Fmcw Documentation

7/28/2019 Fmcw Documentation

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Chapter 1Radar Basics

1.1 Introduction

Acronym RADAR is derived fromRadio Detection and Ranging. It is anelectromagnetic system for detection and location of objects. Radar mainly operates bytransmitting radio waves and receiving echoes from theobject. Two main constraints thatradar takes into account to detect range and velocity are echoes and the Doppler shift of thetransmitted signals.

There are many attributes that radar can detect like

Detecting target

Range of the target from the radar

The relative velocity with respect to the radar and

The direction in which the target is moving

Echo: A portion of the transmitted signal is intercepted by the target and reradiated back in the direction of the radar known as echo.

Doppler shift: Shift in the frequency of the transmitted signal according to therelative motion and velocity of the target.

If the object is coming toward you, the light is shifted toward shorter wavelengths.

If the object is going away from you, the light is shifted toward longer wavelengths.

The amount of shift is bigger if the emitting object is moving faster.

An elementary form of radar consists of a transmitting antenna emitting electromagneticradiation generated by an oscillator of some sort, a receiving antenna, and an energy-detecting device or receiver. A portion of the transmitted signal is intercepted by a reflectingobject (target) and is reradiated in all directions. It is the energy reradiated in the back

direction that is of prime interest to the radar. The receiving antenna collects the returnedenergy and delivers it to a receiver, where it is processed to detect the presence of the targetand to extract its location and relative velocity. The distance to the target is determined bymeasuring the time taken for the radar signal to travel to the target and back. The direction, or angular position, of the target may be determined from the direction of arrival of the reflectedwave-front.


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Figure 1.1 Block diagram of a generic radar system

1.1.1 Radar History

Based Radar history dates back to James Clerk Maxwell. In 1865 the English physicist developed his electromagnetic light theory. In 1887 German Physicist HeinrichHertz began experimenting with radio waves. James Clerk Maxwell predicted the existenceof electromagnetic waves but it was HeinrichHertz who first generated and detectedelectromagnetic waves experimentally.

By the 1900s a German engineer, Christian Huelsmeyer proposed the use of radioechoes to avoid collisions. He invented a device he called the telemobiloscope, whichconsisted of a simple spark gap aimed using a funnel-shaped metal antenna. When areflection was seen by the two straight antennas attached to the receiver, a bell sounded. Thesystem was very simple; it could detect shipping accurately up to about 3 km. However it wasfar away from civil and military applications.

In 1922 A. H. Taylor and L. C. Young from USA Naval Research Laboratory (NRL)located a wooden ship for the first time. During World War II (WWII) significantachievements were obtained on radars. Shortly before the outbreak of World War II severalradar stations known as Chain Home (CH) were constructed in the south of England. CH

successfully operated during Battle of Britain and German bomber aircrafts detected over seawith the aid of radars. The air raids detected earlier and interceptors guided accordingly to

prevent those raids.

1.2Types of Radar

Based on Antennas

Two types of radar are present based on the usage of antennas. They are Mono staticand bistatic. In mono static type of radar, both transmitter and receiver use same antenna asshown in figure whereas in bi static type of radars transmitter and receiver antennas areseparated.

Figure 1.2 Simple Monostatic radar configuration


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Depending on the nature and location of the source of electromagnetic radiation,which supplies information on the radar target and is called a radar signal, one can distinguishactive (or primary) radar, radar with active response (secondary radar), orpassive radar.

Based on Waveform

1. Pulse Radar 2. Continuous Wave Radar (CW radar)

1.2.1 Pulse Radar

Pulse radar transmits a relatively short burst of electromagnetic energy, after whichthe receiver is turned on to listen for the echo. The echo not only indicates that a target is

present, but the time that elapses between the transmission of the pulses and the receipt of theecho is a measure of the distance to the target. Separation of the echo signal and the

transmitted signal is made on the basis of differences in time.

