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ECE 4710: Lecture #37 1 Link Budget Analysis BER baseband performance determined by signal to noise ratio ( S / N ) at input to detector (product, envelope, etc.) How do we predict the received signal and noise power? Link Budget Analysis Predict received signal power at input to Rx »Depends on Tx output power, channel attenuation (path loss), antenna gains (wireless), etc. Predict received noise power at input to Rx »Depends on frequency, antenna field of view, etc. Predict signal + noise power at detector input in Rx »Depends on Rx gain, noise characteristics, etc. »S/N (or E b /N o ) at detector input determines BER of digital system

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ECE 4710: Lecture #37 2 Thermal Noise Noise is present in all communication systems What is thermal noise? Time-varying EM field (just like signal) »Must be time-varying to propagate »Source for all time-varying EM fields is motion of charged particles (e.g. electrons) Channel noise »Wireless: caused by random motion/vibration of electrons in atmosphere and/or outer space (sun, stars, etc). OR »Wired: caused by random motion of free electrons in conducting cable

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ECE 4710: Lecture #37 3 Thermal Noise What is thermal noise? (continued) System Noise »High gain Rx’s amplify signal AND input channel noise »Rx components add additional thermal noise because of random motion of electrons in conducting and resistive (lossy) circuit components »Noise output at baseband is function of: Input channel noise Rx amplification of input noise Additional system noise Thermal? »Motion of free electrons (and therefore noise power) physical temperature

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ECE 4710: Lecture #37 4 Thermal Noise Conductive (lossy) element with resistance R Free electrons have random motion if T > 0° K (absolute zero!) Noise voltage will appear at output terminals across R Noise equivalent circuit for physical resistor: »Noisy resistor = Noise Free Resistor + Equivalent Noise Source

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ECE 4710: Lecture #37 5 Thermal Noise PSD for thermal noise source is At room temperature and for f < 500 GHz the exponential argument is small and e x 1 + x so

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ECE 4710: Lecture #37 6 Thermal Noise For f < 500 GHz then thermal noise is white noise No frequency dependence Equal power at all frequencies white White noise approximation applicable for ALL non- lightwave communication systems »RF & microwave frequencies << 500 GHz »Largest practical wireless communication frequency is 37 GHz Atmospheric attenuation is too large to make practical wireless communication systems higher than 40 GHz Open circuit noise voltage across physical resistor is

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ECE 4710: Lecture #37 7 Noise Power How much noise power is transferred from noise source to noise load? for matched load condition, e.g.

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ECE 4710: Lecture #37 8 Noise Power Noise Power for Matched Load P a is power available at load Does NOT depend on R Does depend on: »System bandwidth : B Must restrict system BW to minimize noise power!! »Noise temperature : T Thermal source then T = physical temperature in °K resistor, cable, etc. Non-thermal source then T is NOT directly related to physical temperature atmosphere, amplifier, etc.

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ECE 4710: Lecture #37 9 Noise Power Convenient specification for non-thermal noise source is noise temperature Noise Characterization for Linear Devices Amplifiers, mixers, cables, etc. All practical devices will have internal noise sources that must be accounted for Goal is to characterize output noise power for each device Two figures of merit describe noise performance »Noise Figure F »Effective Input Noise Temperature T e

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ECE 4710: Lecture #37 10 Device Noise Model #1 Noise free linear device with power gain G a + excess noise source at output port Thermal Noise Source

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ECE 4710: Lecture #37 11 Noise Figure Noise Figure F : measure of the degradation in the S / N ratio caused by the device Device will always add its internal noise to input signal + noise Output S / N ratio will always be worse than input S/N ratio Formal definition F must be > 1 since »Ideal noise-free device has F = 1 Standard input thermal noise temperature T o = 290 K (62.3°F) adopted since F varies with T i

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ECE 4710: Lecture #37 12 Noise Figure Noise Figure Measurement Must specify input noise temperature T i = T o = 290 K »IEEE Standard Measure output noise power N o for standard T o In decibels Output Noise = Amplified Input Noise + Device Noise Amplified Input Noise Power @ Device Output

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ECE 4710: Lecture #37 13 Device Noise Model #2 Noise free linear device with power gain G a + excess noise source at input port

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ECE 4710: Lecture #37 14 Effective Temperature Effective Input Noise Temperature : T e Device specification Additional temperature required at device input to produce observed output noise »Temperature in addition to input noise temperature From device model For real device then so T e > 0 »Ideal noise-free device has T e = 0

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ECE 4710: Lecture #37 15 Noise F and T e Two figures of merit for noisy devices Noise Figure F Effective Noise Temperature T e Relationship to each other Relationship between output/input S / N ’s for any T i (not necessarily T i = T o ) Very useful formula that is not in the book

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ECE 4710: Lecture #37 16 Noise F and T e Typical F, T e, and G Values for Various Amplifiers Device T e (°K) F F (dB) G (dB) Cooled LNA 30 1.1 0.5 10-20 RF LNA 170-435 1.6-2.5 2-4 10-20 IF AMP 870-1500 4-6.3 6-8 30-40 IC OP AMP 1500-4400 6-16 8-12 10-15

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ECE 4710: Lecture #37 17 Example An RF LNA with F = 3 dB and G = 20 dB has an input noise temperature of 500 K and an input signal power of 10 pW for a RC filtered ( r = 0.5 ) QPSK signal with a data rate of 10 Mbps. Determine the input and output S / N ratios.

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