Course: BEng (Hons) in Electrical and Electronic Engineering

1. EEEE6490345 RF AND MICROWAVE ELECTRONICS
Radio Communication Link Budgets
FACULTY OF ENGINEERING AND COMPUTER TECHNOLOGY
BENG (HONS) IN ELECTRICALAND ELECTRONIC ENGINEERING
Ravandran Muttiah BEng (Hons) MSc MIET

2. Radio Communication Link Budgets
Link budgets refer to the calculation of received signal-to-noise ratio
given a specification of transmitted power, transmission medium
attenuation and/or gain, and all sources of noise.
The calculation is based on applying Friis formula. For radio systems the
signal energy is usually lost due radiation other than towards the
receiver.
First we must review important antenna concepts.
1

3. 2
The simplified relation between antenna gain and its effective area is,
𝐺 =
4π𝑎e
𝜆2
(1)
where 𝑎e is the effective antenna receiving area.
We focus on the gain and effective area in the direction of maximum
radiation. The feed struts, etc reduce the physical area, 𝐴ph , by an
efficiency factor, 𝜂ap and give the effective aperture, 𝐴e,
𝐴e = 𝜂ap𝐴ph m2
These aperture losses are in addition to the ohmic losses which when
applied to the effective aperture gives the antenna’s effective area,
𝑎e = 𝜂Ω𝐴e m2
Effective area is thus related to physical area by,
𝑎e = 𝜂ap𝜂Ω𝐴ph m2
Antenna Gain, Effective Area And Efficiency

4. 3
Free Space And Plane Earth Signal Budgets
For a free space radio communication link the received power density
radiated from an isotropic radiator is,
𝑊lossless isotrope =
𝑃T
4π𝑟2
Wm−2
For a transmitter with gain 𝐺T the receiver power density is,
𝑊 =
𝑃T
4π𝑟2
𝐺T Wm−2
(2)
The carrier power at the receive antenna terminals is,
𝑃R = 𝐶 = 𝑊𝑎e W
Substituting equation 2 for 𝑊, gives,
𝐶 =
𝑃T
4π𝑟2
𝐺T𝑎e W

5. 4
Using equation 1 to replace the 𝑎e term by 𝐺R,
𝐶 =
𝑃T
4π𝑟2
𝐺T𝐺R
𝜆2
4π
W = 𝑃T𝐺T𝐺R
𝜆
4π𝑟
2
= 𝑃R W (3)
where 𝐺R is the gain of the receiving antenna.
Figure 1: Free space propagation.
𝑃T
𝐺T
𝐺R
𝑎e m2
𝑟
𝐶 W
𝑊 W m−2

6. 5
This equation (3) can be rewritten as,
𝐶 = 𝑃T𝐺T
𝜆
4π𝑟
2
𝐺R 𝑊 (4)
To give the basic radio free space transmission loss formula.
𝑃T𝐺T is the Effective Isotropic Radiated Power (EIRP) and the
𝜆
4π𝑟
2
is
the Free Space Path Loss (FSPL). FSPL is a function of wavelength
because it converts the receiving antenna area to gain, as well as
incorporating the spreading loss. Equation (4) expressed in decibel,
𝐶 = EIRP − FSPL + 𝐺R dBW
where,
EIRP = 10 log10 𝑃T + 10 log10 𝐺T dBW
and
FSPL = 20 log10
4π𝑟
𝜆
dB

7. 6
Example 1:
Calculate the power density at a distance of 20 km from a microwave
antenna with a directivity of 42 dB, an ohmic efficiency of 95 % for a
4 GHz and 25 dBm transmitter.
Solution:
𝐺 = 𝜂Ω𝐷 = 10 log10 𝜂Ω + 𝐷dB dB
= 10 log10 0.95 + 42 = −0.2 + 42
= 41.8 dB
The received power is EIRP − radiation loss so,
𝑊 =
𝑃T
4π𝑟2
𝐺T = 𝑃T + 𝐺T − 10 log10 4π𝑟2
dBm
m2
= 25 + 41.8 − 10 log10 4π × 20,0002
= −30.2
dBm
m2
= −60.2
dBW
m2