Figure 1.3 Block diagram of pulse radar

1.2.2 CW Radar:

Radar transmitter may be operated continuously rather than pulsed in the case of pulsed radar if the strong transmitted signal is separated from the weak echo. A technique toseparate transmitted and received signal is to observe the change in the frequency shifts of

both signals as early said Doppler shift.

It may be either modulated or unmodulated. When modulated it can be like frequencymodulated or amplitude modulated. Using unmodulated CW radar one can only find thevelocity and not the range. It is not feasible to find the time delay between transmitted andreceived signals to measure the range in unmodulated CW technique.

So for better measurements of range one mostly go for modulated CW technique.Mostly FMCW(Frequency Modulated Continuous Wave radar) radar.


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Figure 1.4 Block diagram of CW radar


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Chapter 2FM-CW Radar

2.1 FM-CW Radar Introduction

FM-CW radars have advantages over pulsed radars such as low probability of interception. It can detect both close and long distance targets with transmitter power measured in mill watts. This feature makes FMCW attractive for use in any battery operatedsystem. The echoes received might be from stationary or moving target. The received signalis shifted in frequency called beat frequency which determines the range and velocity of thetarget. But modulated waveform, for example using saw tooth waveform, only range can be

detected but using triangular waveform we can detect velocity as well.

Conventional CW (Continuous Wave) radars only measures velocity because there isno time reference. If energy is transmitted continuously then the time interval betweentransmitted signal and received signal is not available to measure the range. If we usefrequency modulation in CW radar then it is possible to measure range as well. Because inthis case we have a time reference and can use it to measure the delay between transmittedand received signal which is proportional to range.

The simplest way to modulate the wave is to linearly increase the frequency. In other

words, the transmitted frequency will change at a constant rate. The transmitted waveformhas a time varying frequency f(t) given by

( ) (1)

Where f 0 is the initial frequency, is the Rate of Change of Frequency and T s is the Sweeptime. This is a linearly increasing frequency sweep as shown in Fig.2.1 and Fig.2.2

Figure 2.1 Saw tooth Waveform


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Figure 2.2 Time vs Frequency of Saw tooth Waveform

The frequency is f 0 at the start of the sweep and increases to f 1at the end of the sweep,after a time T scalled the sweep period. The bandwidth B is the difference between f 1and f 0.

The rate of change of frequency is given by

(2)

The phase of the waveform is calculated by

( ) ( ) ( ) (3)

The transmitted waveform travels to the target at distance R and returns after a time delay given by

(4)

where c is the velocity of light in medium. The process of generating beat frequency from thereturn signal can be visualized in Fig.2.3

Figure 2.3 Transmitted and received signals (stationary object)

Where f T(t) and f R (t) represent the transmitted and received signals respectively. Therange of target can be measured by


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Small weight and energy consumption due to absence of high circuit voltages.

Compactness, the dimensions of a radar using modern technology being determined by the dimensions of the microwave block.

2.2 Examples of usage of FMCW radar

2.2.1 Radio Altimeter

Radar altimeter is one of the early applications of FMCW radar that measures the

altitude above the terrain and being used for airplanes or spacecrafts. It provides thedistance between the plane and the ground. This type is used especially for landing in lowvisibility conditions. It is also very critical in low altitude flies and used as terrain avoidance

system.

2.2.2 Proximity Fuse

A proximity fuse is designed to detonate an explosive automatically when thedistance to target becomes smaller than a predetermined value. The proximity fuse wasinvented in the United Kingdom but developed mainly by the U.S. (with Britishcollaboration) during World War II.

2.2.3 Naval Navigational Radar

FMCW radars can be applied to navigational radars with ranges up to severalkilometers but FMCW radar is most useful at short ranges from tens to hundreds of metersthat can be used for surveillance of the sea or large river ports when vessels arrive underconditions of bad visibility. FMCW radar can be used not only to search the water surface of the port but also to measure range and relative speed of any targets within the port.

