Radar Cheat Sheet- 1st Exam

Eng-Sa’di Y. Tamimi

October 15, 2013

These notes can be used as helping material to prepare you to the first exam. So refer toit while you are studying, to test your understanding. Note that these notes cover most ofthe material’s parts (but do not include everything), so it cannot be used as an alternativeto the text-book.

The Radar systems material is divided into three parts as shown below:

1 Basic Concepts

This part is descriptive by its nature! In this part, you are required to define, describe,and talk about the basic Radar concepts such as:

1. What is a Radar? and how it operates?

2. What are Radar types? and their advantages?

3. What information can we extract from the Radar? (mention 3)

4. Mention some Radar applications? Explain one of them?

5. Define the following terms:

• Max unambiguous range?

• Pulse-to-pulse, Scan-to-scan correlation?

2 Mathematical Questions

Grab your calculator and think about these topics!

1. The best start is to review the basic mathematical notations, equations, and the physicalimplications of the following terms:

• Timing parameters: Pulse period(Tp), Pulse width(τp), Pulse delay time(τd), Beamtime on target(τb).

• Beam width (θb), Scan rate(θs).

• Transmitted power, Transmitted power density, Average transmitted power, Re-ceived power.

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• Antenna gain, Amplifier gain (IF and RF stages).

2. Derive the radar equation? then

• Express it in terms of SNR?

• Add other factors to make it more accurate?

• Remember you’ll need some curves when using Radar equation (fluctuating tar-gets, pulse integration, etc. . . ).

3. Illustrate the process of the threshold detection?

• Mention two types of errors?

• What effect do the threshold have on them? plot to explain.

• Calculate the threshold voltage? (see example in the appendix)

4. Illustrate effect of pulse integration:

• Calculate number of pulses that hit the target?

• Coherent vs. Non-coherent?

3 Analytical Questions

This section comes after the mathematical calculations. Make a comment on your results.

1. Is Basic radar equation pessimistic or optimistic, if compared with real world? Explain?

2. What is the relationship between these factors: (try to repeat calculation on differentvalues and compare)

• Rmax as function of PRF?

• Rmax Peak power and pulse duration?

• Rmax as function of operating frequency?

• Rmax as function of target cross section?

• Others . . .

3. Draw the block diagram of a standard Radar system?

• Trace the received signal at each stage?

• State the function of each part of the diagram: Duplexer, Matched Filter, etc ?

4. Based on what you have learned about Radar operation, how can a target (ex: drone)cheat the radar?

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4 Unsolved Examples

Example

Consider radar with transmitted power (Pt), frequency (f), and antenna gain (G). Thereceiver gain is (g), and noise figure (F ), bandwidth (B) at room temperature. If the targetwas at range of (R) and have cross section of (σ dB) Find:

1. Thermal noise floor (Pn)?

2. rms noise voltage (σn)? assume resistor = rΩ

3. Voltage threshold required to achieve mean time between false alarm of (Tfa) hours?

4. Probability of false alarm (Pfa)?

5. Probability of detection (Pd)?

6. Max range for fluctuating target of type (X)?

7. Change some parameters, then comment on the new results . . .

Example

A C-band surveillance radar has the following parameters:

Frequency 5500 MHzReceiver IF Bandwidth 2.0 MHzPulse duration 0.5 microsecondPRF 500 ppsAntenna Gain 40 dBTransmit pulse power 250 kW

1. A target is at a distance of 100 km from the radar. Determine the power flux densityat the target when the antenna points directly at it, in W/m2 and in dBW/m2.

2. The target has a backscatter RCS of 2 m2. Find the maximum received power at theinput to the radar receiver in watts and dBW.

3. The radar receiver has a system noise temperature of 800 K. Find the noise powerreferred to the receiver input in watts and in dBW.

4. The detection threshold is set 15 dB above the rms noise floor of the receiver. Find thepower level of the threshold in dBW.

5. Using your answers from parts (2) and (4) above, determine whether this target will bedetected by the radar. If the target is detected, how many decibels is the signal abovethe threshold?

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6. What is the maximum unambiguous range for this radar? What is the smallest targetRCS that can be detected at this range (i.e. where received Power Pr = thresholdlevel).

7. What is the maximum range at which a target with RCS = 5 m2 can be detected, inkm?

8. If the threshold is lowered to 12 dB, what is the maximum range for the 5m2 target?

9. What is the average RF power of the radar transmitter, in watts?

Example

A long range surveillance radar has the following specification:

Transmit pulse power 0.5 MWAntenna gain 38 dBRF frequency 2.8 GHzTransmitted pulse width 1.0 msAntenna rotation rate 10 rpmPRF 380 HzReceive system noise temperature 800 KReceiver noise bandwidth 1.0 MHz

1. Calculate the thermal noise power referred to the receiver input, in dBW.

2. Calculate the maximum range at which this radar can detect a 1m2 RCS target with asingle pulse assuming a threshold set at 14 dB above rms noise, and no losses.

3. Calculate the maximum unambiguous range for the PRF of 380 Hz.

4. Calculate the time between false alarms for this radar.

5. Calculate the 3 dB antenna beamwidth.

6. Calculate the number of hits on the target between the 3 dB points on the antennapattern as the antenna beam scans the target. Use curves to estimate the non-coherentintegration gain that can be achieved with this number of hits.

7. The radar has losses that total 10.0 dB. Using the non-coherent gain you found in part(6) above find the maximum range at which the radar can detect the 1m2 target witha 12 dB threshold.

8. The threshold setting of the radar is raised to 15.0 dB. What is the new time betweenfalse alarms?

9. What is the maximum range of the radar taking account of integration gain and losses?(Begin this calculation with your result from part (7)). Use this value in subsequentparts of this question.

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10. To resolve range ambiguity, the radar can be operated with a PRF of 650 Hz. What ismaximum range when the 650 Hz PRF is used?

11. A rainstorm is located at a distance of 50 km from the radar and causes 1 dB ofattenuation to 2.8 GHz signals. Find the maximum range of the radar under theseconditions. Dont forget that the radar signal must pass through the rain storm twice.(Use the base PRF of 380 Hz.)

12. It is suggested that the performance of the radar could be improved by slowing theantenna rotation rate to 6 rpm. Is this true? If so, find the new maximum range forthe radar in clear air conditions (no rain in the path) and a PRF of 380 Hz. What isthe disadvantage of the slower rotation rate?

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5 Radar Curves

Some of these curves might be needed in the exam, so bring them with you. (Don’t writeanything on them!)

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Figure 1: Probability of detection and function of SNR and Probability of false alarm.

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Figure 2: Comparison of detection probabilities for five different models of target fluctuationfor n=10 pulses integrated and false-alarm number nf = 108(nf = n/Pfa). Adapted fromSwerling.

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Figure 3: Additional SNR required to achieve a particular Pd, when the target cross sectionfluctuates, as compared with a nonfluctuating target; single hit, n=1.

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Figure 4: Effects of correlation between pulses on Pd; ρ = signal voltge correlation coefficient;square-law detector; Raylieh fluctuation; two pulses integration (n=2)

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