The Friis Transmission Formula
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1 The Friis Transmission Formula If we assume that the antennas are aligned for maximum transmission and reception, then in free space, P RX = G TXA e P TX 4πr 2 where A e is the receiving aperture of the receiving antenna. Since A e = G RXλ 2 4π [ ] λ 2 P RX = G TX G RX P TX 4πr 1 ENGN6521 / ENGN4521: Embedded Wireless L#10
2 Antenna Noise Random noise comes from both objects and the sky (from space): E.G. The cosmic radiation background at 3 o K. Black body radiation => it must be there at finite temperature even in a vacuum! This noise can be picked up by antennas. In a receiver it adds to the noise of the receiver electronics. PSD = N o = KT where K = J/ o K and T is the absolute temperature o Kelvin. The noise power is P N = ktb Such noise picked up by the antenna leads to the definition of antenna temperature. 2 ENGN6521 / ENGN4521: Embedded Wireless L#10
3 Link Budget: Friis transmission Use the Friis transmission formula which applies to propagation between line of sight antennas: λ P RX = G RX G TX P TX (4πr) where P TX and P RX are the transmit and received powers, G TX,G RX are the gains of the antennas at each end of the link. 2 Express in dbm (db w.r.t 1 mw): P(dBm) = 10log 10 P(Watts).001 Express in db with respect to 1 mw.. dbm ( ) λ P RX (dbm) = P TX (dbm)+10log 10 G TX +10log 10 G RX +20log 10 4πr 3 ENGN6521 / ENGN4521: Embedded Wireless L#10
4 Link Budget: Example Determine required parabolic dish diameter of a 4 GHz earth station antenna if its system temperature is 100k for an S/N ratio (SNR) of 20 db, Bw 30MHz and satellite transponder power of 5 Watts, dish diameter 2m Some data... SNR = P RX P N. Here P RX will eventually mean at the very end of the receive chain. Radius of geosynch. orbit = 42164kms Radius of earth = 6371kms Elevation od Geosynch. satellite = kms 4 ENGN6521 / ENGN4521: Embedded Wireless L#10
5 Link Budget: Example Determine required parabolic dish diameter of a 4 GHz earth station antenna if its system temperature is 100k for an SNR of 20 db, Bw 30MHz and satellite transponder power of 5 Watts, dish diameter 2m λ P earth (dbm) = P sat (dbm)+g sat +G earth +20log 10 [ 4π( ) ] λ SNR = P sat (dbm) P N +G sat +G earth +20log 10 [ 4π( ) ] = 20dB λ G earth = ( P sat +20+P n ) G sat 20log 10 [ 4π( ) ] where G sat = 4πA sat = 35.4dB and A λ 2 sat = πdsat 2 /8 = 1.6m2 is the satellite antenna aperture (assuming 50% aperture efficiency). 5 ENGN6521 / ENGN4521: Embedded Wireless L#10
6 Link Budget: Example Using noise and transmitted powers (dbm) P N = 10log 10 (KTB/.001) = 104dBm P TX = 10log 10 (5/.001) = 37dBm we obtain G earth = 39.3dB and A earth = Gλ2 4πe where e = 0.5 is the aperture efficiency, and D earth = 3.12m. A earth = (10 G earth/10 ) λ2 4πe => D earth = 4Aearth π 6 ENGN6521 / ENGN4521: Embedded Wireless L#10
7 Satelllite Frequency Bands 7 ENGN6521 / ENGN4521: Embedded Wireless L#10
8 General Satellite System Block Diagram. 8 ENGN6521 / ENGN4521: Embedded Wireless L#10
9 Typical ground terminal 9 ENGN6521 / ENGN4521: Embedded Wireless L#10
10 Satellite Communications Systems (cont.) The most desired frequency band for satellite communications is 6GHz on the uplink (Earth to satellite) and 4GHz on the downlink (satellite to earth). Why? In this range: 1) equipment is relatively inexpensive, 2) cosmic noise is small and 3) rainfall does not appreciably attenuate the signals (worse for higher f smaller wavelength of order of size of raindrops.) Unfortunately, these bands are already allocated to terrestrial microwave radio relay links so the power density on Earth from satellites operating in these bands is restricted. 10 ENGN6521 / ENGN4521: Embedded Wireless L#10
11 Satellite Communications Systems (cont.) Also need to carefully place receivers for satellites in these bands so that they do not receive interference signals from these microwave links. In the 6GHz/4GHz band, satellites are assigned a spacing of 2. Many satellite transponders do not demodulate the received signal before retransmission. They simply amplify, down-convert (from say 6GHz to 4GHz) and then retransmit. As technology allows, satellites will also process the incoming signals (e.g. filter noise, reshape pulses) before retransmission. Will result in better BER. 11 ENGN6521 / ENGN4521: Embedded Wireless L#10
12 Noise in Electronics - Johnson / Nyquist / thermal Exists everywhere - even in a vacuum - The noise produced by thermal equilibrium (as in Physics) Noise power Power(Watts) = k B T( o K) B(Hz) where k B = J/ o K (Boltzmann s constant) Convert to dbm P(dBm) = 10log 10 k B TB At T = 300 o K and B = 7MHz(TV), P = 105dBm Thermal noise power increases with bandwidth 12 ENGN6521 / ENGN4521: Embedded Wireless L#10
13 Noise in Electronics - Shot or Schottky noise Arises from the discrete nature of charge carriers Noise curremt (r.m.s.) I 2 shot = 2qI dcb where q = Coulomb (electronic charge) Convert to power P shot = 10log 10 2RqI dc B R = 50Ω, I dc = 1mA, P shot = 100dBm. 13 ENGN6521 / ENGN4521: Embedded Wireless L#10
