Vega radar book

Peter Devine
Peter Devine

Radar level
measurement
Radar level measurement
Radar level measurement The user's guide

The user's guide

- The users guide
Peter Devine

written by
Peter Devine
additional information
Karl Grießbaum
type setting and layout
Liz Moakes
final drawings and diagrams
Evi Brucker

© VEGA Controls / P Devine / 2000
All rights reseved. No part of this book may reproduced in any way, or by any means, without prior
permissio 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, Peter
Radar level measurement - The user´s guide
1. Radar
2. Title
621.3´848
ISBN 0-9538920-0-X
Cover by LinkDesign, Schramberg.
Printed in Great Britain at VIP print, Heathfield, Sussex.

Contents
Foreword
Acknowledgement
Introduction

ix
xi
xiii

Part I
1. History of radar
2. Physics of radar
3. Types of radar
1. CW-radar
2. FM - CW
3. Pulse radar

1
13
33
33
36
39

Part II
4. Radar level measurement
1. FM - CW
2. PULSE radar
3. Choice of frequency
4. Accuracy
5. Power

47
48
54
62
68
74

5. Radar antennas
1. Horn antennas
2. Dielectric rod antennas
3. Measuring tube antennas
4. Parabolic dish antennas
5. Planar array antennas
Antenna energy patterns

77
81
92
101
106
108
110

6. Installation
A. Mechanical installation
1. Horn antenna (liquids)
2. Rod antenna (liquids)
3. General consideration (liquids)
4. Stand pipes & measuring tubes
5. Platic tank tops and windows
6. Horn antenna (solids)
B. Radar level installation cont.
1. safe area applications
2. Hazardous area applications

115
115
115
117
120
127
134
139
141
141
144

Foreword
To suggest that any one type of level
transmitter technology could be regarded as 'universal' would be unrealistic
and potentially irresponsible due to the
variation and complexity of available
applications when liquids, powders and
solids are all considered. However, the
rate at which radar based level transmitters have established themselves
over the last couple of years would
tend to suggest that this technology is
closer to that definition that any principle has ever been.
I have personally been involved in
the development, applications, sales
and marketing of level transmitters,
controllers and indicators of most types
over the last twenty years. In that time
nothing has, in my opinion, come close
to matching the significance of radar in
terms of its overall suitability, for not
just conventional but extreme process
conditions applications for the vast
majority of substances in vessels of virtually any size or complexity.
This unique principle combined with
current reflections processing software,
materials of construction, simplicity of
installation and transmitter digital communications allows this to be considered as a day to day 'first consideration'
for level, whereas only a very short
time ago it was regarded as expensive
and specialised - this is no longer the
case.

The purpose of this publication is
quite specific, and that is to explain
some of the principles involved, and to
show that by applying some simple
guidelines, what is obviously a sophisti-cated technology can be simple and
reliably used in an enormously wide
range of industrial and process applications.
We make no apology for including a
chapter on Vega specific products, and
hope this guide stimulates a radar user,
or some greater depth of knowledge if
you have some experience, we look
forward to hearing from you.
Mel Henry
Managing Director
Vega Controls Ltd.

ix

Acknowledgements
In writing and compiling this book I
had the invaluable assistance of several
colleagues from VEGA in Schiltach
both in the developing department and
within the product management.
Particular thanks must go to Karl
Griessbaum for his lucid explanations
of the 'secrets' of pulse radar; his insight into the workings of FM - CW
radar and the drawings to accompany
the explanations. Thanks also to
Juergen Skowaisa and Juergen Motzer
for their technical contributions to the
book.
The publication of 'radar level measurement - the user´s guide' is a reflection of the wealth of product knowledge of radar level application experience
in the VEGA group of companies and
our agents and distributors world wide.
This experience has accelerated
since the advent of the VEGAPULS 50
series two wire, loop powered radar.
I would like to thank all those who
contributed to the section on radar
applications. This in-cludes Doug
Anderson, Dave Blenkiron, Chris
Brennan, Graeme Cross and John
Hulme in the UK, Paal Kvam of
Hyptech in Norway, Dough Groh and
his colleagues at Ohmart VEGA in the
USA, and Juergen Skowaisa and Roger
Ramsden from VEGA Germany. Thank
also to the VEGA marketing department in Germany and the UK for their

assistance in producing and collating
pictures and photographs.
Thank to all the other unnamed contributors.
Finally, the most important contributors to this book are all VEGA radar
users world wide without whom our
high level of expertise in process radar
measurement applications would not be
possible.
Peter Devine
Technical manager
Vega Controls Ltd.

xi

Introduction
The technical benefits of radar as a
level measurement technique are clear.
Radar provides a non-contact sensor
that is virtually unaffected by changes
in process temperature, pressure or the
gas and vapour composition within a
vessel.
In addition, the measurement accuracy is unaffected by changes in density, conductivity and dielectric constant
of the product being measured or by air
movement above the product.
These benefits have become more
significant to the process industry since
the advent of low costs, high performance, two wire loop powered radar
level transmitters.
This breakthrough, in the summer of
1997, produced an unprecedented
boom in the use of non-contact microwave radar transmitters for liquid and
solids process level application.
'Radar level measurement - the
user´s guide' is offered as a reference
book for all those interested in the technology, the application, and the practical installation of radar level sen-sors.
We cover many practical process level
applications rather than the closed
niche market of custody transfer measurement.
Radar history, physics and techniques are presented as well as descriptions of types of ra-dar antenna and
mechanical and electrical installations.

Now radar is an affordable option
for process level measurement. We
compare it closely with all of the other
process level techniques and give many
examples of the myriad applications of
radar across all industries.
Radar level measurement has come
of age. We hope that this book will be
invaluable in helping you to see the
potential of this latest and almost universal level measurement technology.
More than anything, we hope that
you enjoy delving into the pages of this
book.
Peter Devine
Technical manager
Vega Controls Ltd

xiii

1. History of radar
James Clerk Maxwell predicted the
existence of radio waves in his theory
of electromagnetism as long ago as
1864. He showed mathematically that
all electromagnetic waves travel at the
same velocity in free space,
independent of their wavelength. This
velocity is of the order of 300,000 kilometres per second, the speed of light.
Heinrich Rudolf Hertz, verified
Maxwell’s theory by experiments carried out in 1886-87 at Karlsruhe
Polytechnic. He used a spark gap transmitter producing bursts of high frequency electromagnetic waves at about
455 MHz, or a wavelength of 0.66
metres.
Hertz confirmed that these electromagnetic radio waves had the same
velocity as light and could be reflected
by metallic and dielectric bodies. In
addition to their reflective properties,
Hertz demonstrated that radio waves
exhibit refraction, diffraction, polarization and interference in the same way
as light. These early experiments in
reflecting radio waves off metal plates
were the first manifestations of radar as
we know it today.
The first practical form of radar was
produced by a German engineer,
Christian Hülsmeyer. Patented in various countries in 1904 as the
‘Telemobiloscope’, Hülsmeyer’s apparatus was described as ‘A Hertzian
wave projecting and receiving apparatus adapted to indicate or give
warning of the presence of a metallic
body, such as a ship or a train, in the
line of projection of such waves’.
An addition to the patent in the same
year described ‘Improvements in
Hertzian wave projecting and receiving

