lecture 1tcom 7071 tcom 707 advanced link design fall 2004 innovation hall 135 thursdays 4:30 –...
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Lecture 1 TCOM 707 1
TCOM 707Advanced Link Design
FALL 2004
Innovation Hall 135 Thursdays 4:30 – 7:10 p.m.
Dr. Jeremy Allnutt [email protected]
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Lecture 1 TCOM 707 2
General Information - 1
• Contact Information– Room: Science & Technology II, Room 269– Telephone (703) 993-3969– Email: [email protected]– Office Manager: [email protected]
• Office Hours– Mondays and Tuesdays 3:00 – 6:00 p.m.
Please, by appointment only
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Lecture 1 TCOM 707 3
General Information - 2• Course Outline
– Go to http://ece.gmu.edu/coursepages.htmor http://telecom.gmu.edu and click on Course Schedule
– Scroll down to TCOM 707
• Snow days: call (703) 993-1000
• You MUST have a Mathematical Calculator – please, simple ones only
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Lecture 1 TCOM 707 4
General Information - 3
• Homework Assignments– Feel free to work together on these, BUT– All submitted work must be your own work
• Web and other sources of information– You may use any and all resources, BUT– You must acknowledge all sources– You must enclose in quotation marks all parts copied
directly – and you must give the full source information
As a general rule, no more than 40% of any paper should be drawn directly from another source
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Lecture 1 TCOM 707 5
General Information - 4
• Exam and Homework Answers– For problems set, most marks will be given for
the solution procedure used, not the answer– So: please give as much information as you can
when answering questions: partial credit cannot be given if there is nothing to go on
– If something appears to be missing from the question set, make – and give – assumptions used to find the solution
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Lecture 1 TCOM 707 6
General Information - 7
• Class Grades
• Emphasis on overall effort and results
• Balance between HW, tests, and class project:– Homework - 10%– Tests - 30 + 30%– Project Presentation - 30%
This is the final exam
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Lecture 1 TCOM 707 7
TCOM 707 Course Plan
- Go to http://ece.gmu.edu/coursepages.htm or http://telecom.gmu.edu and click on Course Schedule; scroll down to TCOM 707
- In-Class Tests scheduled for- October 7th, 2004 – Radar systems- November 4th, 2004 – Satellite Systems
- In-Class Final exam (Project presentation)- December 16th, 2004
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Lecture 1 TCOM 707 8
TCOM 707 Lecture 1 Outline
• Introduction to Radar Systems– Background– Time, frequency, and spectrum considerations– Range calculations– Pulse repetition frequency issues– Derivation of radar equation– Radar applications
Check out “Introduction to Radar Systems”, 2nd ed., Merrill I. Skolnik,
McGraw-Hill, 2001, ISBN 0-07-290980-3
And special thanks to Dr. Tim Pratt of VT, primary author of ECE 5635
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Lecture 1 TCOM 707 9
TCOM 707 Lecture 1 Outline
• Introduction to Radar Systems– Background– Time, frequency, and spectrum considerations– Range calculations– Pulse repetition frequency issues– Derivation of radar equation– Radar applications
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Lecture 1 TCOM 707 10
Background – 1
• RADAR = Radio Detection And Ranging– Detection of targets (primary – skin reflection)– Range (time delay)– Velocity (differential time delay or Doppler)– Angle (azimuth)– Target Characteristics (echo properties)– Ground mapping (under, above, space)
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Lecture 1 TCOM 707 11
Background – 2
• Radar principles:– Transmit a very short (~ 1s) burst of radio
waves (usually at microwave frequencies)– Wait for reflected radiowaves (the “echo”) to
come back to the radar– Process the returned signal (the echo) using
radar parameters
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Lecture 1 TCOM 707 12
Background – 3
• Echo Strength– This is proportional to the Radar Cross Section
(RCS) of the target, and it tells us about the SIZE of the target in radar terms
• Delay Time– This is proportional to the range from the radar
to the target (and back!)
