ecen5633 radar theory lecture #3 20 january 2015 dr. george scheets n read 2.1 & 2.5 n problems...

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