Lecture 1TCOM 7071 TCOM 707 Advanced Link Design FALL 2004 Innovation Hall 135 Thursdays 4:30 –...

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]


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


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



• 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



• 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



• 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


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


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


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)


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


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!)


Background – 4

scatterer

Short RF pulse (kW)

Received pulse (pW)t1

t2

Time delay = t2 – t1 = td


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


Chain Home – 1“Curtain Array”

Transmit Receive

Receive crossed dipoles

240´360´


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


Chain Home – 3

Here, five CH radars cover a large section

of the coast


Chain Home – 4

A-Scan display PPI display

Amplitude

Distance

Possible targets

Clutter?

Possible targets

Clutter

Movement of radar trace


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


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


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



• 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!



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


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


Time, frequency, and spectrum considerations – 4B

• The E vector may rotate – leading to another special case: Circular Polarization


This is a right hand circularly polarized

wave

E = Electric field

E




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



• 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



• 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



• 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



• 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



• 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



• 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



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)



• 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


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



• 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



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


Range Calculation – 4A

Primary radar prf = 10 kHz

Target #1, range 6 km


Time, seconds


Range Calculation – 4B

Primary radar prf = 10 kHz



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


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


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



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



• 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


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


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



• 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



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)


Radar Equation – 1

Ever expanding spheres of

flux

Isotropic antenna radiating equally in every direction



• 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



• 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



• 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



• 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



• 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


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



• 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



• 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



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



• 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



Second side lobe

Third side lobeFirst side lobe

Main lobe

Boresight direction



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



• 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


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



• 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!



• 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



• 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



• 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



• 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


Basic Pulse Radar

TX

Transmitter

RXReceiver

Switch

C

Controller

Antenna

Display unit


Basic Pulse Radar

TX

Transmitter

RXReceiver

Switch

C

Controller

Antenna

Display unit

This is the T/R cell


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


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)

Lecture 1TCOM 7071 TCOM 707 Advanced Link Design FALL 2004 Innovation Hall 135 Thursdays 4:30 –...

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Transcript of Lecture 1TCOM 7071 TCOM 707 Advanced Link Design FALL 2004 Innovation Hall 135 Thursdays 4:30 –...