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Lecture 1 TCOM 707 13
Background – 4
scatterer
Short RF pulse (kW)
Received pulse (pW)t1
t2
Time delay = t2 – t1 = td
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Lecture 1 TCOM 707 14
Background – 5
• First radar was Chain Home– Primitive ‘COTS’ approach– HF (four spot frequencies, 20 to 55 MHz)– Tall transmit towers– Dipole detectors– A-Scan display
For more details, please visit http://www.radarpages.co.uk/mob/ch/chainhome.htm
Necessitated by imminence of
WW II
We’ll take a brief look
at CH
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Lecture 1 TCOM 707 15
Chain Home – 1“Curtain Array”
Transmit Receive
Receive crossed dipoles
240´360´
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Lecture 1 TCOM 707 16
Chain Home – 2
Plan view of transmit facility with a schematic of the antenna pattern
Backlobe
Forwardlobe
Transmit towers
The radar did not track – it
merely ‘floodlit’ the
area to be investigated.
Receive lobes were similar
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Lecture 1 TCOM 707 17
Chain Home – 3
Here, five CH radars cover a large section
of the coast
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Lecture 1 TCOM 707 18
Chain Home – 4
A-Scan display PPI display
Amplitude
Distance
Possible targets
Clutter?
Possible targets
Clutter
Movement of radar trace
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Lecture 1 TCOM 707 19
Background – 6
• CH and all subsequent surveillance radars are Primary Radars
• Primary Radars use skin echo to detect targets
• Most airports and controlled airspaces use both Primary and Secondary Radars
• Secondary radars relies on a cooperative target to relay information from a transponder
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Lecture 1 TCOM 707 20
Background – 7
• Secondary radars transmit an encoded signal to the target’s transponder
• The transponder replies with an encoded message with information about the airplane
• A typical transponder can be set to any of 4096 identifying codes1
• Military transponders are called IFF (Identification, Friend or Foe)
1see http:/virtualskies.arc.nasa.gov/communication/youDecide/Transponder and http://www.trvacc.org/web/training/ref/squak.asp
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Lecture 1 TCOM 707 21
TCOM 707 Lecture 1 Outline
• Introduction to Radar Systems– Background– Time, frequency, and spectrum considerations– Range calculations– Pulse repetition frequency issues– Derivation of radar equation– Radar applications
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Lecture 1 TCOM 707 22
Time, frequency, and spectrum considerations – 1
c = f , where c = velocity of light in vacuo = 3 108 m/s, f = frequency, in Hz and = wavelength, in meters
Example:What is the wavelength for a frequency of 3 GHz?
Answer:Wavelength = = c/f = (3 108)/(3 109) = 10-1
= 0.1m = 10 cm Important note on units
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Lecture 1 TCOM 707 23
Time, frequency, and spectrum considerations – 2
• Radar engineers use a wide mix of units:– Miles, yards, meters, nautical miles, knots,
hours, etc.
• Calculations are easier if a standard set of units are used
• The international standards for electrical engineers is the MKS system– meters, kilograms, seconds Do NOT mix units!
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Lecture 1 TCOM 707 24
Time, frequency, and spectrum considerations – 3
Scaling in MKS units 1,000 or 103 kilo k 1,000,000 or 106 Mega M 1,000,000,000 or 109 Giga G 1,000,000,000,000 or 1012 Tera T
1,000 (or 10-3) milli m 1,000,000 (or 10-6) micro 1,000,000,000 (or 10-9) nano n
1,000,000,000,000 (or 10-12) pico p 1,000,000,000,000,000 (or 10-15) femto
f
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Lecture 1 TCOM 707 25
Time, frequency, and spectrum considerations – 4A
• All radio waves are polarized
• The direction of the E field defines the polarization sense
Direction of travel (z-axis)
E
H
E = Electric fieldH = Magnetic field
E, H, and z-axes are mutually orthogonal
This is a linearly
polarized wave
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Lecture 1 TCOM 707 26
Time, frequency, and spectrum considerations – 4B
• The E vector may rotate – leading to another special case: Circular Polarization
Direction of travel (z-axis)
This is a right hand circularly polarized
wave
E = Electric field
E
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Lecture 1 TCOM 707 27
Time, frequency, and spectrum considerations – 5
Direction of travel (z-axis)
E
H
The E and H fields vary sinusoidally at the frequency of the wave and with distance from the source (and reflector)
This is a linearly
polarized wave
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Lecture 1 TCOM 707 28
Time, frequency, and spectrum considerations – 6
• Radio waves are reflected by smooth conducting surfaces; e.g. a metal sheet, water
• Treat reflection using ray theory, as in optics.
