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Radar level measurement- The users guide

Peter Devine

© VEGA Controls / P Devine / 2000All rights reseved. No part of this book may reproduced in any way, or by any means, without priorpermissio in writing from the publisher:VEGA Controls Ltd, Kendal House, Victoria Way, Burgess Hill, West Sussex, RH 15 9NF England.

British Library Cataloguing in Publication Data

Devine, PeterRadar level measurement - The user´s guide1. Radar2. Title621.3´848

ISBN 0-9538920-0-X

Cover by LinkDesign, Schramberg.Printed in Great Britain at VIP print, Heathfield, Sussex.

written byPeter Devine

additional informationKarl Grießbaum

type setting and layoutLiz Moakes

final drawings and diagramsEvi Brucker

Foreword ixAcknowledgement xiIntroduction xiii

Part I1. History of radar 12. Physics of radar 133. Types of radar 33

1. CW-radar 332. FM - CW 363. Pulse radar 39

Part II4. Radar level measurement 47

1. FM - CW 482. PULSE radar 543. Choice of frequency 624. Accuracy 685. Power 74

5. Radar antennas 771. Horn antennas 812. Dielectric rod antennas 923. Measuring tube antennas 1014. Parabolic dish antennas 1065. Planar array antennas 108Antenna energy patterns 110

6. Installation 115A. Mechanical installation 115

1. Horn antenna (liquids) 1152. Rod antenna (liquids) 1173. General consideration (liquids) 1204. Stand pipes & measuring tubes 1275. Platic tank tops and windows 1346. Horn antenna (solids) 139

B. Radar level installation cont. 1411. safe area applications 1412. Hazardous area applications 144

Inhalt

13

The velocity of light in free space is299,792,458 metres per second, butwho is timing? For the purposes of thecalculations in this book, we will call it300,000 kilometres per second or3 x 108 metres per second.

Maxwell’s theories of electro-magnetism were confirmed by theexperiments of Heinrich Hertz. Theseshow that all forms of electromagneticradiation travel at the speed of light infree space. This applies equally to longwave radio transmissions, microwaves,infrared, visible and ultraviolet lightplus X-rays and Gamma rays.

Maxwell showed that the velocity oflight in a vacuum in free space is givenby the expression :Examples :-

The original cavity magnetron hada wavelength of 9.87 centimetres.This corresponds to a frequency of3037.4 MHz (3.0374 GHz).

The frequency of a pulse radarlevel transmitter may be 26 GHzor 26 x 108 metres per second. The wavelength is 1.15 centimetres.

The electromagnetic waves have anelectrical vector E and a magnetic vec-tor B that are perpendicular to eachother and perpendicular to the directionof the wave. This will be discussed andillustrated further in the section onpolarization. The electrical vector hasthe major influence on radar applica-tions.

2. Physics of radar

Fig 2.1

ampl

itude

λ direction of wave

Electromagnetic waves

c velocity of electromagneticwaves in metres / second

f frequency of wave in second -1

λ wavelength in metres

[Eq. 2.1]

[Eq. 2.2]

co

c

)1

=

=

(µo x εo

f x λ

The velocity of an electromagneticwave is the product of the frequencyand the wavelength.

co velocity of electromagntic wavein a vacuum in metres / second

µµo the permeability of free space (4 π x 10 -7 henry / metre)

εεo the permittivity of free space(8.854 x 10 -12 farad / metre)

14

108 107 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4

101 102 103 10

100 MHz 1 GHz 10 GHz 100 GHz

3 m 0.3 m 3 cm 3 mm

4 105 106 107 108 109 1010 1011 1012

infraradio waveselectric waves

The microwave frequencies of the electromagnetic spectrum.Radar level transmitters range between 5.8 GHz (5.2cm) and 26 GHz (11.5mm)

The Electromagnetic spectrum

15

2. Physics of radar

10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 m

1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 Hz

gamma raysX raysultra violetred

Fig 2.2 Electromagnetic spectrum.All electromagnetic waves travel at the speed of light in free space. This spectrumshows the range of frequencies and wavelengths from electric waves togamma rays

PermittivityIn electrostatics, the force between

two charges depends upon the magni-tude and separation of the charges andthe composition of the mediumbetween the charges. Permittivity ε isthe property of the medium that effectsthe magnitude of the force. The higherthe value of the permittivity, the lowerthe force between the charges. Thevalue of the permittivity of freespace (in a vacuum) εo, is calculatedindirectly and empirically to be:8.854 x 10-12 farad / metre.