James Clerk Maxwell predicted the existence of radio waves in
his theory of electromagnetism
(Pic. 1.1 - J.C.M.F)

Heinrich Hertz Hertz confirmed by experiment that electromagnetic radio waves have the same
velocity as light and can be reflected by
metallic and dielectric bodies
(Pic. 1.2 - I.N.T)

1

Prior to World War II, radar was
being developed independently in a
number of different countries, including Britain, Germany, the United
States, Italy, France and the Soviet
Union.
In 1934, following a series of experiments at the Naval Research
Laboratory in the United States, a
patent was granted to Taylor, Young
and Hyland for a ‘System for detecting
objects by radio’.
In February 1935, British scientist,
Robert Watson-Watt presented a paper
on ‘The detection and location of aircraft by radio methods’ to the Tizard
Committee for the Scientific Survey of
Air Defence.
Christian Hülsmeyer
produced the first practical radar
patented in 1904
(Pic. 1.3 - D.M.M)

apparatus for locating the position of
distant metal objects’.
A successful demonstration of the
telemobiloscope was made at the
International Shipping Congress in
Rotterdam in 1904, and also to the
German navy. However, the telemobiloscope was considered to be limited
and was not a commercial success.
Guglielmo Marconi, is famous for
pioneering trans-Atlantic radio communications. In 1922 Marconi had also
recognised the potential of using short
wave radio for the detection of metallic
objects. Marconi envisaged the use of
radio for ship to ship detection at night
or in fog. However, he did not appear
to receive the support or have the
resources to carry these ideas further at
the time.
2

Guglielmo Marconi
recognised the potential of using short
wave radio for the detection of metallic
objects in 1922
(Pic. 1.4 - GEC Marconi)

1. History of radar

Sir Robert Watson - Watt
was a senior figure in the development
of British radar in the 1930’s & 40’s
(Pic. 1.5 - I.W.M)

Subsequently, a practical demonstration was carried out using a BBC radio
transmitter at Daventry. About five and
a half miles (9 km) away, a separate
radio receiver connected to an oscilloscope was used to detect the presence
of a Handley Page Heyford aircraft as
it flew between the transmitter and
receiver.
Both the American system and
Watson-Watt’s Daventry experiment
were types of continuous wave (CW)
radar. Called CW wave-interference
radar or bistatic CW radar, a continuous single frequency was transmitted
from one point and detected by a
receiver at a separate location. The
receiver also detects doppler shifted
echoes from the target object. The
interference between the frequency of
the direct signal and reflected signals at

a slightly different frequency indicated
the presence of the target object.
If you are unfortunate enough to live
on an airport flight path, you may have
witnessed this effect on your television
screen. As an aircraft approaches, the
picture on the screen may flicker with
regular horizontal bands scrolling vertically on the screen. These diminish
when the aircraft is directly overhead
and then continue as the aircraft moves
away.
Although it proved a point at
Daventry, CW wave-interference radar
was not a practical device. It could
detect the presence but not the position
of the target.
After Daventry, the British effort
continued at Orford Ness and then
nearby Bawdsey Manor on the Suffolk
coast. It was clear that pulse radar
would be needed to provide the
required distance and direction information essential for a defensive radio
detection system.
The British, under the direction of
Watson-Watt developed a defensive
system of CH (Chain Home) radar stations which eventually covered all of
the coastal approaches to Britain. The
standard chain home radars had a relatively low frequency of between 22 &
30 MHz (wavelength 10 to 13.5
metres). They had a power of 200 kilowatts and a range of up to 190 kilometres.
However, the long range CH radar
transmitters were blind to low flying
aircraft and therefore they were supplemented by CHL (Chain Home Low)
radar transmitters which had a shorter
range and covered the lower altitudes
that were overlooked by the main CH
3

British Chain Home Radar aerials Radar was instrumental in the defence
of Britain during the second world war
(Pic. 1.6 - I.W.M)

transmitters. They operated on a frequency of 200 MHz (wavelength 1.5
metres).
It is well documented that the CH
and CHL network of radar stations
were a crucial factor during the Battle
of Britain in the summer of 1940. It
enabled the fighters of the Royal Air
Force to be deployed when and where
they were needed and rested when the
threat receded. The limited resources in
men and machines were not wasted in
long standing patrols.
German radar research was also conducted in secret in the late 1930’s.
Whereas the development effort in
Britain was focused on air defence, in
Germany separate radar developments
were carried out for the Navy, Army
and Luftwaffe.
Companies involved in German
naval research produced a range of ship
4

mounted sea search radar transmitters
called Seetakt. These were delivered as
early as 1938 with a frequency of 366
MHz (wavelength 82 cm) and were
installed on many vessels including the
famous battleships, Bismarck and Graf
Spee.
German Naval developments also
produced the Freya range of search
radars operating on 125 MHz (wavelength 2.4 metres). These were found to
be effective for tracking aircraft at long
range, and were subsequently supplied
to the Luftwaffe for early warning.
However, they could not provide altitude information.
Other German radars in wide use
were the parabolic antenna Würzburg
and Würzburg Riese (Giant Würzburg)
transmitters. The standard Würzburgs
were generally used for directing
searchlights and flak batteries and the
Würzburg Riese for tracking individual
intruders and directing night fighters to
intercept them.
In a similar fashion to the British
Chain Home system, the Germans built
a defensive network of ‘Himmelbett’
radar stations. The literal translation of
Himmelbett is four poster bed. The
four ‘posts’ of the bed consisted of a
Freya early warning radar, a Würzburg
radar for tracking the intruding aircraft,
a Würzburg radar to guide the night
fighter to the intruder and a Seeburg
plotting table (Seeburgtisch) to monitor
the interception.
This defensive radar system became
known by the British as the
‘Kammhuber Line’ after the German
general in charge of night fighters.

1. History of radar

Above - The famous aerial reconnaissance
photograph of a German Würzburg radar
antenna at Bruneval in northern France.
This image alerted the British to the
presence and advanced state of German
defensive radar which led to a commando
action in which components from the
radar were taken back to Britain for
analysis
(Pic. 1.7 - I.W.M)

Right - The German Würzberg radar was
used for directing searchlights and flak
batteries and for tracking individual targets and directing interceptors to them
(Pic. 1.8 - P.D)

5

Both Britain and Germany developed airborne radar for fighter interception by night. British airborne radar
trials started in 1937 with the production AI Mark 1 taking to the air in May
1939. The first practical British
Airborne Interception radar was the AI
Mark IV which was first tested in
August 1940.
In Germany the Lichtenstein airborne radar was available in mid 1941.
The characteristic external radar aerial
array of the Lichtenstein caused significant aerodynamic drag. This could
reduce the aircraft speed by as much as
40 kilometres per hour. By 1943 the
range had been extended to 6000
metres.

It became clear to radar researchers
that a shorter ‘centimetric’ wavelength
would be more useful for a number of
applications. This would enable a more
focused airborne radar that would not
suffer from the ground returns that
restricted capabilities of the first airborne radars. The higher frequency
could be used for a ground mapping
radar unit to locate towns and other
geographic features.
The problem was how to find a
method of generating sufficient power
at the desired wavelength of 10
centimetres.