Normal to surface
Incident ray Reflected ray
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Lecture 1 TCOM 707 29
Time, frequency, and spectrum considerations – 7A
• Non-conductive materials allow radio waves to pass through, but ….
• If dielectric constant 1.0 (air), partial reflection will occur
Medium 1 Medium 2
Incident ray
Partially reflected ray
Partially transmitted ray
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Lecture 1 TCOM 707 30
Time, frequency, and spectrum considerations – 7B
• Can take the real part of the dielectric constant = refractive index = n
• reflection coefficient, ,can be found from the two refractive indices of media 1 and 2
= 1 - (n1 - n2)2
(n1 + n2)2
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Lecture 1 TCOM 707 31
Time, frequency, and spectrum considerations – 8
• How to measure the energy of a radio wave?– Difficult to measure volts and amps above about
100 MHz– Can measure power (watts)
• All radar calculations are carried out in Watts– but more likely in W, nW, pW, etc.;– or in dBW, dBm, etc. Preferred units for link
budget calculations
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Lecture 1 TCOM 707 32
Time, frequency, and spectrum considerations – 9
• All radio signals have a defined bandwidth
• Many definitions of bandwidth– null-to-null, 3 dB, absolute, noise, etc.
• In general, bandwidth = amount of frequency space occupied by the signal
• Some examples are– FM radio (200 kHz)– Analog TV (video + sound = 6 MHz)
Otherwise known as spectrum occupancy
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Lecture 1 TCOM 707 33
Time, frequency, and spectrum considerations – 10A
• Bandwidth (spectrum) is related to the time waveform through the Fourier transform, V(f)
• Rectangular pulse {(sin x)/(x)} spectrum
V(t)
t (s)0 T
f (Hz)
V(f)
-2/T +2/T-1/T +1/T
0
This is a “Two-sided” spectrum
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Lecture 1 TCOM 707 34
Time, frequency, and spectrum considerations – 10B
f (Hz)fc -2/T fc +2/Tfc -1/T fc +1/T
This is a “One-sided” spectrum
V(t)
t (s)0 T
Radar pulse at a carrier frequency of fc
fc
V(f)
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Lecture 1 TCOM 707 35
Time, frequency, and spectrum considerations – 11
• Radio receiver bandwidth is defined by filters (usually at IF)
• Noise bandwidth = B Hz
V(f)V(f)
0 B
f f
fcfc - B/2 fc + B/2
Ideal
Real
Baseband Passband
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Lecture 1 TCOM 707 36
TCOM 707 Lecture 1 Outline
• Introduction to Radar Systems– Background– Time, frequency, and spectrum considerations– Range calculations– Pulse repetition frequency issues– Derivation of radar equation– Radar applications
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Lecture 1 TCOM 707 37
Range Calculation - 1
• Velocity, v, = distance/time• Can assume v = 3 108 m/s = 300
m/s• Round trip distance = 150 m/s
Example: if the delay is 1,500 s, the range to the target is 225 km
• Some useful numbersTime delay = 1 s per 150 m of target rangeTime delay for a target at 1 km = 6.67 s
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Lecture 1 TCOM 707 38
Range Calculation - 2
• Range, R = (c TR)/2 (eqn. 1.1 in Skolnik)where TR is the time taken for the round trip of the pulse from the radar to the target and back again, in seconds. The factor 2 appears in the denominator because of the two-way (round- trip) propagation.
With the range in kilometers (km) or nautical miles (nmi), and TR in microseconds (s), eqn. (1.1) becomes
• R(km) = 0.15TR(s) or R(nmi) = 0.081 TR (s)
Example
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Lecture 1 TCOM 707 39
Range Calculation - 3
What is the range in kilometers and nautical miles to a target with a time delay of 27 s?
