ecen5633 radar theory lecture #3 20 january 2015 dr. george scheets n read 2.1 & 2.5 n problems...
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ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #3 20 January 2015Lecture #3 20 January 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633
ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #3 20 January 2015Lecture #3 20 January 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633
Read 2.1 & 2.5Read 2.1 & 2.5 Problems 1.11, 14, & 16Problems 1.11, 14, & 16 Quiz #1Quiz #1
Live: 29 January Live: 29 January DL DL << 5 February 5 February
ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #4 22 January 2015Lecture #4 22 January 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633
ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #4 22 January 2015Lecture #4 22 January 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633
Read 2.8 & 2.9Read 2.8 & 2.9 Problems 2.1, 3, & 5Problems 2.1, 3, & 5 Quiz #1Quiz #1
Live: 29 January Live: 29 January DL DL << 5 February 5 February
Last TimeLast Time
Doppler ShiftDoppler Shift x(at) ↔ X(f/a)/|a|x(at) ↔ X(f/a)/|a|
Transmitting Frequency = f1?Transmitting Frequency = f1?Received Frequency = f1(1 Received Frequency = f1(1 ++ 2v 2vrr/c)/c)
> f1 if target approaching > f1 if target approaching
Frequency Shift = Frequency Shift = ++ 2v 2vrr / /λλ
Free Space EquationsFree Space Equations RF Link EquationRF Link Equation
PPrr = P = Ptt*G*Gtt*G*Grr**λλ22/(4/(4ππd)d)22
Radar EquationRadar Equation PPrr = = σσ*P*Ptt*G*G22
antant**λλ22/[(4/[(4ππ))33dd44]]
If PIf Ptt = peak power, P = peak power, Prr does also does also
If PIf Ptt = average power, P = average power, Prr does also does also
Free Space EquationsFree Space Equations Provide Provide estimatesestimates of the power delivered of the power delivered
to the to the outputoutput of receiving antenna… of receiving antenna… ……provided that provided that Polarization is correctPolarization is correct
XMTR \ RCVR Horizontal Vertical Right Circular
Left Circular
Horizontal 1.0 0.0 About 1/2 About 1/2
Vertical 0.0 1.0 About 1/2 About 1/2
Right Circular About 1/2 About 1/2 1.0 0.0
Left Circular About 1/2 About 1/2 0.0 1.0
Change in Pr
Antenna RCSAntenna RCS
Horizontally Polarized EM →Horizontally Polarized EM →Vertically Polarized AntennaVertically Polarized Antenna
It's all reradiated.It's all reradiated. Horizontally Polarized EM →Horizontally Polarized EM →
Horizontally Polarized Horizontally Polarized AntennaAntennaSome is reradiated.Some is reradiated.
Antennas can have a high RCSAntennas can have a high RCS
F-22 RaptorF-22 Raptor
Pulse Radar Range Ambiguity & Resolution
Pulse Radar Range Ambiguity & Resolution
Want RTT Want RTT << T – Tp T – Tp T = 1/PRFT = 1/PRF Tp = Pulse WidthTp = Pulse Width If RTT > T - Tp, reported range is too smallIf RTT > T - Tp, reported range is too small
Two targets distance d apart, where 2d/c < Tp?Two targets distance d apart, where 2d/c < Tp? Returned echoes will overlap in timeReturned echoes will overlap in time Can't resolve targetsCan't resolve targets
MultipathMultipath
Multipath (20 m antenna height)Multipath (20 m antenna height)
Radar Radiation PatterRadar Radiation Patter
source: Communication and Radar Systems, by Nicolaos Tzannes
Ludwig BoltzmannLudwig Boltzmann Austrian PhysicistAustrian Physicist Born 1844Born 1844 Died 1906Died 1906 Statistical MechanicsStatistical Mechanics
How atomic properties How atomic properties (mass, charge, etc.) affect(mass, charge, etc.) affectphysical propertiesphysical properties
k = 1.381(10 k = 1.381(10 -23-23) watts/(Hz*K)) watts/(Hz*K) Relates energy with temperatureRelates energy with temperature source: Wikipedia
Noise Temp depends on GDNoise Temp depends on GD
What Main Lobe is What Main Lobe is pointing at is pointing at is important!important! Side Lobe gains are Side Lobe gains are
16 dB down = 1016 dB down = 101.6 1.6
= 39.81 times weaker = 39.81 times weaker
Miteq LNAMiteq LNA
JS3-18002200-15-10PJS3-18002200-15-10P Gain 26 dB minimumGain 26 dB minimum
10102.62.6 = 398.1 = 398.1 Noise Temp = 122Noise Temp = 122o o KK
Source: www.miteq.com
Free Space EquationsFree Space Equations RF Link EquationRF Link Equation
PPrr = P = Ptt*G*Gtt*G*Grr**λλ22/[(4/[(4ππd)d)22LLoo]]
Radar EquationRadar Equation PPrr = = σσ*P*Ptt*G*G22
antant**λλ22/[(4/[(4ππ))33dd44LLoo]]
LLo o = All other losses= All other losses polarization, impedance mismatches, rain, etc.polarization, impedance mismatches, rain, etc.