British Airborne Radar - AI Mark IV
developed for fighter interception by night
in 1940

German Airborne Radar ‘Lichtenstein’
available in mid 1941 - the external aerial
radar caused significant aerodynamic drag

(Pic. 1.9 - I.W.M)

(Pic. 1.10 - I.W.M)

6

1. History of radar

In late February 1940, an historic
breakthrough was made by John
Randall and Harry Boot, researchers at
the University of Birmingham, when
they tested their world changing invention the Cavity Magnetron.
The heart of this cavity magnetron
was a simple solid copper block with
six cavities machined into it. In the
centre was the cathode. When a strong
magnetic field and high voltage was
applied between the copper block and
the cathode, the stream of electrons resonated in unison within the cavities
instead of passing directly to the copper
block anode. The frequency of oscillation was calculated to be about 3 GHz
(10 centimetre wavelength).
The theoretical calculations of the
prototype cavity magnetron were correct. The actual wavelength was found
to be 9.87 centimetres and the all
important power of the prototype was
400 Watts.

Cavity Magnetron the world changing invention by John
Randall and Harry Boot invented in 1940
(Pic. 1.11 - GEC)

Production of cavity magnetrons followed very quickly and the power output was significantly increased. Britain
developed microwave airborne interception AI radar sets for night fighters
which had a vastly improved long and
near range. The British microwave airborne interception radar was the AI
Mark VII which was introduced in mid
1942. The improved AI Mark VIII was
mass produced and in wide use by
early 1943.

The Cavity Magnetron was used in centrimetric ‘microwave’ airborne radar and
duced a quantum leap in performance. The radar dish was protected inside a
plastic nose assembly

pro-

(Pic. 1.12 & 1.13 - H.R.A)

7

Britain also used the cavity magnetron in the development of a ground
mapping radar called H2S. This device
enabled aircraft to be accurately navigated to their destinations without the
aid of ground based beacons or beams.
Britain shared this secret microwave
technology with the United States
where additional development took
place at the Radiation Laboratory within the Massachusetts Institute of
Technology. From the work carried out
at MIT, further airborne interception
radars and gun laying radars were mass
produced and delivered to the allied
forces. The American SCR-720 (known
as AI Mark X in Britain) was first
delivered to the USAAF by late 1942.
This radar unit became a standard
device long after the war had finished.
War time secrecy meant that radio
detection devices were given coded
names. In Britain, the early chain home
radar was called RDF after the existing
Radio Direction Finding systems in the
hope that it would mislead their real

function.
In the same way in Germany,
radar was disguised as ‘Dezimeter
Telegraphie’ or ‘De-Te’, translated as
decimetric telegraphy
It was the Americans who introduced the now universally used palindrome, RADAR or RAdio Detection
And Ranging.
The history of the development of
radar during the course of the Second
World War is a huge subject in
itself. Many devices were developed.
Measures and counter measures were
taken in the radar war.
Since 1945, radar has been used for
an increasing number of peaceful applications. The giant Würzburg parabolic
radar transmitters of the Second World
War became post war radio telescopes.
The basic designs were developed and
enlarged and can be seen at the well
known Jodrell Bank Observatory near
Manchester which has a dish diameter
of 75 metres.
Viewed from Earth, the planet Venus

Modern radar systems are exemplified by this ‘AWAC’ airborne early warning aircraft.
Multiple targets can be detected at extreme range
(Pic. 1.14 - P.D)

8

1. History of radar

is one of the brightest celestial bodies.
However, the mysteries of our close
neighbour in the Solar System were
only uncovered with the assistance of
radar. The surface of Venus is shrouded
in dense clouds of vapour including
carbon dioxide gas at pressures of 90
bar and an average temperature of
750 K.
Earth bound pulse radar measurements over an extended period of time
were used to calculate the radius of the
orbit of Venus. Doppler shift measurements from the surface were used to
calculate the rate of rotation of the
shrouded planet. The Venus ‘day’ was
found to be 243 Earth days.
During the 1970’s, radar mapping of
the planet’s surface by space probe
uncovered surface features such as
craters.
Jodrell Bank - the observatory near
Manchester which has a 75 metre
dish diameter
(Pic. 1.15 - P.D)

Detection by radar is not always desirable. Huge sums of money have been spent
reducing the radar signature of the F117 stealth fighter
(Pic. 1.16 - P.D)

9

Radar technology is part of our
everyday lives. The cavity magnetron
is used in microwave ovens.
Continuous wave (CW) radars are used
in automatic door detection and vehicle
speed measurement. Other well known
civilian radar applications include air
traffic control, shipping and weather
radar.
Radar altimeters developed in the
1930’s use a form of radar called
FM - CW or Frequency Modulated
Continuous Wave radar.
In the 1970’s, the same FM - CW
measurement technique was used in
the production of the first radar level
tank gauge. Initially these radar level
transmitters were used to measure
petroleum products in supertankers.
Further developments of FM - CW
level transmitters led to their use on
shore based storage tanks in the mid
1980’s. Originally these were expensive, high accuracy systems for fiscal
measurement of petroleum products.

Later, lower accuracy FM - CW radar
transmitters became available for the
process industry.
In the late 1980’s, pulse radar level
transmitters were developed for process
measurement applications. The availability of suitable crystals and solid
state components such as GaAs FET
oscillators enabled cost effective radar
level transmitters to enter the market.
In 1997 a significant improvement
in the specification of radar level transmitters was achieved. VEGA produced
the world’s first two wire, loop powered, intrinsically safe radar level transmitter. For the first time low cost, high
specification radar level transmitters
became available.
It is likely that these advances will
continue into the new millennium and
that radar level transmitters will
become a commodity item in the same
way as differential pressure transmitters.

In the field of radar level
measurement, technological
advances have resulted in
two wire, intrinsically safe
transmitters
(Pic. 1.17 - Vega)

10

1. History of radar
Comparing the old with the new

A raw oscilloscope echo trace had to be interpreted by skilled operators using the British
war time Chain Home Low radar
(Pic. 1.18 & 1.19 - I.W.M)

Comprehensive information is available on the PC echo trace of the latest two wire loop
powered radar level transmitters
(Pic. 1.20 - Vega Pic. 1.21 - Vega)

11

Inhalt
Foreword
Acknowledgement
Introduction

ix
xi
xiii

Part I
1. History of radar
2. Physics of radar
3. Types of radar
1. CW-radar
2. FM - CW
3. Pulse radar

1
13
33
33
36
39

Part II
1. FM - CW
2. PULSE radar
3. Choice of frequency
4. Accuracy
5. Power

47
48
54
62
68
74

5. Radar antennas
1. Horn antennas
2. Dielectric rod antennas
3. Measuring tube antennas
4. Parabolic dish antennas
5. Planar array antennas
Antenna energy patterns

77
81
92
101
106
108
110

6. Installation
A. Mechanical installation
1. Horn antenna (liquids)
2. Rod antenna (liquids)
3. General consideration (liquids)
4. Stand pipes & measuring tubes
5. Platic tank tops and windows
6. Horn antenna (solids)
B. Radar level installation cont.
1. safe area applications
2. Hazardous area applications

115
115
115
117
120
127
134
139
141
141
144

2. Physics of radar
Electromagnetic waves
Th e velocity of light in free space is
299,792,458 metres per second, but
who is timing? For the purposes of the
calculations in this book, we will call it
300,000 kilometres per second or
3 x 108 metres per second.
Maxwell’s theories of electromagnetism were confirmed by the
experiments of Heinrich Hertz. These
show that all forms of electromagnetic
radiation travel at the speed of light in
free space. This applies equally to long
wave radio transmissions, microwaves,
infrared, visible and ultraviolet light
plus X-rays and Gamma rays.
Maxwell showed that the velocity of
light in a vacuum in free space is given
by the expression :
Examples :-

