This document discusses radio frequency (RF) propagation and link budget analysis. It begins by describing the basic components of a transmission system including the transmitter, propagation path, and receiver. It then covers concepts such as free space path loss, antenna gain, effective isotropic radiated power (EIRP), and the near and far field regions. The document also presents models for calculating path loss in different environments, including the free space and Hata models. It concludes by explaining how link budget analysis can be used to determine the maximum allowable path loss between transmitter and receiver given their power levels, antenna gains, losses, and receiver sensitivity.

1. Ron Milione Ph.D.Ron Milione Ph.D.
W2TAPW2TAP

2. Information Modulator Amplifier
Ant
Feedline
Transmitter
Information Demodulator Pre-Amplifier
Ant
Feedline
Receiver
Filter
Filter
RF Propagation
This presentation concentrates
on the propagation portion

3.  As the wave propagates, the
surface area increases
 The power flux density
decreases proportional to
1/d2
• At great enough distances
from the source, a portion of
the surface appears as a
plane
• The wave may be modeled
as a plane wave
• The classic picture of an EM
wave is a single ray out of
the spherical wave

4.  Most real antennas do not
radiate spherically
 The wavefront will be
only a portion of a sphere
• The surface area of the wave
is reduced
• Power density is increased!
• The increase in power
density is expressed as
Antenna Gain
• dB increase in power along
“best” axis
• dBi = gain over isotropic
antenna
• dBd = gain over dipole
antenna
Gain in
this area

5.  Radiated power often referenced to power radiated
by an ideal antenna
ttGPEIRP =
Pt
= power of transmitter
Gt
= gain of transmitting antenna system
• The isotropic radiator radiates power uniformly in all
directions
• Effective Isotropic Radiated Power calculated by:
Gt = 0dB = 1 for isotropic antenna
This formula assumes power and gain is expressed linearly. Alternatively,
you can express power and gain in decibels and add them: EIRP = P(dB) + G(dB)
The exact same formulas and
principles apply on the
receiving side too!

6. λ
2
2D
d f =
• Large-scale (Far Field) propagation model
• Gives power where random environmental effects
have been averaged together
• Waves appear to be plane waves
• Far field applies at distances greater than the
Fraunhofer distance:
D = largest physical dimension of antenna
λ = wavelength
• Small-scale (Near Field) model applies for shorter
distances
• Power changes rapidly from one area/time to the next

7. 2
2
2
2
)4()4(
)(
c
fdd
P
P
linlossFree
r
t π
λ
π
===
For Free Space (no buildings, trees, etc.)
dBdf
c
fd
dBlossFree 56.147log20log20
4
log10)( 1010
2
10 −+=





=
π
f = frequency
d = distance (m)
λ= wavelength (m)
c = speed of light
hb
= base station antenna height (m)
hm
= mobile antenna height (m)
a(hm
) is an adjustment factor for the type of environment and the
height of the mobile.
a(hm
) = 0 for urban environments with a mobile height of 1.5m.
Note: Hata valid only with d in range 1000-20000, hb in range 30-200m
)3)(loglog55.60.44(
)(log82.13)6(log16.2655.69)(
1010
1010
−−+
−−−+=
dh
hahfdBlossHata
b
mb
For Urban environments, use the Hata model

8. A transmission system transmits a signal at 960MHz with a power of 100mW using
a 16cm dipole antenna system with a gain of 2.15dB over an isotropic antenna.
At what distance can far-field metrics be used?
λ = 3.0*108
m/s / 960MHz = 0.3125 meters
Fraunhofer distance = 2 D2
/ λ = 2(0.16m)2
/0.3125 = 0.16m
What is the EIRP?
Method 1: Convert power to dBm and add gain
Power(dBm) = 10 log10 (100mW / 1mW) = 20dBm
EIRP = 20dBm + 2.15dB = 22.15dBm
Method 2: Convert gain to linear scale and multiply
Gain(linear) = 102.15dB/10
= 1.64
EIRP = 100mW x 1.64 = 164mW
Checking work: 10 log10 (164mW/1mW) = 22.15dBm

9. A transmission system transmits a signal at 960MHz with a power of 100mW
using a 16cm dipole antenna system with a gain of 2.15dB over an isotropic
antenna.
What is the power received at a distance of 2km (assuming free-space
transmission and an isotropic antenna at the receiver)?
Loss(dB) = 20 log10(960MHz) + 20 log10(2000m) – 147.56dB
= 179.6dB + 66.0dB – 147.56dB = 98.0dB
Received power(dBm) = EIRP(dB) – loss
= 22.15dBm – 98.0dB = -75.85dBm
Received power(W) = EIRP(W)/loss(linear)
= 164mW / 1098.0dB/10
= 2.6 x 10-8
mW = 2.6 x 10-11
W
Checking work: 10 -75.85dBm/10
= 2.6x 10-8
mW
What is the power received at a distance of 2km (use Hata model with base
height 30 m, mobile height 1.5 m, urban env.)?
Loss(dB) = 69.55+26.16(log(f)-6) – 13.82(log(hb)) – a(hm)+ 44.9-6.55(log(hb))(log(d)-3)
=69.55 + 78.01 – 27.79 – 0 + (35.22)(0.30)
= 130.34 dB  Received power = 22.15dBm – 130.34dB = -108.19dBm