R(km) = 0.15TR(s) or R(nmi) = 0.081 TR (s) = 0.15 27 or = 0.081 27 = 4.05 km or = 2.187 nmi
This calculation is for a single pulse. Most radars send more than one pulse to provide for sample averaging and updates on target position in the required time interval for tracking resolution. Echo from a distant target can arrive
after the second pulse in the pulse train, leading to range ambiguities
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Lecture 1 TCOM 707 40
Range Calculation – 4A
Primary radar prf = 10 kHz
Target #1, range 6 km
Target #2, range 18 km
Time, seconds
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Lecture 1 TCOM 707 41
Range Calculation – 4B
Primary radar prf = 10 kHz
Target #1, range 6 km
Target #2, range 18 km
Time, seconds
Remembering Range in km = 0.15TR(s), let’s look at the A-scan
A prf of 10 kHz gives one pulse every
0.0001 s = 0.1 ms
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Lecture 1 TCOM 707 42
Range Calculation – 5
Amplitude
Time, t, in ms0 0.04 0.1 0.12 0.14
Transmit pulse Transmit pulse
Target #1 Target #1Target #2
A range of 6 km gives a delay time of 40 s and a range of 18 km gives a delay time of 120 s
Note that target #2 is so far away that the echo does not reach the radar until after the next
pulse, giving an incorrect range of 3 km
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Lecture 1 TCOM 707 43
TCOM 707 Lecture 1 Outline
• Introduction to Radar Systems– Background– Time, frequency, and spectrum considerations– Range calculations– Pulse repetition frequency issues– Derivation of radar equation– Radar applications
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Lecture 1 TCOM 707 44
Pulse Repetition Frequency Issues – 1
• Unambiguous range = Runamb=c/(2fp)where fp = the pulse repetition frequency (prf)
• NOTE:Keep the units the same! If the velocity of light is in m/s, the range will be in meters
• Example:fp = 1 kHz = 1,000 HzRunamb = c/(2fp) = (3 108)/(2 1,000)
= 1.5 105 = 150 km
Equation 1.2 in Skolnik
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Lecture 1 TCOM 707 45
Pulse Repetition Frequency Issues – 2
Example: We require an unambiguous range of at least 200 km. What is the maximum prf to meet this requirement?
Round trip time = tp = (2 range)/c seconds = (2 2 105)/(3 108) seconds
= 1.33 10-3 seconds = 1.33 ms
Thus max. prf = fp = 1/tp = 1/(1.33 10-3) = 751.8797 750 Hz Alternatively, since Runamb= c/(2fp), fp = c/(2 200 103) = (3 108)/(2 200 103) = 750 Hz
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Lecture 1 TCOM 707 46
Pulse Repetition Frequency Issues – 3
• Typical prf values– 300 Hz long range radar – 500 km max. range
(strategic defense and airport facilities)
– 8,000 Hz very short range radar – 18.75 km max. range(local defense against missiles)
– 300 – 1,700 Hz are widely used values of prf
C- and S-band radars
Ku- and Ka-band radars
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Lecture 1 TCOM 707 47
Radar Frequencies – 1Specific radiolocation
Band Nominal (radar) bands based on ITUdesignation frequency range assignments for Region 2
HF 3 – 30 MHzVHF 30 – 300 MHz 138 – 144; 216 – 225 MHzUHF 300 – 1000 MHz 420 – 450; 890 – 942 MHzL 1000 – 2000 MHz 1215 – 1400 MHzS 2000 – 4000 MHz 2300 – 2500; 2700 – 3700 MHzC 4000 – 8000 MHz 5250 – 5925 MHzX 8000 – 12,000 MHz 8500 – 10680 MHzKu 12 – 18 GHz 13.4 – 14.0; 15.7 – 17.7 GHz K 18 – 27 GHz 24.05 – 24.25 GHzKa 27 – 40 GHz 33.4 – 36.0 GHzmm 40 – 300 GHz
Table 1.1 in Skolnik
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Lecture 1 TCOM 707 48
Radar Frequencies – 2
• Low frequencies (<6 GHz)– Little rain attenuation, hence– Long(er) range, which requires– High(er) power and– Low prf– Large dead zone possible– Simpler T/R cell design– Best for large area defense
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Lecture 1 TCOM 707 49
Radar Frequencies – 3
• High frequencies (>8 GHz)– Rain attenuation becoming significant, hence– Short(er) range, which can use– Low(er) power and– High prf– Large dead zone NOT possible– More complicated T/R cell design– Best for local defense
Eased by low power needs
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Lecture 1 TCOM 707 50
Radar Frequencies – 4
Plane wavefront
launched by radar
High frequencies and elevation angles, very directive
As frequencies/ elevation angles reduce, energy forms strong ground wave and can also produce some scattered energy over the horizon (OTH)
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Lecture 1 TCOM 707 51
TCOM 551 Lecture 1 Outline
• Introduction to Radar Systems– Background– Time, frequency, and spectrum considerations– Range calculations– Pulse repetition frequency issues– Derivation of radar equation– Radar applications
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Lecture 1 TCOM 707 52
Radar Equation – 1
Ever expanding spheres of
flux
Isotropic antenna radiating equally in every direction
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Lecture 1 TCOM 707 53
Radar Equation – 2
• If the isotropic antenna has a transmit power of Pt watts, what is the flux density at any given distance, R (range), from the isotropic antenna?