1

co =

µo
εo

o

x

εo)

[Eq. 2.1]

velocity of electromagntic wave
in a vacuum in metres / second
the permeability of free space
(4 π x 10 -7 henry / metre)
the permittivity of free space
(8.854 x 10 -12 farad / metre)

c =

f xλ
[Eq. 2.2]

c

velocity of electromagnetic
waves in metres / second

f
λ

frequency of wave in second -1
wavelength in metres

The original cavity magnetron had
a wavelength of 9.87 centimetres.
This corresponds to a frequency of
3037.4 MHz (3.0374 GHz).
The frequency of a pulse radar
level transmitter may be 26 GHz
or 26 x 108 metres per second.
The wavelength is 1.15 centimetres.
The electromagnetic waves have an
electrical vector E and a magnetic vector B that are perpendicular to each
other and perpendicular to the direction
of the wave. This will be discussed and
illustrated further in the section on
polarization. The electrical vector has
the major influence on radar applications.

λ

direction of wave

amplitude

co

(µ

The velocity of an electromagnetic
wave is the product of the frequency
and the wavelength.

Fig 2.1
13

The Electromagnetic spectrum

10 8

10 7

10 6

10 5

10 4

10 3

10 2

electric waves
10 1

10 2

10 1

10 0

10 -1

10 -2

10 -3 10 -4

radio waves
10 3

10 4

10 5

10 6

10 7

10 8

infra
10 9

10 10

10 11

10 12

3m

0.3 m

3 cm

3 mm

100 MHz

1 GHz

10 GHz

100 GHz

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

14

2. Physics of radar

10 -5

10 -6

red
10 13

10 -7

10 -8

ultra violet
10 14

10 15

10 16

10 -9

10 -10 10 -11 10 -12 10 -13 10 -14 10 -15 10 -16

X rays
10 17

10 18

m

gamma rays
10 19

10 20

10 21

10 22

10 23

10 24

Hz

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

15

Permittivity
In electrostatics, the force between
two charges depends upon the magnitude and separation of the charges and
the composition of the medium
between the charges. Permittivity ε is
the property of the medium that effects
the magnitude of the force. The higher
the value of the permittivity, the lower
the force between the charges. The
value of the permittivity of free
space (in a vacuum) εo, is calculated
indirectly and empirically to be:
8.854 x 10-12 farad / metre.

Relative permittivity or
dielectric constant εr

The ratio of the permittivity of a
medium to the permittivity of free
space is a dimensionless property
called ‘relative permittivity’ or ‘dielectric constant’. For example, at 20° C
the relative permittivity of air is close
to that of a vaccum and is only about
1.0005 whereas the relative permittivity of water at 20° C is about 80.
(Dielectric constant is also widely
known as DK.)
The value of the dielectric constant
of the product being measured is very
important in the application of radar to
level measurement. In non-conductive
products, some of the microwave energy will pass through the product and
the rest will be reflected off the surface.
This feature of microwaves can be
used to advantage or, in some circumstances, it can create a measurement
problem.

16

Permeability µ and relative
permeability µr
The magnetic vector, B, of an electromagnetic wave also has an influence
on the velocity of electromagnetic
waves. However, this influence is negligible when considering the velocity in
gases and vapours which are non-magnetic. The relative permeability of the
product being measured has no significant effect on the reflected signal when
compared with the effects of the relative permittivity or dielectric constant.
For the non-magnetic gases above the
product being measured, the value of
the relative permeability, µr = 1.

Frequency, velocity and wavelength
As we have already stated, the frequency (f), velocity (c) and wavelength
(λ) of the electromagnetic waves are
related by the equation c = f x λ.
The frequency remains uninfluenced
by changes in the propagation medium.
However, the velocity and wavelength
can change depending on the electrical
properties of the medium in which they
are travelling. The speed of propagation can be calculated using equation
2.3.

c =

co

(µ x ε )
r

c
co
µr
εr

r

[Eq. 2.3]

velocity of electromagnetic wave
in the medium in metres/second
velocity of electromagnetic
waves in free space
the relative permeability
(µ medium / µo)
the relative permittivity

2. Physics of radar

Changes in the wavelength and
velocity of microwaves are apparent in
certain radar level applications.
Changes in temperature, pressure and
gas composition have a small effect on
the running time of microwaves
because the dielectric constant of the
propagation medium is altered to a
greater or lesser extent. This is discussed in detail later.
Radar level transmitters can be used
to measure conductive liquids through
low dielectric ‘windows’ such as glass,
polypropylene and PTFE. The optimum thickness of the low dielectric
window is a half wavelength or multiple of half wavelength.
For example, polypropylene has a
dielectric constant εr of 2.3 and the
half wavelength at a frequency of 5.8
GHz is 17 mm compared with a half
wavelength of about 26 mm in a vacuum. It follows that the speed of
Empty vessel: large echo
from metal
bottom

microwaves in polypropylene is about
two thirds of the speed in air.
As with low dielectric windows,
non-conductive, low dielectric constant
liquids may absorb more power than
they reflect from the surface. The
velocity of the microwaves within the
liquid is slower than in the vapour
space above.
For example, if there is about 0.5
metres of solvent in the bottom of a
metallic vessel, a radar level transmitter
may see a larger echo from the vessel
bottom than from the product. This
large echo will appear to be further
away than it really is because the running time within the solvent is slower.
For this reason, special considerations
must be made within the echo processing software to ensure that the radar
follows the solvent level and does not
follow the vessel bottom as it apparently moves away!
As the vessel fills with
solvent two echoes
are received. The
echo from the vessel
bottom appears
further away because
the running time of
the microwaves in
solvent is slower

solvent echo

Fig 2.3 - Effect of dielectric constant on the running time of a microwave radar
17

The same effect can be experienced when looking at interface detection using
guided microwave level transmitters to detect oil and water or solvent and aqueous
based liquids.
Fig 2.4 Oil/water interface
detection using a
guided microwave
level transmitter. Note
that the water echo
has a reduced amplitude and appears to be
further away. The
running time of
microwaves in oil is
slower than in air

reference echo
(water without oil)

oil echo

water echo

Effects on the propagation
speed of microwaves
Microwave radar level transmitters
can be applied almost universally
because, as a measurement technique,
they are virtually unaffected by process
temperature, temperature gradient, vacuum and normal pressure variations,
gas or vapour composition and movement of the propagation medium.
However, changes in these process
conditions do cause slight variations in
the propagation speed because the
dielectric constant of the propagation
medium is altered.

Calculating the propagation
speed of microwaves
The temperature, pressure and the
gas composition of the vapour space all
have an effect on the dielectric constant
of the propagation medium through
which the microwaves must travel.
This in turn affects the propagation
speed or running time of the instrument.