10.  A Link Budget analysis determines if there is
enough power at the receiver to recover the
information
Information Modulator Amplifier
Ant
Feedline
Transmitter
Information Demodulator Pre-Amplifier
Ant
Feedline
Receiver
Filter
Filter
RF Propagation
Gain
Gain
Loss

11.  Begin with the power output of the transmit amplifier
 Subtract (in dB) losses due to passive components in the transmit
chain after the amplifier
 Filter loss
 Feedline loss
 Jumpers loss
 Etc.
 Add antenna gain
 dBi
 Result is EIRP
Information Modulator Amplifier
Ant
Feedline
Transmitter
Filter
RF Propagation

12. dBi12Antenna gain
dB(1.5)150 ft. at 1dB/100 footFeedline loss
dB(1)Jumper loss
dB(0.3)Filter loss
dBm4425 WattsPower Amplifier
ScaleValueComponent
dBm53Total
All values are example values

13.  The Receiver has several gains/losses
 Specific losses due to known environment around the receiver
 Vehicle/building penetration loss
 Receiver antenna gain
 Feedline loss
 Filter loss
 These gains/losses are added to the received signal strength
 The result must be greater than the receiver’s sensitivity
InformationDemodulatorPre-Amplifier
Ant
Feedline
Receiver
Filter

14.  Sensitivity describes the weakest signal power level
that the receiver is able to detect and decode
 Sensitivity is dependent on the lowest signal-to-noise ratio
at which the signal can be recovered
 Different modulation and coding schemes have different
minimum SNRs
 Range: <0 dB to 60 dB
 Sensitivity is determined by adding the required
SNR to the noise present at the receiver
 Noise Sources
 Thermal noise
 Noise introduced by the receiver’s pre-amplifier

15.  Thermal noise
 N = kTB (Watts)
 k=1.3803 x 10-23
J/K
 T = temperature in Kelvin
 B=receiver bandwidth
 Thermal noise is usually very small for reasonable
bandwidths
 Noise introduced by the receiver pre-amplifier
 Noise Factor = SNRin/SNRout (positive because
amplifiers always generate noise)
 May be expressed linearly or in dB

16.  The smaller the sensitivity, the better the receiver
 Sensitivity (W) =
kTB * NF(linear) * minimum SNR required (linear)
 Sensitivity (dBm) =
10log10(kTB*1000) + NF(dB) + minimum SNR
required (dB)

17.  Example parameters
 Signal with 200KHz bandwidth at 290K
 NF for amplifier is 1.2dB or 1.318 (linear)
 Modulation scheme requires SNR of 15dB or 31.62 (linear)
 Sensitivity = Thermal Noise + NF + Required SNR
 Thermal Noise = kTB =
(1.3803 x 10-23
J/K) (290K)(200KHz)
= 8.006 x 10-16
W = -151dBW or -121dBm
 Sensitivity (W) = (8.006 x 10-16
W )(1.318)(31.62) = 3.33 x 10-14
W
 Sensitivity (dBm) = -121dBm + 1.2dB + 15dB = -104.8dBm
 Sensitivity decreases when:
 Bandwidth increases
 Temperature increases
 Amplifier introduces more noise

18.  Transmit/propagate chain produces a received
signal has some RSS (Received Signal Strength)
 EIRP minus path loss
 For example 50dBm EIRP – 130 dBm = -80dBm
 Receiver chain adds/subtracts to this
 For example, +5dBi antenna gain, 3dB feedline/filter
loss  -78dBm signal into receiver’s amplifier
 This must be greater than the sensitivity of the
receiver
 If the receiver has sensitivity of -78dBm or lower, the
signal is successfully received.

19. Information Modulator Amplifier
Ant
Feedline
Transmitter
Information Demodulator Pre-Amplifier
Ant
Feedline
Receiver
Filter
Filter
RF Propagation
EIRP
Prop Loss
RSS
Sensitivity

20.  A Link Budget determines what maximum path loss a system can
tolerate
 Includes all factors for EIRP, path loss, fade margin, and
receiver sensitivity
 For two-way radio systems, there are two link budgets
 Base to mobile (Forward)
 Mobile to base (Reverse)
 The system link budget is limited by the smaller of these two
(usually reverse)
 Otherwise, mobiles on the margin would have only one-way
capability
 The power of the more powerful direction (usually forward) is
reduced so there is no surplus
 Saves power and reduces interference with neighbors

21.  Forward (Base to Mobile)
 Amplifier power 45dBm
 Filter loss (2dB)
 Feedline loss (3dB)
 TX Antenna gain 10dBi
 Path loss X
 Fade Margin (5dB)
 Vehicle Penetration
(12dB)
 RX Antenna gain 3dBi
 Feedline loss (3dB)
 Signal into mobile’s LNA has
strength 33dBm – path loss
 If Mobile Sensitivity is -100dBm
 Maximum Path loss = 133dB
• Reverse (Mobile to Base)
• Amplifier power 28dBm
• Filter loss (1dB)
• Feedline loss (3dB)
• TX Antenna gain 3dBi
• Fade Margin (5dB)
• Vehicle Penetration (12dB)
• Path Loss X
• RX Antenna gain 10dBi
• Feedline loss (3dB)
• Signal into base’s LNA has
strength 17dBm – path loss
• If Base Sensitivity is -105dBm
• Maximum Path loss = 122dB
Unbalanced – Forward path can tolerate 11dB more loss (distance) than reverse