dB and G = 20 dB has an input noise temperature of 500 K and an input signal power of 10 pW for a RC filtered (r = 0.5) QPSK signal with a data rate of 10 Mbps. Determine the input and output S/N ratios.

0.5 and 4for 1.33 360 pg. 6-5 Table rM

W102.5 and MHz5.7 so / 14 BTkNBRB iiTT

dB 22.8or 192pW 0.052pW / 10 ii NS nW 1 pW10100 io SGS

dB 20.8or 7.121

500

2901101192

)1(1

110/31

i

oio T

TFNSNS