# Ron Milione Ph.D. W2TAP W2TAP InformationModulatorAmplifier Ant Feedline Transmitter InformationDemodulatorPre-Amplifier Ant Feedline Receiver Filter.

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Ron Milione Ph.D. W2TAP W2TAP

InformationModulatorAmplifier Ant Feedline Transmitter InformationDemodulatorPre-Amplifier Ant Feedline Receiver 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/d 2 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 P t = power of transmitter G t = gain of transmitting antenna system The isotropic radiator radiates power uniformly in all directions Effective Isotropic Radiated Power calculated by: G t = 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!

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

For Free Space (no buildings, trees, etc.) f = frequency d = distance (m) = wavelength (m) c = speed of light h b = base station antenna height (m) h m = mobile antenna height (m) a(h m ) is an adjustment factor for the type of environment and the height of the mobile. a(h m ) = 0 for urban environments with a mobile height of 1.5m. Note: Hata valid only with d in range 1000-20000, h b in range 30-200m For Urban environments, use the Hata model

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? = 3.0*10 8 m/s / 960MHz = 0.3125 meters Fraunhofer distance = 2 D 2 / = 2(0.16m) 2 /0.3125 = 0.16m What is the EIRP? Method 1: Convert power to dBm and add gain Power(dBm) = 10 log 10 (100mW / 1mW) = 20dBm EIRP = 20dBm + 2.15dB = 22.15dBm Method 2: Convert gain to linear scale and multiply Gain(linear) = 10 2.15dB/10 = 1.64 EIRP = 100mW x 1.64 = 164mW Checking work: 10 log 10 (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 log 10 (960MHz) + 20 log 10 (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 / 10 98.0dB/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(h b )) – a(h m )+ 44.9-6.55(log(h b ))(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 InformationModulatorAmplifier Ant Feedline Transmitter InformationDemodulatorPre-Amplifier Ant Feedline Receiver Filter RF Propagation 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 InformationModulatorAmplifier 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 = SNR in /SNR out (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) = 10log 10 (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.

InformationModulatorAmplifier Ant Feedline Transmitter InformationDemodulatorPre-Amplifier Ant Feedline Receiver 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 power45dBm  Filter loss(2dB)  Feedline loss(3dB)  TX Antenna gain10dBi  Path lossX  Fade Margin(5dB)  Vehicle Penetration (12dB)  RX Antenna gain3dBi  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 power28dBm Filter loss(1dB) Feedline loss(3dB) TX Antenna gain3dBi Fade Margin(5dB) Vehicle Penetration(12dB) Path LossX RX Antenna gain10dBi 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

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