## Link Budget

### PROF. MICHAEL TSAI

### 2011/9/22

### What is link budget?

•

**Accounting all losses and gains from the transmitter, the ** **medium, to the receiver.**

• Therefore the word “budget”.

•

**Generally, **

_{}

### − =

_{}

**.**

•

**There is a minimum required **

_{}

**, **

**associated with the minimum required “service quality”.**

•

**How much you can spend on the channel loss?**

• Range

•

**How much transmission power do you need?**

• Energy

•

**How much sensitivity do you need?**

• Cost

GainLoss

Transmitter

*N*

### SINGLE LINK

### The link budget – a central concept

*P*^{TX}

”POWER” [dB]

*L ** ^{f ,TX }*G

^{a ,TX}Noise reference level

Antenna Propagation gain loss Transmit Feeder

*L*^{p}

Antenna Noise

Receiver

*G** ^{a , RX }*L

^{f , RX}*C*

gain

Feeder Received

Required C/N at receiver

input This is a simple

version of the link budget.

CRITERION TO MEET:

### dB in general

When we convert a measure X into decibel scale, we always divide by a
reference value X^{ref}:

Independent of the dimension of X (and

_{ }), this value is
always dimension-

less.

The corresponding dB value is calculated as:

_{ }

### = 10 log |

_{ }

_{ }

### |

_{ }

### Power

### We usually measure power in Watt (W) and milliWatt [mW]

### The corresponding dB notations are dB and dBm

Non-dB dB

Watt:

milliWatt:

RELATION:

= 10 log |_{}

1|_{} = 10 log

= 10 log |_{}

1|_{} = 10 log

= 10 log |_{}

0.001|_{} = 10 log

+ 30

=

+ 30

GSM base station TX: 40 W = 16 dBW or 46 dBm Vacuum cleaner: 1600 W = 32 dBW or 62 dBm

### Example: Power

Sensitivity level of GSM RX: 6.3x10^{-14 }W = -132 dBW or -102 dBm
Bluetooth TX: 10 mW = -20 dBW or 10 dBm

GSM mobile TX: 1 W = 0 dBW or 30 dBm

Car engine: 100 kW = 50 dBW or 80 dBm

TV transmitter (Hörby, SVT2): 1000 kW ERP = 60 dBW or 90 dBm ERP Nuclear powerplant (Barsebäck): 1200 MW = 91 dBW or 121 dBm

ERP – Effective Radiated Power

### Amplification and attenuation

(Power) Amplification:

The amplification is already

dimension-less and can be converted directly to dB:

(Power) Attenuation:

The attenuation is already

dimension-less and can be converted directly to dB:

Note: It doesn’t matter if the power

is in mW or W.

Same result!

_{
} _{ } _{
} _{ }

! 1/#

_{ } = !_{
} ⇒ ! = _{ }

_{
} _{ } = _{
}

# ⇒ # = _{
}

_{ }

! = 10 log_{%&}! #

= 10 log_{%&}#

### Example: Amplification and attenuation

30 dB

4 dB

10 dB 10 dB

Detector Ampl. Cable Ampl. Ampl.

A B

The total amplification of the (simplified) receiver chain (between A and B) is

*G*

^{A, B }### |

^{dB }### = 30 − 4 + 10 + 10 = 46

### Noise sources

### The noise situation in a receiver depends on several noise sources

Detector Noise picked up by the antenna

Analog circuits Thermal

noise

Output signal with requirement on quality

Wanted signal

### Man-made noise

Copyright: IEEE

### Receiver noise: Equivalent noise source

### To simplify the situation, we replace all noise sources with a single equivalent noise source.

Detector

Output signal with requirement on quality

Wanted signal

C

Noise free N

Analog circuits Noise free

Same “input quality”, signal-to-noise ratio, C/N in the whole chain.

How do we determine N from the other

sources?

### Receiver noise: Noise sources (1)

The power spectral density of a noise source is usually given in one of the following three ways:

1) Directly [W/Hz]:

2) Noise temperature [Kelvin]:

3) Noise factor [1]:

*N *

^{s}*T*

^{s}*F*

^{s}The relation between the tree is

*N*

^{s }### = *kT*

^{s}### = *kF*

^{s}*T*

^{0}where k is Boltzmann’s constant (1.38 ( 10^{)*+} W/Hz) and T^{0 }is the,
so called, room temperature of 290 K (17-).

This one is sometimes given i dB and

**called noise**
**figure.**

### Receiver noise: Noise sources (2)

Antenna example

Noise temperature of antenna 1600 K

Power spectral density of antenna noise is and its noise factor/noise figure is

### .

_{/}

### = 1600 / 290 = 5.52 = 7.42 dB

Noise free antenna

N^{a}
Model

0_{/} = 1.38 ( 10^{)*+} ( 1600 = 2.21 ( 10^{)*&}3/45 = −196.6 783/45

System component Noise factor F

Model System

component Noise free

### Receiver noise: System noise

N^{sys}

Due to a definition of noise factor (in this case) as the ratio of noise
powers on the output versus on the input, when a resistor in room
temperature (T^{0}=290 K) generates the input noise, the PSD of the
equivalent noise source (placed at the input) becomes

*N*

^{sys }### = *k * ( ^{F } ^{−} ^{1} ) ^{T}

^{F }

^{T}

^{0 }

^{W/Hz}

Equivalent noise temperature Don’t use dB value!