18

The dielectric constant or relative
permittivity can be calculated as
follows :

εr = 1 + (εrN - 1) x θN x P

θ x PN
[Eq. 2.4]

εr
εrN

calculated dielectric constant
(relative permittivity)
dielectric constant of gas/vapour
under normal conditions
(temperature 273 K, pressure 1 bar
absolute)

θN
PN
θ
P

temperature under normal
conditions, 273 Kelvin
pressure under normal
conditions, 1 bar absolute
process temperature in Kelvin
process pressure in bar absolute

2. Physics of radar

From equation 2.4 and equation 2.3,
we can calculate the percentage error
caused by variations in the dielectric
constant of different gases and vapours
and the relative effects of changes in
process temperature and pressure.

Gases and vapours
By definition, the dielectric constant
in a vacuum is equal to 1.0. The dielectric constants of the gases and vapours
that may be present above the product

differ but they have only a very small
effect on the accuracy of radar.
Radar level transmitters are usually
calibrated in air. For this reason, the
following tables show
1. Dielectric constant of different gases
at normal temperature and pressure
(273K, 1 Bar A)
2. Percent error in the running time in
the gases compared with air

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

% Error from air (at
normal temperature
and pressure)

Vacuum
Air
Argon
Ammonia / NH 3
Hydrogen Bromide HBr
Hydrogen Chloride HCl
Carbon Monoxide / CO
Carbon Dioxide / C0 2
Ethane / C 2 H6
Ethylene / C 2H4
Helium

ε rN (dielectric
constant at normal
conditions)
1.0000
1.000633
1.000551
1.006976
1.002994
1.004078
1.000692
1.000985
1.001503
1.001449
1.000072

Hydrogen / H 2
Methane / CH 4
Nitrogen / N 2
Oxygen / O 2

1.000275
1.000878
1.000576
1.000530

+ 0.0179
- 0.0122
+ 0.00285
+ 0.0052

Gas / Vapour

+ 0.0316
0.0
+ 0.0041
+ 0.3154
- 0.1178
- 0.1717
- 0.00295
- 0.0176
- 0.0434
- 0.0407
+ 0.0280

19

Temperature
High temperature or large temperature gradients have very little effect on the
transit time of microwaves within an air or vapour space. At a temperature of
2000° C the variation is only 0.026% from the measurement value at 0° C. Radar
level transmitters with air or nitrogen gas cooling are used on molten iron and steel
applications.

0.03
0.025

% error

0.02
0.015
0.01
0.005
0.0
0

250

500

750

1000

1250

1500

1750

2000

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

20

2. Physics of radar
Pressure
Pressure does have a small but more significant influence on the velocity of
electromagnetic waves. At a pressure of 30 Bar, the error is only 0.84%. However
this becomes more significant and at a pressure of 100 Bar there is a velocity
change of 2.8%. If the pressure is varying constantly between atmospheric pressure
and 100 Bar, the velocity variations can be compensated using a pressure transmitter.

10

% error

8
6
4
2
0
0

50

100

150

200

250

300

350

400

Pressure in Bar (absolute)
Fig 2.6 The influence of pressure on radar measurement in air at a constant temperature
of 273 K

21

Waveguides, stilling tubes & bypass tubes
In the preceding equations, we have
assumed that the microwaves are
travelling in ‘free space’ in a vacuum.
However, in practice the proximity
of metallic vessel walls and other
structures will have an influence on
the propagation velocity of the
microwaves. This is particularly true
when microwave radar level transmitters are fitted inside bypass tubes or
stilling tubes or when a horn antenna is
fitted with a waveguide extension.
When microwaves are propagating

within a metallic tube the running time
appears to slow down because the
microwaves travel further bouncing
off the inside wall of the tube and
currents are set up on the inside surface
of the tube.
This effect is discussed in more
detail in the chapters on antennas and
mechanical installations. The waveguide effect can be compensated during
calibration and the use of stilling tubes
and bypass tubes can be beneficial in
some level applications.

Electromagnetic waves exhibit the same properties as light.

·
·
·

Reflection
Polarization
Diffraction

·
·

Refraction
Interference

Reflection of electromagnetic waves
Conductive products
Using a spark gap transmitter,
Heinrich Hertz demonstrated that electromagnetic waves could be reflected
off metallic objects and objects with a
relatively high dielectric constant.
In the same way, radar can easily
measure conductive aqueous liquids
such as acids and caustic and other
conductive products ranging from
molten metal to saturated spent grain in
the brewing process.
When microwaves from a radar hit a
conductive surface the electrical field E
is short circuited. The resultant current
in the conductive product causes the
microwaves to be re-transmitted or
reflected from the surface.

22

Radar level transmitters have no
problem in measuring conductive liquids and solids because the microwaves
with frequencies between 5.8 GHz and
26GHz are readily reflected off a conductive surface producing relatively
large echoes.
Non-conductive products
If a liquid or solid is non-conductive,
the value of the dielectric constant (relative permittivity εr) becomes more
important. The theoretical amount of
reflection at a dielectric layer can be calculated using equation 2.5

2. Physics of radar
W1
Transmitted power:
W2
Reflected power:
Dielectric constant:
εr
Then the percentage of reflected
power at the dielectric layer,

Π = 1-

4 x εr

(1 + ε )

2

r

W2

Π =

[Eq. 2.5]

W1

Typical examples are as follows:
Acetone
Solvent with a dielectric constant,
εr = 20

Toluene
Solvent with a low dielectric consta t
n,
εr = 2.4

Π = 1-

(2.4)

4x

(1 +

Π = 1-

2

(2.4))

4.46% power is reflected

4x

(1 +

( 20 )
(20)

2

)

40 % power is reflected

Π x 100% power reflected

100
80
60
40
20
0
0

10

20

30

40

50

60

70

80

Dielectric constant, εr

Fig 2.7 Reflected radar power depends upon the dielectric constant of the product
being measured
23

In radar level measurement the reflected energy from a product surface becomes
more critical at a dielectric constant (εr) of less than 5. The following graph shows
this important region.
Π x 100% power reflected

20
15

10
5
0
1.0

1.5

2.0

3.0
2.5
3.5

4.0

4.5

5.0

Fig 2.8 Reflected radar power depends upon the dielectric constant of the product being
measured. This graph shows the critical region where care must be taken over
choice of radar antenna
0

Loss L, dB

- 10
- 20
- 40

- 60
3.0
3.5
2.5
Fig 2.9 Reflection loss in dB: loss L = 10 log Π
1.0

1.5

2.0

4.0

4.5

5.0

Most electrically conductive products or products with a dielectric constant of
more than 1.5 can be measured using microwave radar level transmitters. Stilling
tubes can be used to concentrate the microwaves for lower dielectric constant
products.

24

2. Physics of radar
Polarization
Electromagnetic waves have an
electrical vector E and magnetic vector
B that are in phase but perpendicular to
each other. The direction of propagation of the waves is perpendicular to
the electrical and magnetic vectors as
shown in the diagram below.
Polarization defines the orientation
of the electromagnetic waves and refers
to the direction of the electrical vector
E. Most process radar level transmitters
exhibit linear polarization as in the dia-

gram. The direction of the linear polarization is set by the orientation of the
signal coupler from the microwave
module. The properties of the polarization of microwaves can be important in
the application of radar to level measurement.
In television and microwave communications, linear polarization is also
referred to as horizontal or vertical
polarization depending on the relative
orientation of the aerials or antennas.