• Since the isotropic antenna radiates equally in every direction, we need to find the surface area of the sphere at distance, R
• Surface area of the sphere = 4R2
Hence we can find the power flux density
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Lecture 1 TCOM 707 54
Radar Equation – 3
• The power flux density (pfd) at a distance R from the isotropic antenna is given by:
pfd = Pt / 4R2 W/m2
Example
Skolnik equation 1.3
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Lecture 1 TCOM 707 55
Radar Equation – 4
• If an isotropic antenna radiates 10 watts of power, what is the power flux density at a distance of 1 km?
• pfd = Pt / 4R2 = 10 / 4(1,000)2
= 10 / 12,566,370.62 = 0.7957747 10-6W/m2
= 0.7957747 W/m2
= 795.8 nW/m2
Note 1: keep the units correct
Note 2: this value is very small
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Lecture 1 TCOM 707 56
Radar Equation – 5
• The power flux density (pfd) at a distance R from the isotropic antenna is given by:
pfd = Pt / 4R2 W/m2
• But what if the antenna is NOT isotropic?
• A non-isotropic antenna will have a preferred direction in which more energy is transmitted
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Lecture 1 TCOM 707 57
Radar Equation – 6
• Most radar antennas are not isotropic
• Additional power in the required direction is the “gain” of the antenna over that of an isotropic antenna
• Define antenna gain, G, as
G = Flux density with Test Antenna at range R
Flux density with Isotropic Antenna at range R
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Lecture 1 TCOM 707 58
Radar Equation – 7Maximum
power in this direction
Minimum power in this
direction
360o Contour, referred to as an antenna pattern,
showing the power radiated in the given directions
0o
90o
180o
270o
The difference in power can be described
by the gain in these directions
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Lecture 1 TCOM 707 59
Radar Equation – 8
• Antennas that radiate in a preferred direction are called directional antennas
• The Gain, G() over the preferred angular range , is given by
G() = (P()) / (Po / 4)
Power transmitted per unit solid angle by the antenna
Total power transmitted by the antenna in all directions
4 is the total solid angle from the center of a sphere
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Lecture 1 TCOM 707 60
Radar Equation – 9
• There are two different measures for describing the power distribution around an antenna– The directivity of the antenna; and– The gain of the antenna (sometimes more correctly
called the power gain)
• Directivity is referenced to the mean power radiated
• Gain is referenced to an isotropic antennaThis is the more important descriptor.