MultipathMultipath May cause actual PMay cause actual Prr to deviate from calculated to deviate from calculated
Thermal NoiseThermal Noise Good Power Spectrum ModelsGood Power Spectrum Models
White NoiseWhite Noise Band limited White Noise Band limited White Noise
Gaussian Distributed voltagesGaussian Distributed voltages Zero MeanZero Mean
Scope snapshot would look like this.
Discrete TimeWhite Noise Waveforms
(255 point Gaussian Noise)Thermal Noise is Gaussian Distributed.
Discrete TimeWhite Noise Waveforms
(255 point Gaussian Noise)Thermal Noise is Gaussian Distributed.
Time
Volts
0
15 bin Histogram(255 points of Gaussian Noise)15 bin Histogram(255 points of Gaussian Noise)
Volts
BinCount
15 bin Histogram(2500 points of Gaussian Noise)15 bin Histogram(2500 points of Gaussian Noise)
Volts
BinCount
0
400
Carl Frederich GaussCarl Frederich Gauss
German Mathematician & PhysicistGerman Mathematician & Physicist Born 1777Born 1777 Died 1855Died 1855 Ranks as one of history'sRanks as one of history's
greatest Mathematiciansgreatest Mathematicians Normal PDF's namedNormal PDF's named
after himafter him
source: Wikipedia
Noise Model for any DeviceNoise Model for any Device
Sin
&Nin
GSin
&G(Nin + Nd)
G
Nd = kToWn
+
+
G = 1/L
Active Device? Get To off spec sheet.Passive Device? To = (L-1)To
physical
Noise BandwidthNoise Bandwidth Low PassLow Pass
Given Transfer Function H(f)Given Transfer Function H(f) Find Power Transfer Function |H(f)|Find Power Transfer Function |H(f)|22 = H(f)H = H(f)H**(f)(f) Find area under |H(f)|Find area under |H(f)|22
Call this Area1 Call this Area1
Note |H(0)|Note |H(0)|22 Take an ideal filter… Take an ideal filter…
… … with same height |H(0)|with same height |H(0)|2 2 as actual filter…as actual filter… … … adjust max frequency 'til ideal filter has area = Area1adjust max frequency 'til ideal filter has area = Area1 Max frequency value of ideal filter = WnMax frequency value of ideal filter = Wn
Noise BandwidthNoise Bandwidth Band PassBand Pass
Given Transfer Function H(f)Given Transfer Function H(f) Find Power Transfer Function |H(f)|Find Power Transfer Function |H(f)|22 = H(f)H = H(f)H**(f)(f) Find area under |H(f)|Find area under |H(f)|22
Call this Area1 Call this Area1
Note |H(fNote |H(fcc)|)|22
Take an ideal band pass filter…Take an ideal band pass filter… … … centered at fcentered at fcc Hz… Hz…
… … with same height |H(fwith same height |H(fcc)|)|2 2 as actual filter…as actual filter… … … adjust width 'til ideal filter has area = Area1adjust width 'til ideal filter has area = Area1 Positive frequency width of ideal filter = WnPositive frequency width of ideal filter = Wn