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

Information Modulator Amplifier

Ant

Feedline

Transmitter

Information Demodulator Pre-Amplifier

Ant

Feedline

Receiver

Filter

Filter

RF Propagation

This presentation concentrates on the propagation portion

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

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

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 andprinciples apply on the receiving side too!

22Dd 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

= wavelength

• Small-scale (Near Field) model applies for shorter distances

• Power changes rapidly from one area/time to the next

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2

2 )4()4()(

c

fdd

P

PlinlossFree

r

t

For Free Space (no buildings, trees, etc.)

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fddBlossFree 56.147log20log20

4log10)( 1010

2

10

f = frequencyd = distance (m)= 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

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dh

hahfdBlossHata

b

mb

For Urban environments, use the Hata model

A transmission system transmits a signal at 960MHz with a power of 100mW usinga 16cm dipole antenna system with a gain of 2.15dB over an isotropic antenna.At what distance can far-field metrics be used?

= 3.0*108 m/s / 960MHz = 0.3125 meters

Fraunhofer distance = 2 D2/ = 2(0.16m)2/0.3125 = 0.16m

What is the EIRP?

Method 1: Convert power to dBm and add gainPower(dBm) = 10 log10 (100mW / 1mW) = 20dBmEIRP = 20dBm + 2.15dB = 22.15dBm

Method 2: Convert gain to linear scale and multiplyGain(linear) = 102.15dB/10 = 1.64EIRP = 100mW x 1.64 = 164mW

Checking work: 10 log10 (164mW/1mW) = 22.15dBm

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 = -75.85dBmReceived 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

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

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

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

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

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

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

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)

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

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.

Information Modulator Amplifier

Ant

Feedline

Transmitter

Information Demodulator Pre-Amplifier

Ant

Feedline

Receiver

Filter

Filter

RF Propagation

EIRP

Prop Loss

RSS

Sensitivity

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

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