We will look at how it increase the flux density
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Lecture 1 TCOM 707 61
Radar Equation – 10
Antenna Gain = GPower = Pt watts
1 m2 surface
R
Power flux density, F, for a directive antenna with gain, G, is
F = G Pt
4 R2Equation 1.4 in Skolnik
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Lecture 1 TCOM 707 62
Radar Equation – 11
• When the gain, G, of an antenna is referred to, it is usually the maximum gain that is being spoken of
• The Maximum Gain, G, is usually achieved on “Bore Sight”, i.e. on the principal axis of the antenna
• Antenna patterns are reference to 0 dB (the gain of an isotropic antenna) – most calculations are carried out in dB
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Lecture 1 TCOM 707 63
Radar Equation – 12
Second side lobe
Third side lobeFirst side lobe
Main lobe
Boresight direction
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Lecture 1 TCOM 707 64
Radar Equation – 13
Gain (dB)
-10
-20
-30
-40
-30
3 dB down from peak gain
3 dB beamwidth
Rectangular (or Cartesian) plot of the angle off bore sight
Main lobe
Side lobes
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Lecture 1 TCOM 707 65
Radar Equation – 14
• Parabolic antennas are the most common form of directive antennas in microwave communications
• The gain of a parabolic antenna is given bygain = 4A/2 = (D/)2
A = Aperture area = (radius)2 = (diameter/2)2
Therefore, 4A/2 = 4 ((diameter/2)2)/2 = 4 2D2/42 = (D/)2
Example
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Lecture 1 TCOM 707 66
Radar Equation – 15• A parabolic antenna has an aperture diameter,
D, of 2m. It will operate at 12 GHz. What is the gain, both as a ratio and dB value?
Answer: First find the wavelengthVelocity of radio wave = frequency wavelength, i.e. c = f Thus 3 108 = 12 109 , and so = 3 108 / 12 109 m = 0.025 m
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Lecture 1 TCOM 707 67
Radar Equation – 16
• Now we can find the gain from
gain = 4A/2 = (D/)2 and so the gain, G, of the parabolic antenna is
G = ( 2 / 0.025)2 = 63,165.46817 = 63,165 or, in dB, G = 10 log (63,165.46817) = 48 dB
But this is only the theoretical answer!
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Lecture 1 TCOM 707 68
Radar Equation – 17
• Antennas are never perfect
• The actual gain achieved is therefore less than the theoretical gain calculated
• The difference can be thought of as the efficiency of the antenna,
• Actual gain = Theoretical gain value is between 1 (perfect) and 0
Example
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Lecture 1 TCOM 707 69
Radar Equation – 18
• Example:The calculated gain of an antenna is 50 dB. The efficiency of the antenna is 75%. What is the real gain of the antenna?Answer:First: change 50 dB to a ratio 100,000Second: Multiply by 0.75 gain of 75,000Third: convert back to dB 48.8 dBThe real gain of the antenna is 48.8 dB
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Lecture 1 TCOM 707 70
Radar Equation – 19
• Sometimes, the real gain is calculated from a knowledge of the effective aperture
• The effective aperture of an antenna is the physical aperture , that is:
Ae = A
• This is the same “efficiency” used earlierExample
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Lecture 1 TCOM 707 71
Radar Equation – 20
• A 2m diameter antenna has an efficiency of 75%. What are the real and effective apertures?– Real aperture, A = (radius)2 = (1)2 =
= 3.14 m2
– Effective aperture = Ae = A = 3.14 = 0.75 3.14 = 2.36 m2
Derivation of Radar Equation
will be in lecture #2
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Lecture 1 TCOM 707 72
TCOM 707 Lecture 1 Outline
• Introduction to Radar Systems– Background– Time, frequency, and spectrum considerations– Range calculations– Pulse repetition frequency issues– Derivation of radar equation– Radar applications
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Lecture 1 TCOM 707 73
Basic Pulse Radar
TX
Transmitter
RXReceiver
Switch
C
Controller
Antenna
Display unit
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Lecture 1 TCOM 707 74
Basic Pulse Radar
TX
Transmitter
RXReceiver
Switch
C
Controller
Antenna
Display unit
This is the T/R cell
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Lecture 1 TCOM 707 75
Types of Radar – 1
Type ApplicationPulse (incoherent) Target detection
Range MeasurementSurveillance
Doppler (coherent) Velocity measurements
MTI Separates moving targets from clutter
Pulse Doppler Range and Velocity
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Lecture 1 TCOM 707 76
Types of Radar – 2
Type ApplicationTracking Range and Angle measurement
Fire control, Guidance
Synthetic Aperture High spatial resolutionVery rapid tracking
AEW (AWACS) Airborne pulse Doppler:separates moving targets from clutter using a moving radar(Highly complicated space-time adaptive processing)