Relative permittivity ordielectric constant εεr

The ratio of the permittivity of amedium to the permittivity of freespace is a dimensionless propertycalled ‘relative permittivity’ or ‘dielec-tric constant’. For example, at 20° Cthe relative permittivity of air is closeto that of a vaccum and is only about1.0005 whereas the relative permittivi-ty of water at 20° C is about 80.(Dielectric constant is also widelyknown as DK.)

The value of the dielectric constantof the product being measured is veryimportant in the application of radar tolevel measurement. In non-conductiveproducts, some of the microwave ener-gy will pass through the product andthe rest will be reflected off the surface.

This feature of microwaves can beused to advantage or, in some circum-stances, it can create a measurementproblem.

Permeability µ and relativepermeability µr

The magnetic vector, B, of an elec-tromagnetic wave also has an influenceon the velocity of electromagneticwaves. However, this influence is neg-ligible when considering the velocity ingases and vapours which are non-mag-netic. The relative permeability of theproduct being measured has no signifi-cant effect on the reflected signal whencompared with the effects of the rela-tive permittivity or dielectric constant.For the non-magnetic gases above theproduct being measured, the value ofthe relative permeability, µr = 1.

Frequency, velocity and wave-length

As we have already stated, the fre-quency (f), velocity (c) and wavelength(λ) of the electromagnetic waves arerelated by the equation c = f x λ.

The frequency remains uninfluencedby changes in the propagation medium.However, the velocity and wavelengthcan change depending on the electricalproperties of the medium in which theyare travelling. The speed of propaga-tion can be calculated using equation2.3.

16

c velocity of electromagnetic wavein the medium in metres/second

co velocity of electromagneticwaves in free space

µ r the relative permeability(µ medium / µo)

εεr the relative permittivity

[Eq. 2.3]

c)

co

=(µr x εr

2. Physics of radar

Changes in the wavelength andvelocity of microwaves are apparent incertain radar level applications.Changes in temperature, pressure andgas composition have a small effect onthe running time of microwavesbecause the dielectric constant of thepropagation medium is altered to agreater or lesser extent. This is dis-cussed in detail later.

Radar level transmitters can be usedto measure conductive liquids throughlow dielectric ‘windows’ such as glass,polypropylene and PTFE. The opti-mum thickness of the low dielectricwindow is a half wavelength or multi-ple of half wavelength.

For example, polypropylene has adielectric constant εr of 2.3 and thehalf wavelength at a frequency of 5.8GHz is 17 mm compared with a halfwavelength of about 26 mm in a vacu-um. It follows that the speed of

microwaves in polypropylene is abouttwo thirds of the speed in air.

As with low dielectric windows,non-conductive, low dielectric constantliquids may absorb more power thanthey reflect from the surface. Thevelocity of the microwaves within theliquid is slower than in the vapourspace above.

For example, if there is about 0.5metres of solvent in the bottom of ametallic vessel, a radar level transmittermay see a larger echo from the vesselbottom than from the product. Thislarge echo will appear to be furtheraway than it really is because the run-ning time within the solvent is slower.For this reason, special considerationsmust be made within the echo process-ing software to ensure that the radarfollows the solvent level and does notfollow the vessel bottom as it apparent-ly moves away!

Empty vessel: large echofrom metalbottom

As the vessel fills withsolvent two echoesare received. Theecho from the vesselbottom appearsfurther away becausethe running time ofthe microwaves insolvent is slower

Fig 2.3 - Effect of dielectric constant on the running time of a microwave radar

solvent echo

17

18

Effects on the propagationspeed of microwaves

Microwave radar level transmitterscan be applied almost universallybecause, as a measurement technique,they are virtually unaffected by processtemperature, temperature gradient, vac-uum and normal pressure variations,gas or vapour composition and move-ment of the propagation medium.

However, changes in these processconditions do cause slight variations inthe propagation speed because thedielectric constant of the propagationmedium is altered.

Calculating the propagationspeed of microwaves

The temperature, pressure and thegas composition of the vapour space allhave an effect on the dielectric constantof the propagation medium throughwhich the microwaves must travel.This in turn affects the propagationspeed or running time of the instru-ment.