E

direction of wave

B

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

25

Another form of polarization is
elliptical polarization. A specific form
of elliptical polarization is circular
polarization where the electrical vector
E and magnetic vector B rotate through
360° within the space of a single wavelength, when a linear or circular polarized signal is reflected the direction of
polarization is reversed. With circular
polarization it is possible to use the
reversal of polarization to distinguish
between a direct echo and an echo that
has made two reflections.

Circular polarization can also be
used in search radars to separate the
reflections from aircraft or ships from
interference echoes from rain. The
almost spherical shape of the rain drops
causes a definite reversal of polarization which can be easily rejected by the
receiving antenna. However, the scattered reflections from the ship or aircraft provide roughly equal amounts of
reversed and un-reversed energy that
enables detection.

λ

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

26

2. Physics of radar

The linear polarization that is common with process radar level transmitters can be used to minimise the effects
of false echo returns from the internal
structure of a process vessel. These
false echoes could be reflected from
probes, welds, agitators and baffles.

In some applications, the effect of
false echoes within a vessel can be significantly reduced by rotating the radar
in the connection flange or boss. The
principle is illustrated below and
detailed in the section on mechanical
installations in Chapter 6.

Polarization can be used to reduce the amplitude of false echoes
E

Direction of wave

B
Large echo

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

E

Direction of wave

Small echo
B

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
27

Diffraction
Beam angle is often discussed in
relation to radar transmitters. This can
give the impression that the radar
antenna can direct a finely focused
beam towards the target. Unfortunately
this is not the case.
In practice, although they are
designed to produce a directed beam, a
radar antenna radiates some energy in
all directions. As well as the main lobe

which accounts for most of the radiated
power, there are also weaker side lobes
of energy. This phenomenon is caused,
in part, by diffraction. In addition to
this, destructive interference causes the
null points or notches that form the
characteristic side lobes.
Chapter 5 provides a detailed explanation of beam angles, side lobes and
types of antennas.

side lobes

main lobe

antenna

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

Refraction
In the same way as light is refracted
at an air/glass or air/water interface,
microwaves are refracted when they
encounter a change in dielectric. This
could be a low dielectric window
(PTFE/glass/polypropylene) or a nonconductive low dielectric liquid such as
a solvent.

reflected
energy

The angle of refraction depends on
the angle of the incident wave and also
on the ratio of the dielectric constants
at the interface.
It is possible to utilise the refractive
properties of electromagnetic waves to
construct a dielectric lens that will
focus microwaves.

a

a

Fig 2.15 Refraction & reflection

microwave
interface
dielectric window / product
refracted
energy

28

B

2. Physics of radar
Interference - Phase
Problematic interference effects are caused primarily by the inadvertent mixing
of signals that are out of phase. The microwave signals have a sinusoidal waveform.
Phase angle

45°

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

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

constructive interference

180° out of phase

destructive interference

Fig 2.17 Illustration of constructive and destructive interference

29

Interference
Microwaves can manifest interference effects in exactly the same way as
light. Potentially this can cause measurement problems. The causes of
interference should be understood and
avoided by design and installation considerations.
The wrong choice of antenna, installation of an antenna up a nozzle, positioning transmitters too close to vessel
walls or other obstructions can all lead

to interference of the signal. The chapter on mechanical installation should
help a radar level user to avoid this
potential problem.
However, we use destructive interference to our advantage when we
apply pulse radar level measurement
through a low dielectric ‘window’ to
measure conductive or high dielectric
liquids.

A

+

=

C
B’

B

B”

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

30

2. Physics of radar

The thickness of the dielectric window must be a half wavelength of the
window material. When the half wavelength is used, there is destructive interference between the reflection off the
top surface of the window and the
reflection off the internal second surface
of the window.
There is a 180° phase shift between
these reflections and they cancel each

emitted wave

plastic vessel ceiling

other out. This type of installation
is explained more fully in Chapter 6
on the mechanical installations of
radar level transmitters together with
a table showing the optimum thickness
of most important plastics and glasses
which are suitable for penetration with
radar sensors.

reflection with
phase shift from top
surface
reflection without
phase shift from
internal surface

D

emitted wave
reflection with phase shift off
top surface of window
reflection without phase shift
off internal face of window
Fig 2.19 Destructive interference is a benefit when using pulse radar to measure through
a low dielectric window. The reflection from the top surface and the reflection
from the internal second surface cancel each other if the thickness is a half
wavelength
31

3. Types of radar
1a. CW, continuous wave radar
In continuous wave or CW Radar, a
continuous unmodulated frequency is
transmitted and echoes are received
from the target object. If the target
object is stationary, the frequency of
the return echoes will be the same as
the transmitted frequency. The range of
the object cannot be measured.
However, the frequency of the return
signal from a moving object is changed
depending on the speed and direction
of the object. This is the well known
‘doppler effect’. The doppler effect is
apparent when the siren note of an
emergency vehicle changes as it speeds
past a pedestrian. The pitch of the siren

note is higher as it approaches the listener and lower as it recedes. The
doppler effect is also used by
astronomers to monitor the expansion
of the Universe. By measuring the ‘red
shift’ of the spectrum of distant stars
and galaxies the rate of expansion can
be measured and the age of distant
objects can be estimated.
In the same way, when an object that
has been illuminated by a CW Radar
approaches the transmitter, the frequency of the return signal will be higher
than the transmitted frequency. The
echo frequency will be lower if the
object is moving away.

yv

elocit

rece

requ
ived f

tv
targe

f + f dp
ency t

itted

m
trans

ave
yf w
uenc t,

lengt

hλ

freq

Fig 3.1 CW radar uses doppler shift to derive speed measurement

33

In Fig 3.1, the aircraft is travelling
towards the CW radar. Therefore the
received frequency is higher than
the transmitted frequency and the sign
of fdp is positive. If the aircraft was
travelling away from the radar at the

v =

λ x fdp
2

=

same speed, the received frequency
would be ft - fdp.
The velocity of the target in the
direction of the radar is calculated by
equation 3.1

c x fdp

c
v
ft

2 x ft

fdp

[Eq. 3.1]

ft+fdp

is the velocity of microwaves
is the target velocity
is the frequency of the
transmitted signal
is the doppler beat frequency
which is proportional to velocity
is received frequency. The sign
of fdp depends upon whether the
target is closing or receding

1b. CW wave-interference radar or bistatic CW radar
We have already mentioned that CW
radar was used in early radar detection
experiments such as the famous
Daventry experiment carried out by
Robert Watson - Watt and his colleagues. In this case, the transmitter
and receiver were separated by a considerable distance. A moving object
was detected by the receiver because
there was interference between the fre-

quency received directly from the
transmitter and the doppler shifted frequency reflected off the target object.
Although the presence of the object is
detected, the position and speed cannot
be calculated.
In essence, this is what happens
when a low flying aircraft interferes
with the picture on a television screen.
See Fig 3.2.

1c. Multiple frequency CW radar
Standard continuous wave radar is
used for speed measurement and, as
already explained, the distance to a stationary object can not be calculated.
However, there will be a phase shift
between the transmitted signal and the
return signal.
If the starting position of the object
is known, CW radar could be used to
detect a change in position of up to half
wavelength (λ/2) of the transmitted
wave by measuring the phase shift of
the echo signal. Although further
movement could be detected, the range
34

would be ambiguous. With microwave
frequencies this means that the useful
measuring range would be very limited.
If the phase shifts of two slightly
different CW frequencies are measured
the unambiguous range is equal to the
half wavelength (λ/2) of the difference
frequency. This provides a usable distance measurement device.
However, this technique is limited to
measurement of a single target.
Applications include surveying and
automobile obstacle detection.

transmitter

transmitted signal direct

television interference

reflected signal
(doppler shift)

Fig 3.2 The effect of low flying aircraft on television reception is similar to the method of
detection by CW wave-interference radar

transmitted
signal indirect

target

3. Types of radar

35

2.