2.2.4 Vehicle Collision Avoidance Radar

Vehicle collision warning systems have been developed in response to thesubstantial traffic growth in cities. This system usually includes four radar located at front,tail and two side mirrors. The front radar is critical, it provides continuous range and relativespeed for targets and if necessary, a danger signal generated which can activate the brakesystem.

2.2.5 Measurement of Very Small Motions

A typical example of small motion measurement is the observation of vibrations of various components of machines. For such measurement, a device, which has no physicalcontact with the vibrating component, is needed. FMCW radar simply solves problem for thisapplication.


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2.2.6 Hidden Object Detection

Examples of this type of application are the detection of voids in walls, the testing of homogeneity of building materials and the verification of the presence of reinforcing bars inconcrete. In such applications, the depth of penetration is less of a problem, the mainrequirement being high resolution. In these cases, FMCW radar has considerable benefitsover pulse radars.

2.3 Basic Radar Range Equation

The radar equation relates the range of radar to the characteristics of the transmitter,receiver, antenna, target and environment. If the power of the radar transmitter is denoted byP t, and if an isotropic antenna used, then the power density of the signal at distance R will beP t/4R 2.

If the antenna is directional it will have GAIN (G) in any particular direction. Gainis simply the power density produced in a particular direction RELATIVE to the power density produced by an isotropic antenna.

Thus if the radar antenna has gain, then the power density at distance R becomesP tG/4R

2. When the signal reaches a target some of the energy is reflected back towards thetransmitter. Assume for now that the target has an area and it reflects the interceptedenergy equally in all directions.

Thus the power radiated from the target is (P tG/4R 2)*

And the power density back at the radar is (P tG/4R 2)*(/4R 2)

The radar antenna has an effective areaA e and thus the power passed on to thereceiver isP r = (P tG/4R

2)*(/4R 2)*A e. The minimum signal detectable by receiver is S min and this occurs at the maximum range R max . Thus

Smin = (P tG/4R max 2)*(/4R max 2)*A e

( )

Where P t = transmitted power, watts

G = antenna gain

Ae=antenna effective aperture, m 2

=radar cross section, m 2

Smin= minimum detectable signal, watts


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2.4 Operation of FM-CW Radar

TheFM-CW radar operates with continuous wave (CW) instead of pulse modulation.

FM-CW is a subclass of CW radars. But in addition to CW (which has only speed detection)it has range detection capability.

Doppler Effect is a well-known fact that if the observer and source of oscillation is inmotion with respect to each other, a shift occurs in the frequency. Assume the wavelength of transmitted wave is and the range from radar to object is R, then the total phase differencebetween the transmitted and the received waves is given by 4R / . In the case of relativemotion, R and ch ange with time. This change is expressed with angular frequency asfollows:

WhereV r is the radial velocity of object with respect to radar. If f 0 is the frequency of oscillation of radar then using above equation, Doppler frequency is:

In FM-CW radars the transmitted signal is frequency modulated. Hence the delayedsignal is received with a different frequency even if the target is stationary. The received andthe transmitted waves are mixed in the radar to give a mixed signal which carries informationabout speed and range of the target. Fig.2.4 shows the block diagram of a simple FM-CWradar.

Figure 2.4 Block diagram of FMCW radar


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Figure 2.5 Frequency time relation in FMCW radar. Solid curve represents transmitted

signal ; dashed curve represents echo. (a) Linear frequency modulation (b) triangular frequency modulation (c)beat frequency of (b);

Beat frequency:

At any instant in time, the transmitted and received signals are multiplied by a mixer. Sincemultiplying two sinusoidal signals together results in a sum and difference terms, after low

pass filtering, we are left with only the difference term. The frequency of this signal is given by f b, the beat frequency. When there is no Doppler shift in the signal, the beat frequency is ameasure of the targets range and f b= f r where f r is the beat frequency due only to the targets

range. If the slope of the frequency change of the transmitted signal is k then:


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f b = T . K = 2R/C .K

Range(R) = CT/2

Range Resolution (R) =CT/2

Minimum resolvable separation in time between two targets is given by

As shown in the Fig 2.5(c) beat frequency is constant except at the turn-around region. If thefrequency is modulated at a rate f m and deviation of frequency is f then the beat frequencyexcept the turn around region is:

K = = 2 f m . f

f b =

if K =

then f b= K.R

If the target is moving, there will be a Doppler frequency shift superimposed to the beatfrequency and it should be considered in the demodulation. The Doppler frequency shifts thefrequency time plot of the echo (received) signal according to relative direction of thetargets velocity. The frequency time plot of the transmitted and the echo signals for moving target is given in the below fig.

Figure 2.6 Frequency of the transmitted and echo signals with Doppler shift


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Figure 2.7 The beat frequency with Doppler shift

As shown in Fig 2.7 on one portion of the frequency modulation cycle, the beat frequency isincreased by the Doppler shift, while on the other portion it is decreased by the same amount.Therefore the beat frequency is switched between f b1= f r + f d and f b= f r - f d . For thissituation switching the frequency counter every half cycle and measuring the beat frequencyseparately as f b1and f b2is needed. The beat frequency directly related to target range, , f r isextracted by averaging the two beat frequencies that is ( f b1+f b2 )/ 2 also the Doppler frequency can be extracted by subtracting two beat frequencies that is

f d = (f b1 - f b2 )/2

2.5 Measurement of errors in FMCW radar system

The accuracy of the radar is usually of more importance at short ranges than the longranges. Errors of a few meters might not be of significance for long ranges but are importantfor short-range measurements. The theoretical accuracy with which distance can be measureddepends on the bandwidth of the transmitted signal and the ratio of signal energy to noiseenergy (SNR). In addition, measurement accuracy might be limited by such practicalrestrictions as the accuracy of the frequency-measuring device, linear frequency sweepnonlinearities, errors caused by multiple reflections and transmitter leakage, the residual pathlength error caused by circuits and transmission lines and the frequency error due to the turnaround regions of the frequency modulation.

If cycle counter, which measures the number of cycles or half cycles of the beatduring the modulation period, is used as a frequency-measuring device then the total cyclecount is a discrete number since the counter is unable to measure fractions of a cycle. Thediscreteness of the frequency measurement gives rise to an error called the fixed error, or quantization error. The average number of cycles N of the beat frequency bf in one period of the modulation cycle f m is f b /f m where the bar over f b denotes time average.


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Since output of the frequency counter N is an integer, the range will be an integral multiple of

and will give rise to quantization

Besides these non-ideal properties the FM to AM distortion is another importanteffect that is a combined effect of all the individual modules. All the modules have frequencydependent transfer characteristics which result in a AM distortion in the signal.

Range resolution:

Range resolution is the ability of a radar system to distinguish between two or moretargets on the same bearing but at different ranges. Pulse width is the primary factor in rangeresolution. A well-designed radar system, with all other factors at maximum efficiency,

should be able to distinguish targets separated by one-half the pulse width time .

Sr C 0 /2

The range resolution is a critical concept for the FMCW radars as for the other radar types. There are theoretical restrictions in the range resolution. In addition, the non-ideal

properties of the modules used in the systems negatively affects the range resolution. Thetransmitter leakage, non-linear frequency sweep, FM to AM distortion and measurementerrors are some of the critical non-ideal properties. The problems arising from these non-ideal

properties further restrict the range resolution of FMCW radars. Another important concept

for the range resolution that can be obtained from FMCW radars is the signal processingmethod.

NOISE FIGURE:

Noise figure represents the noise introduced by the devices such as amplifiers, mixersetc. Noise figure and sensitivity are closely related, and both are objective figures of merit.The output signal to noise ratio depends on two things the input signal to noise ratio and thenoise figure.


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