The dielectric constant or relativepermittivity can be calculated asfollows :

The same effect can be experienced when looking at interface detection usingguided microwave level transmitters to detect oil and water or solvent and aqueousbased liquids.

reference echo(water without oil)

water echooil echo

εεr calculated dielectric constant(relative permittivity)

εεrN dielectric constant of gas/vapourunder normal conditions (temperature 273 K, pressure 1 barabsolute)

θN temperature under normalconditions, 273 Kelvin

PN pressure under normalconditions, 1 bar absolute

θ process temperature in Kelvin

P process pressure in bar absolute

Fig 2.4 Oil/water interfacedetection using aguided microwavelevel transmitter. Notethat the water echohas a reduced ampli-tude and appears to befurther away. Therunning time ofmicrowaves in oil isslower than in air

εr = + x1 θN x P

θ x PN

(εrN - 1)[Eq. 2.4]

2. Physics of radar

From equation 2.4 and equation 2.3,we can calculate the percentage errorcaused by variations in the dielectricconstant of different gases and vapoursand the relative effects of changes inprocess temperature and pressure.

Gases and vapoursBy definition, the dielectric constant

in a vacuum is equal to 1.0. The dielec-tric constants of the gases and vapoursthat may be present above the product

differ but they have only a very smalleffect on the accuracy of radar.

Radar level transmitters are usuallycalibrated in air. For this reason, thefollowing tables show

1. Dielectric constant of different gasesat normal temperature and pressure(273K, 1 Bar A)

2. Percent error in the running time inthe gases compared with air

Gas / VapourεεrN (dielectric

constant at normalconditions)

% Error from air (atnormal temperature

and pressure)

Vacuum 1.0000 + 0.0316Air 1.000633 0.0

Argon 1.000551 + 0.0041

Ammonia / NH 3 1.006976 + 0.3154

Hydrogen Bromide HBr 1.002994 - 0.1178Hydrogen Chloride HCl 1.004078 - 0.1717

Carbon Monoxide / CO 1.000692 - 0.00295Carbon Dioxide / C0 2 1.000985 - 0.0176

Ethane / C 2H6 1.001503 - 0.0434

Ethylene / C 2H4 1.001449 - 0.0407Helium 1.000072 + 0.0280

Hydrogen / H 2 1.000275 + 0.0179

Methane / CH 4 1.000878 - 0.0122Nitrogen / N 2 1.000576 + 0.00285

Oxygen / O 2 1.000530 + 0.0052

Table 2.1 The dielectric constants under normal conditions, εεrN and the error caused bythe dielectric constant of typical process gases under normal conditions

19

20

Temperature

Fig 2.5 Temperature effect on radar measurement of air at a constant pressure of 1 BarA

High temperature or large temperature gradients have very little effect on thetransit time of microwaves within an air or vapour space. At a temperature of2000° C the variation is only 0.026% from the measurement value at 0° C. Radarlevel transmitters with air or nitrogen gas cooling are used on molten iron and steelapplications.

Temperature in ° C

0

0.005

0.0

0.01

0.015

0.02

0.025

0.03

250 500 750 1000 1250 1500 1750 2000

% e

rror

21

2. Physics of radar

Fig 2.6 The influence of pressure on radar measurement in air at a constant temperatureof 273 K

Pressure does have a small but more significant influence on the velocity ofelectromagnetic waves. At a pressure of 30 Bar, the error is only 0.84%. Howeverthis becomes more significant and at a pressure of 100 Bar there is a velocitychange of 2.8%. If the pressure is varying constantly between atmospheric pressureand 100 Bar, the velocity variations can be compensated using a pressure transmit-ter.

Pressure

0

0

2

4

6

8

10

50 100 150 200 250 300 350 400

Pressure in Bar (absolute)

% e

rror

22

In the preceding equations, we haveassumed that the microwaves aretravelling in ‘free space’ in a vacuum.However, in practice the proximityof metallic vessel walls and otherstructures will have an influence onthe propagation velocity of themicrowaves. This is particularly truewhen microwave radar level transmit-ters are fitted inside bypass tubes orstilling tubes or when a horn antenna isfitted with a waveguide extension.

When microwaves are propagating

within a metallic tube the running timeappears to slow down because themicrowaves travel further bouncingoff the inside wall of the tube andcurrents are set up on the inside surfaceof the tube.

This effect is discussed in moredetail in the chapters on antennas andmechanical installations. The wave-guide effect can be compensated duringcalibration and the use of stilling tubesand bypass tubes can be beneficial insome level applications.

Conductive productsUsing a spark gap transmitter,

Heinrich Hertz demonstrated that elec-tromagnetic waves could be reflectedoff metallic objects and objects with arelatively high dielectric constant.

In the same way, radar can easilymeasure conductive aqueous liquidssuch as acids and caustic and otherconductive products ranging frommolten metal to saturated spent grain inthe brewing process.