FM-CW, frequency modulated continuous wave radar
If the distance to the target is R,
and c is the speed of light, then the
time taken for the return journey is:-

2xR
c

∆t =

[Eq. 3.2]

We can see from Fig. 3.3 that if
we know the linear rate of change of
the transmitted signal and measure the
difference between the transmitted and
received frequency fd, then we can
calculate the time ∆t and hence derive
the distance R.

frequency

Single frequency CW radar cannot
be used for distance measurement
because there is no time reference mark
to gauge the delay in the return echo
from the target. A time reference mark
can be achieved by modulating the frequency in a known manner.
If we consider the frequency of the
transmitted signal ramping up in a
linear fashion, the difference between
the transmitting frequency and the
frequency of the returned signal will be
proportional to the distance to the
target.

cy

en

u
eq

r

df

itte

m

ns

tra

re

∆t
fd

c

e
eiv

df

re

e
qu

nc

y

∆t =

2xR
c
time

Fig 3.3 The principle of FM - CW radar

36

3. Types of radar

In practice, the FM - CW signal has
to be cyclic between two different frequencies. Radio altimeters modulate
between 4.2 GHz and 4.4 GHz. Radar
level transmitters typically modulate
between about 9 GHz and 10 GHz or

24 GHz and 26 GHz.
The cyclic modulation of FM - CW
radar transmitter takes different forms.
These are sinusoidal, saw tooth or
triangular wave forms.

FM - CW wave forms

transmitted frequency
received frequency

frequency

Fig 3.4 Sine wave

Commonly used on aircraft radio altimeters
between 4.2 and
4.4 GHz

4.4GHz

time
4.2GHz

frequency
Fig 3.5 Triangular wave

Used on FM - CW
radar transmitters
time

frequency

Fig 3.6 Saw tooth wave

10 GHz

9 GHz
time

Most commonly used
on most FM - CW
process radar level
transmitters

37

If we look at a triangular wave
form we can see that there is an interruption in the output of the difference
frequency , fd. In practice, the received
signal is heterodyned with part of the
transmitted frequency to produce the
difference frequency which has a posi-

tive value independent of whether the
modulation is increasing or decreasing.
The diagram below makes the
assumption that the target distance is
not changing. If the target is moving,
there will be a doppler shift in the difference frequency.

frequency

time

difference
frequency

fd
time

Fig 3.7 & 3.8 The change in direction between the ramping up and down of the frequency
creates a short break in the measured value of the difference frequency.
This has to be filtered out. The transmitted frequency is represented by the
red line and the received frequency is represented by the dark blue line.
The difference frequency is shown in light blue on the bottom graph

38

3. Types of radar
3. Pulse radar
a. Basic pulse radar
Pulse radar is and has been used
widely for distance measurement since
the very beginnings of radar technology. The basic form of pulse radar is a
pure time of flight measurement. Short
pulses, typically of millisecond or
nansecond duration, are transmitted
and the transit time to and from the target is measured.
The pulses of a pulse radar are not
discrete monopulses with a single peak

of electromagnetic energy, but are in
fact a short wave packet. The number
of waves and length of the pulse
depends upon the pulse duration and
the carrier frequency that is used.
These regularly repeating pulses
have a relatively long time delay
between them to allow the return echo
to be received before the next pulse is
transmitted.

t

τ

3rd pulse

2nd pulse

1st pulse

Transmitted pulses
Fig 3.9 Basic pulse radar

The inter pulse period (the time
between successive pulses) t is the
inverse of the pulse repetition
frequency fr or PRF. The pulse duration
or pulse width, τ, is a fraction of the
inter pulse period.
The inter pulse period t effectively
defines the maximum range of the
radar.
Example
The pulse repetition frequency
(PRF) is defined as

fr =

1
t

If the pulse period t is 500 microseconds, then the pulse repetition frequency is two thousand pulses per second.
In 500 microseconds, the radar pulses
will travel 150 kilometres. Considering
the return journey of an echo reflected
off a target, this gives a maximum theoretical range of 75 kilometres.
If the time taken for the return
journey is T, and c is the speed of light,
then the distance to the target is

R=

Txc
2

[Eq. 3.3]

39

b. Pulse doppler radar
The pulses transmitted by a standard
pulse radar can be considered as a very
short burst of continuous wave radar.
There is a single frequency with no
modulation on the signal for the duration of the pulse.
If the frequency of the waves of the
transmitted pulse is ft and the target is
moving towards the radar with velocity
v, then, as with the CW radar already
described, the frequency of the return
pulse will be ft + fdp , where fdp is the
doppler beat frequency. Similarly, the
received frequency will be ft - fdp if the
target is moving away from the radar.
Therefore, a pulse doppler radar can
be used to measure speed, distance and
direction.
The ability of the pulse doppler
radar to measure speed allows the system to ignore stationary targets. This is
also commonly called ‘moving target
indication’ or MTI radar.
In general, an MTI radar has accurate range measurement but imprecise
speed measurement, whereas a pulse
doppler radar has accurate speed measurement and imprecise distance measurement.

40

The velocity of the target in the
direction of the radar is calculated in
equation 3.4:

c =

c x fdp
λ x fdp
=
2 x ft
2
[Eq. 3.4]

This is the same calculation as for
CW radar. The distance to the target is
calculated by the transit time of the
pulse, equation 3.3.

R =

Txc
2

[Eq. 3.3]

As well as being used to monitor
civil and military aircraft movements,
pulse doppler radar is used in weather
forecasting. A doppler shift is measured
within storm clouds which can be distinguished from general ground clutter. It is also used to measure the
extreme wind velocities within a tornado or ‘twister’.

R

Fig 3.10 Pulse doppler radar provides target speed, distance and direction

f t + f dp

ft

Pulse doppler radar

3. Types of radar

41

c. Pulse compression and ‘Chirp’ radar

frequency

With pulse radar, a shorter pulse
duration enables better target resolution
and
therefore
higher
accuracy.
However, a shorter pulse needs a significantly higher peak power if the
range performance has to be maintained. If there is a limit to the maximum power available, a short pulse
will inevitably result in a reduced
range.
With limited peak power, a longer
pulse duration, τ , will provide more

radiated energy and therefore range but
(with a standard pulse radar) at the
expense of resolution and accuracy.
Pulse compression within a ‘Chirp’
radar is a method of achieving the
accuracy benefits of a short pulse radar
together with the power benefits of
using a longer pulse. Essentially, Chirp
radar is a cross between a pulse radar
and an FM - CW radar.

f1

f2
time

t2

t1

amplitude

τ

time

Fig 3.11 Chirp radar wave form. Chirp is a cross between pulse and FM - CW radar
42

3. Types of radar

Each pulse of a Chirp radar has linear frequency modulation and a constant amplitude.
The echo pulse is processed through
a filter that compresses the echo by
creating a time lag that is inversely

proportional to the frequency.
Therefore, the low frequency that
arrives first is slowed down the most
and the subsequent higher frequencies
catch up producing a sharper echo signal and improved echo resolution.