14 Man Made Noise 14 ENGN6521 / ENGN4521: Embedded Wireless L#10
15 Noise Performance of Amplifiers When a signal of SNR, SNR i, with noise power N i enters an amplifier (any electronic device with gain) and exits with a new SNR, SNR o with noise power N o then we define the Noise Factor (F) of the network as, F = SNR i SNR o Notice that SNR i is always > SNR o. The Noise Figure is defined as, NF = 10log 10 (F) If the noise is only amplified then the NF is 0. In practice of course amplifiers make things worse. 15 ENGN6521 / ENGN4521: Embedded Wireless L#10
16 The Noise Performance of Cascaded Amplifiers The noise factor of cascaded amplifiers is given by, F TOT = F 1 + F 2 1 G 1 + F 3 1 G 1 G where G k are the power gains of the various amplifiers and F k are the noise factors Provided that the amplifier gains are much larger than unity, the noise factor (and therefore the noise figure) of a receiver chain is dominated by that of the first amplifier.... F1,G1 F2,G2 F3,G3 Fk,Gk 16 ENGN6521 / ENGN4521: Embedded Wireless L#10
17 Noise Performance of Lossy Networks If noise enters a lossy circuit then the NF is equal to the insertion loss (IL) of the circuit. NF = IL(dB) Insertion Loss (IL) refers to that fraction of the signal power which is dissipated in the network. Insertion Loss (IL) is another name for the (power) transfer function 17 ENGN6521 / ENGN4521: Embedded Wireless L#10
18 Example Noise Power Calculation. Consider the following receiver chain which is typical of that in a wireless receiver. The noise figure of the mixer and filter (both passive devices with the given insertion losses) is 11dB. Find the overall noise figure of the receiver 18 ENGN6521 / ENGN4521: Embedded Wireless L#10
19 Example Noise Power Calculation. (Contd) The noise factor of the amplifier is 2 (=10 3/10 ). The noise figure of the mixer and filter is 11 db and so the noise factor is 12.6 (=10 11/10 ). Thus, F TOT = F 1 + F 2 1 G 1 = 2+(12.6 1)/10 = Finally we obtain NF = 10log 10 (3.16) = 5dB. 19 ENGN6521 / ENGN4521: Embedded Wireless L#10
20 Receiver Noise Calculations The thermal noise added to a signal when passing through a system is given by, In dbm N o = k B TB N o = 10log 10 k B TB If N o and the NF are known, then the required input signal level for a given output SNR can be calculated, S i = NF +N o +SNR o 20 ENGN6521 / ENGN4521: Embedded Wireless L#10
21 Receiver Noise Calculations (Example) In the above example compute the required input signal level for a 10 db output SNR and a 1.25 MHz bandwidth. N o = 10log 10 ( )(293)( ) = 113dBm Therefore S i = NF +N o +SNR o = 5dB 113dBm+10dBm = 98dBm Notice that Johnson noise was assumed as the baseline input noise to the receiver. This is rarely the case in practice 21 ENGN6521 / ENGN4521: Embedded Wireless L#10
22 22 ENGN6521 / ENGN4521: Embedded Wireless L#10
23 23 ENGN6521 / ENGN4521: Embedded Wireless L#10
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25 Dealing with Noise In telecommunications the effects of noise are mitigated by the choice of receiver components that have a low NF. That is: NF is the parameter to look for in active component datasheets. Because it is that first amplifier in the receiver chain which determines the noise figure, it is usually chosen to be a Low Noise Amplifier (LNA) ( 10dB NF). To determine the sensitivity of a receiver in a particular application, one needs to measure the input noise from the antenna in situ and this will depend on the quietness of the site where the receiver is located. Site test. 25 ENGN6521 / ENGN4521: Embedded Wireless L#10
26 How to Measure Noise in Radio Receivers: SINAD (Signal to Noise And Distortion) The method of measuring noise in arbitrary loads (e.g. antennas) and FM receivers Load under test N(t) W(t) Coupler 1 khz FM Modulated N(t) + W(t) FM Detector Audio amp with AGC carrier at RF frequency RMS Volta meter Galvanometer set for 12 db SINAD I Khz Notch filter 26 ENGN6521 / ENGN4521: Embedded Wireless L#10
27 Spectrum Analyser Revision LO Sweep generator is mixed with incoming signal IF signal is passed through two filters. IF filter : Resolution Bandwidth. DC filter : Video Bandwidth. Thus be wary when measuring the phase noise with a spectrum analyser. 27 ENGN6521 / ENGN4521: Embedded Wireless L#10
28 Transfer Function, Insertion Loss (Conversion Loss) and Attenuation. The Transfer function of a four port network is the ratio of its output voltage V o when terminated (in Z o ) to that when the network is replace by Z o. Transfer function must be unity if the network is lossless. Insertion loss is the same as the transfer function. Attenuation only includes the loss from input to the output in terms of the voltage. Transfer Function = 2V o Z o Attenuation = V o V i Transfer Function = Attenuation (1+ρ) ρ = Z i Z o Z i + Z o 28 ENGN6521 / ENGN4521: Embedded Wireless L#10
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