When microwaves from a radar hit aconductive surface the electrical field Eis short circuited. The resultant currentin the conductive product causes themicrowaves to be re-transmitted orreflected from the surface.

Radar level transmitters have noproblem in measuring conductive liq-uids and solids because the microwaveswith frequencies between 5.8 GHz and26GHz are readily reflected off a con-ductive surface producing relativelylarge echoes.

Non-conductive productsIf a liquid or solid is non-conductive,

the value of the dielectric constant (rela-tive permittivity εr) becomes moreimportant. The theoretical amount ofreflection at a dielectric layer can be cal-culated using equation 2.5

Waveguides, stilling tubes & bypass tubes

Reflection of electromagnetic waves

Electromagnetic waves exhibit the same properties as light.

· Reflection · Refraction· Polarization · Interference· Diffraction

23

2. Physics of radar

TolueneSolvent with a low dielectric constant,

εr = 2.4

AcetoneSolvent with a dielectric constant,εr = 20

Fig 2.7 Reflected radar power depends upon the dielectric constant of the productbeing measured

Transmitted power: W1

Reflected power: W2

Dielectric constant: εrThen the percentage of reflectedpower at the dielectric layer,

Π x

100

% p

ower

ref

lect

ed

0

0

20

40

60

80

100

10 20 30 40 50 60 70 80

Π

Π [Eq. 2.5]

=

=

1-

W2

W1

4 x εr

1 + εr( )2

Typical examples are as follows:

4.46% power is reflected 40 % power is reflected

Π = 1- 4 x 4 x2.4

1 + (2.4)(

(

)

)2

Π = 1- 20

1 + (20)(

(

)

)2

Dielectric constant, εr

24

In radar level measurement the reflected energy from a product surface becomesmore critical at a dielectric constant (εr) of less than 5. The following graph showsthis important region.

Most electrically conductive products or products with a dielectric constant ofmore than 1.5 can be measured using microwave radar level transmitters. Stillingtubes can be used to concentrate the microwaves for lower dielectric constantproducts.

Fig 2.8 Reflected radar power depends upon the dielectric constant of the product beingmeasured. This graph shows the critical region where care must be taken overchoice of radar antenna

Π x

100

% p

ower

ref

lect

edLo

ssL,

dB

1.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0

5

10

15

20

1.5 2.0 3.0 3.5 4.0 4.5 5.02.5

Fig 2.9 Reflection loss in dB: loss L = 10 log ΠΠ

- 60

- 40

- 20

- 10

0

Dielectric constant, εr

Dielectric constant, εr

2. Physics of radar

Electromagnetic waves have anelectrical vector E and magnetic vectorB that are in phase but perpendicular toeach other. The direction of propaga-tion of the waves is perpendicular tothe electrical and magnetic vectors asshown in the diagram below.

Polarization defines the orientationof the electromagnetic waves and refersto the direction of the electrical vectorE. Most process radar level transmittersexhibit linear polarization as in the dia-

gram. The direction of the linear polar-ization is set by the orientation of thesignal coupler from the microwavemodule. The properties of the polariza-tion of microwaves can be important inthe application of radar to level mea-surement.

In television and microwave com-munications, linear polarization is alsoreferred to as horizontal or verticalpolarization depending on the relativeorientation of the aerials or antennas.

Fig 2.10 Diagram showing linear polarization and the relative orientation of the electricvector E, the magnetic vector B and the direction of propagation of themicrowaves

direction of wave

E

B

Polarization

25

26

Fig 2.11 Circular polarization involves rotation of the electrical and magnetic vectorsthrough 360° within a wavelength

Another form of polarization iselliptical polarization. A specific formof elliptical polarization is circularpolarization where the electrical vectorE and magnetic vector B rotate through360° within the space of a single wave-length, when a linear or circular polar-ized signal is reflected the direction ofpolarization is reversed. With circularpolarization it is possible to use thereversal of polarization to distinguishbetween a direct echo and an echo thathas made two reflections.

Circular polarization can also beused in search radars to separate thereflections from aircraft or ships frominterference echoes from rain. Thealmost spherical shape of the rain dropscauses a definite reversal of polariza-tion which can be easily rejected by thereceiving antenna. However, the scat-tered reflections from the ship or air-craft provide roughly equal amounts ofreversed and un-reversed energy thatenables detection.

λλ

27

2. Physics of radar

The linear polarization that is com-mon with process radar level transmit-ters can be used to minimise the effectsof false echo returns from the internalstructure of a process vessel. Thesefalse echoes could be reflected fromprobes, welds, agitators and baffles.