System 1 System 2

F^{1} F^{2}

### Receiver noise: Sev. noise sources (1)

A simple example
T^{a}

*1*

*N*

^{a }### = *kT*

^{a}*N*

^{1 }### = *k * ( ^{F } ^{−} ^{1} ) ^{T}

^{F }

^{1}

^{T}

^{0}*N*

^{2 }### = *k * ( ^{F}

^{F}

^{2 }^{−} ^{1} ) ^{T}

^{1}

^{T}

^{0}Noise free

System 1

Noise

System 2

Noise

N^{2}
N^{a }N^{1}

### Receiver noise: Sev. noise sources (2)

After extraction of the noise sources from each component, we need to move them to one point.

When doing this, we must compensate for amplification and attenuation!

G Amplifier:

Attenuator:

1/L N

N

G

1/L

NG

N/L

### The isotropic antenna

The isotropic antenna radiates equally in all directions

Radiation pattern is spherical

Elevation pattern

Azimuth pattern

This is a theoretical antenna that cannot

be built.

Azimuth pattern

### λ

^{/ 2}

Feed

A dipole can be of any length, but the antenna patterns shown

are only for the λ/2-dipole. Antenna pattern of isotropic

antenna.

### The dipole antenna

Elevation pattern

### λ

^{/ 2 }

^{-dipole}

This antenna does not radiate straight up or down. Therefore, more energy is available in other directions.

THIS IS THE PRINCIPLE BEHIND WHAT IS CALLED ANTENNA GAIN.

### Antenna gain (principle)

Antenna gain is a relative measure.

We will use the isotropic antenna as the reference.

Radiation pattern

Isotropic and dipole, with equal input power!

Isotropic, with increased input power.

The amount of increase in input power to the isotropic antenna, to

obtain the same maximum radiation is called the antenna gain!

Antenna gain of the λ/2 dipole is 2.15 dB.

### A note on antenna gain

Sometimes the notation dBi is used for antenna gain (instead of dB).

The ”i” indicates that it is the gain relative to the isotropic antenna (which we will use in this course).

Another measure of antenna gain frequently encountered is dBd, which is relative to the λ/2 dipole.

*G |*

^{dBi }### = *G |*

^{dBd }### + 2.15

**Be careful! Sometimes**
it is not clear if the

antenna gain is given in dBi or dBd.

### EIRP: Effective Isotropic Radiated Power

EIRP = Transmit power (fed to the antenna) + antenna gain

Answers the questions:

How much transmit power would we need to feed an isotropic antenna to obtain the same maximum on the radiated power?

How ”strong” is our radiation in the maximal direction of the antenna?

This is the more important one, since a limit on EIRP is a limit on the radiation in

the maximal direction.

9:;

= _{<=}

!_{<=}

GainLoss

*G*^{TX |dB}*P*^{TX |dB}

### EIRP and the link budget

”POWER” [dB]

*EIRP*

9:;

= _{<=}

!_{<=}

### Path loss

Distance, d

TX RX

Received power [log scale]

∝ 1/7^{*}

∝ 1/7^{>}

_{?=} = _{<=}!_{?=}!_{<=} @
4B7

*

_{?=} = _{<=}!_{?=}!_{<=} @
4B7_{C /D}

* 7_{C /D}
7

>

### Fading margin

1. Fading channel loss is time-variant (stochastic process) 2. Sometimes received power could be smaller than desired

3. Add some extra transmission power to decrease that probability
**4. The extra transmission power **** Fading margin**

DETECTOR CHARACTERISTIC Quality OUT

Quality IN (C/N)

### Required C/N – another central concept

DETECTOR Quality IN

(C/N) Quality OUT

The detector characteristic is different for different system design choices.

REQUIRED QUALITY OUT:

Audio SNR

Perceptive audio quality Bit-error rate

Packet-error rate etc.

### Example:

### Mobile radio system

•

### Consider a mobile radio system at 900-MHz carrier frequency, and with 25-kHz bandwidth.

• It is affected only by thermal noise (temperature of the environment
E_{} = 300F).

• Antenna gains at the TX and RX sides are 8 dB and -2 dB, respectively.

• Losses in cables, combiners, etc. at the TX are 2 dB.

• The noise figure of the RX is 7 dB.

• The 3-dB bandwidth of the signal is 25 kHz.

• The required operating SNR is 18 dB and the desired range of coverage is 2 km.

• The breakpoint is at 10-m distance; beyond that point, the path loss exponent is 3.8.

• The fading margin is 10 dB.

•

### What is the minimum TX Power?

•

### Textbook p42 (example 3.2)

### Noise and interference limited links

C

N

Distance Min C/N

Power

Max distance

C

N

Distance Power

Min C/I

I

Max distance

TX RX TX RX TX

NOISE LIMITED INTERFERENCE LIMITED

### What is required distance between BSs?

Copyright: Ericsson