8. 7
For an identical receiving antenna 20 km from transmitter, the received
carrier power, 𝐶, is calculated via,
𝜆 =
𝑐
𝑓
=
3 × 108
4 × 109
= 0.075 m
The antenna effective area,
𝑎e = 𝐺R
𝜆2
4π
= 10
41.8
10
0.075 2
4π
= 6.775 m2
𝐶 = 𝑊𝑎e = 9.52 × 10−7
× 6.775 = 6.45 × 10−6
W = −21.9 dBm

9. 8
The receiving antenna temperature, 𝑇ant is,
𝑇ant =
available NPSD at antenna terminals
Boltzmann′s constant
=
𝐺N 𝑓
𝑘
K
where 𝐺N 𝑓 is white and the NPSD is one sided.
Above 1 GHz galactic noise is relatively weak. Atmospheric and ground
noise is approximately flat with frequency up to about 10 GHz.
As elevation increases from 0°
to 90°
the thickness of atmosphere through
which the beam passes decreases as does the influence of the ground,
leading to a decrease in received thermal noise.
In the 1 − 10 GHz frequency range a zenith-pointed antenna in clear sky
may have a noise temperature close to the cosmic background temperature
of 3 K.
Above 10 GHz resonance effects (of water vapour molecules at 22 GHz
and oxygen molecules at 60 GHz) increase atmospheric attenuation and
thermal noise.
Antenna Temperature And Radio Noise Budgets

10. 9
Figure 2: Antenna sky noise temperature as a function of frequency and antenna elevation angle.
10 MHz 100 MHz 1 GHz 10 GHz 100 GHz
10
1
102
103
104
105
106
107
108
Frequency
Antenna
Temperature
(K)
Cosmic Noise
Galactic Centre
Atmospheric Absorption Noise
Galactic Pole
Antenna Angle
from Zenith
90°
80°
0°
Wet
Dry
Dry
Wet
Ambient
Temperature
(290 K)

11. 10
Example 2:
For a 10 GHz terrestrial Line-Of-Sight (LOS) link, the received antenna
signal power is −40 dBm, receiver noise figure is 5 dB and the bandwidth
is 20 MHz. Estimate the clear sky antenna terminal Carrier-to-Noise Ratio
(CNR) for an antenna ohmic efficiency of 95 % at 280 K.
Solution:
From figure 2 the aperture temperature, 𝑇A at 10 GHz for a horizontal link
is 100 K. Including the physical temperature 𝑇ph gives,
𝑇ant = 𝑇A𝜂Ω + 𝑇ph 1 − 𝜂Ω
= 100 × 0.95 + 280 1 − 0.95 = 95 + 14 = 109 K
𝑁 = 𝑘𝑇𝐵 = 1.38 × 10−23
× 109 × 20 × 106
= 3.01 × 10−14
W
The received antenna signal power is −40 dBm = −70 dBW
The clear sky antenna CNR for a received −70 dBW is,
𝐶
𝑁
= −70 − −135.2 = 65.2 dB

12. 11
The receiver noise temperature is,
𝑇e = 𝑓 − 1 290 = 10
5
10 − 1 290 = 627 K
The system noise temperature (at the antenna output),
𝑇syst in = 𝑇ant + 𝑇e = 109 + 627 = 736 K
The effective system noise power (at the antenna output),
𝑁 = 𝑘𝑇syst in𝐵 = 1.38 × 10−23
× 736 × 20 × 106
= −126.9 dBW
The effective carrier to noise ratio is thus,
𝐶
𝑁 eff
= 𝐶 − 𝑁 dB = −70 − −126.9 = 56.9 dB

13. 12
(1) Spiros Louvros, System Noise and Communications Link Budgets,
Computer and Informatics Engineering, Technological Educational
Institute, Greece, 2014.
References