In some applications, the effect offalse echoes within a vessel can be sig-nificantly reduced by rotating the radarin the connection flange or boss. Theprinciple is illustrated below anddetailed in the section on mechanicalinstallations in Chapter 6.

Fig 2.12 If a metallic or high dielectric object is orientated in the same plane as theelectrical vector of the polarized microwaves, the radar level transmitter willreceive a large amplitude echo

Fig 2.13 If the same object is orientated at right angles to the plane of the electrical vector,the received echo will have a smaller amplitude

Large echo

Small echo

Direction of wave

E

B

Polarization can be used to reduce the amplitude of false echoes

Direction of wave

B

E

Beam angle is often discussed inrelation to radar transmitters. This cangive the impression that the radarantenna can direct a finely focusedbeam towards the target. Unfortunatelythis is not the case.

In practice, although they aredesigned to produce a directed beam, aradar antenna radiates some energy inall directions. As well as the main lobe

which accounts for most of the radiatedpower, there are also weaker side lobesof energy. This phenomenon is caused,in part, by diffraction. In addition tothis, destructive interference causes thenull points or notches that form thecharacteristic side lobes.

Chapter 5 provides a detailed expla-nation of beam angles, side lobes andtypes of antennas.

Fig 2.14 The lobe structure of antenna beams is caused by diffraction and destructiveinterference

Fig 2.15 Refraction & reflection

RefractionIn the same way as light is refracted

at an air/glass or air/water interface,microwaves are refracted when theyencounter a change in dielectric. This could be a low dielectric window(PTFE/glass/polypropylene) or a non-conductive low dielectric liquid such asa solvent.

The angle of refraction depends onthe angle of the incident wave and alsoon the ratio of the dielectric constantsat the interface.

It is possible to utilise the refractiveproperties of electromagnetic waves toconstruct a dielectric lens that willfocus microwaves.

Diffraction

main lobeside lobes

antenna

a a

B

microwave

interface

refracted energy

dielectric window / product

reflected energy

28

29

2. Physics of radar

Problematic interference effects are caused primarily by the inadvertent mixingof signals that are out of phase. The microwave signals have a sinusoidal wave-form.

Fig 2.16 In this illustration both of the sine waves have an identical frequency andamplitude but the second wave has a 45° phase lag

Interference - Phase

Phase angle

45°

Interference can be ‘constructive’ where in-phase signals produce a signal with ahigher amplitude or it can be destructive where signals that are 180° out of phaseeffectively cancel each other out.

signals in-phase

180° out of phase

constructive interference

destructive interference

Fig 2.17 Illustration of constructive and destructive interference

30

Microwaves can manifest interfer-ence effects in exactly the same way aslight. Potentially this can cause mea-surement problems. The causes ofinterference should be understood andavoided by design and installation con-siderations.

The wrong choice of antenna, instal-lation of an antenna up a nozzle, posi-tioning transmitters too close to vesselwalls or other obstructions can all lead

to interference of the signal. The chap-ter on mechanical installation shouldhelp a radar level user to avoid thispotential problem.

However, we use destructive inter-ference to our advantage when weapply pulse radar level measurementthrough a low dielectric ‘window’ tomeasure conductive or high dielectricliquids.

Interference

Fig 2.18 Interference caused by positioning an antenna too close to the vessel wall. If aradar level transmitter is installed too close to the vessel wall it is possible thatinterference will occur. With indirect reflection A B’ B’’ C, the phase may bealtered by 180° when compared with the direct reflection A B C. For this reasonthe microwaves may partially cancel out due to destructive interference

+ =

C

A

B’

B B”

31

2. Physics of radar

The thickness of the dielectric win-dow must be a half wavelength of thewindow material. When the half wave-length is used, there is destructive inter-ference between the reflection off thetop surface of the window and thereflection off the internal second surfaceof the window.

There is a 180° phase shift betweenthese reflections and they cancel each

other out. This type of installationis explained more fully in Chapter 6on the mechanical installations ofradar level transmitters together witha table showing the optimum thicknessof most important plastics and glasseswhich are suitable for penetration withradar sensors.

Fig 2.19 Destructive interference is a benefit when using pulse radar to measure througha low dielectric window. The reflection from the top surface and the reflectionfrom the internal second surface cancel each other if the thickness is a halfwavelength

emitted wavereflection withphase shift from topsurface

plastic vessel ceiling

reflection withoutphase shift frominternal surface

D

emitted wave

reflection with phase shift offtop surface of window

reflection without phase shiftoff internal face of window