Time lag

Filter

Frequency
Long frequency modulated echo pulse
Compressed
signal
Fig 3.12 Pulse compression of chirp radar echo signal

Pulse compression of chirp radar echo signal
Another method of echo compression uses binary phase modulation
where the transmitted signal is specially encoded with segments of the pulse
either in phase or 180° out of phase.
The return echoes are decoded by a filter that produces a higher amplitude
and compressed signal.
The name ‘Chirp’ radar comes from
the short rapid change in frequency of
the pulse which is analogous to the
chirping of a bird song.

The above methods of radar detection are used widely in long range distance or speed measurement. In the
next chapter we look at which of these
methods can be applied to the unique
problems involved in measuring liquid
or solid levels within process vessels
and silos.

43

Part II
Radar antennas
Radar level installations

45

radar_applied_to_level_rb.qxd

15.01.2007

18:46

Seite 47

The benefits of radar as a level measurement technique are clear.
Radar provides a non-contact sensor
that is virtually unaffected by changes
in process temperature, pressure or the
gas and vapour composition within a
vessel.
In addition, the measurement accuracy is unaffected by changes in density, conductivity and dielectric constant
of the product being measured or by air
movement above the product.
The practical use of microwave
radar for tank gauging and process vessel level measurement introduces an
interesting set of technical challenges
that have to be mastered.
If we consider that the speed of light
is approximately 300,000 kilometres
per second. Then the time taken for

a radar signal to travel one metre
and back takes 6.7 nanoseconds or
0.000 000 006 7 seconds.
How is it possible to measure this
transit time and produce accurate vessel contents information?
Currently there are two measurement techniques in common use for
process vessel contents measurement.
They are frequency modulated continuous wave (FM - CW) radar and PULSE
radar
In this chapter we explain FM - CW
and PULSE radar level measurement
and compare the two techniques. We
discuss accuracy and frequency considerations and explore the technical
advances that have taken place in
recent years and in particular two wire,
loop powered transmitters.

47


15.01.2007

18:46

Seite 48

FM-CW, frequency modulated continuous wave
The FM - CW radar measurement
technique has been in use since the
1930's in military and civil aircraft
radio altimeters. In the early 1970's this
method was developed for marine use
measuring levels of crude oil in supertankers. Subsequently, the same technique was used for custody transfer
level measurement of large land based
storage vessels. More recently, FM CW transmitters have been adapted for
process vessel applications.
FM - CW, or frequency modulated
continuous wave, radar is an indirect
method of distance measurement. The
transmitted frequency is modulated
between two known values, f1 and f2,
and the difference between the transmitted signal and the return echo
signal, fd, is measured. This difference
frequency is directly proportional to the

transit time and hence the distance.
(Examples of FM - CW radar level
transmitters modulation frequencies are
8.5 to 9.9 GHz, 9.7 to 10.3 GHz and 24
to 26 GHz).
The theory of FM - CW radar is
simple. However, there are many practical problems that need to be
addressed in process level applications.
An FM - CW radar level transmitter
requires a voltage controlled oscillator,
VCO, to ramp the signal between the
two transmitted frequencies, f1 and f2.
It is critical that the frequency sweep is
controlled and must be as linear as possible. A linear frequency modulation is
achieved either by accurate frequency
measurement circuitry with closed loop
regulation of the output or by careful
linearisation of the VCO output including temperature compensation.

f2

frequency

Transmitted signal
fd
∆t

Received
signal
f1
t1

time

Fig 4.1 The FM - CW radar technique is an indirect method of level measurement.
fd is proportional to ∆t which is proportional to distance

48

f(t)

Directional
Coupler

Signal sampling
and
Fast Fourier transforms (FFT)

Frequency
Measurement

Intermediate
frequency
Amplifier

Filter

Mixer

f (t + Dt)

Directional
Coupler
f (t + Dt)

Fig 4.2 Typical block diagram of FM - CW radar. A very accurate linear sweep is required

Signal Microprocessor

Front end control function

Linear ramp generator

Voltage
Control

V(t)

Linear sweep
control loop

Voltage Controlled Oscillator VCO

f(t)


49


15.01.2007

FM - CW block diagram (Fig 4.2)
The essential component of a frequency modulated continuous wave
radar is the linear sweep control circuitry. A linear ramp generator feeds a
voltage controller which in turn ramps
up the frequency of the Voltage
Controlled Oscillator. A very accurate
linear sweep is required. The output
frequency is measured as part of the
closed loop control.
The frequency modulated signal is
directed to the radar antenna and

18:46

Seite 50

hence towards the product in the vessel. The received echo frequencies are
mixed with a part of the transmission
frequency signal. These difference frequencies are filtered and amplified
before Fast Fourier Transform (FFT)
analysis is carried out. The FFT
analysis produces a frequency spectrum on which the echo processing and
echo decisions are made.

Pic 2 Typical glass lined
agitated process
vessel. A radar
must be able to
cope with various
false echos from
agitatior blades
and baffles

Simple storage applications usually
have a large surface area with very little agitation, no significant false echoes
from the internal structure of the tank
and relatively slow product movement.
These are the ideal conditions for
which FM - CW radar was originally
developed.
However, in process vessels there is
more going on and the problems
become more challenging.

50

Low amplitude signals and false
echoes are common in chemical reactors where there is agitation and low
dielectric liquids.
Solids applications can be troublesome because of the internal structure
of the silos and undulating product surfaces which creates multiple echoes.
An FM - CW radar level sensor
transmits and receives signals simultaneously.


15.01.2007

18:46

Seite 51


fd1, -f d2 , -fd3, -fd4, -fd5

f2

f1

t1
Transmitted signal
Real echo signal
False echo signals
Fig 4.3a FM - CW radar level transmitters in an active process vessel

In an active process vessel, the various echoes are received as frequency
differences compared with the frequency of the transmitting signal. These frequency difference signals are received
by the antenna at the same time. The
amplitude of the real echo signals are
small compared with the transmitted
signal. A false echo from the end of the
antenna may have a significantly higher amplitude than the real level echo.
The system needs to separate and identify these simultaneous signals before
processing the echoes and making an
echo decision.
The separation of the various
received echo frequencies is achieved
using Fast Fourier Transform (FFT)
analysis. This is a mathematical proce-

dure which converts the jumbled array
of difference frequencies in the time
domain into a frequency spectrum in
the frequency domain.
The relative amplitude of each frequency component in the frequency
spectrum is proportional to the size of
the echo and the difference frequency
itself is proportional to the distance
from the transmitter.
The Fast Fourier Transform requires
substantial processing power and is a
relatively long procedure.
It is only when the FFT calculations
are complete that echo analysis can be
carried out and an echo decision can be
made between the real level echo and a
number of possible false echoes.

51


15.01.2007

18:46

Seite 52

Mixture of frequencies received by FM - CW radar

Signal amplitude

fd1, fd2, fd3, fd4, fd5 etc combined

Fig 4.3b combined echo frequencies are received simultaneously

Signal amplitude

Combination of mixed difference frequencies received by FM - CW radar
Individual difference frequencies fd1, f d2 , fd3, are shown

Fig 4.3c The individual frequencies must be separated from
the simultaneously received jumble of frequencies

52


15.01.2007

18:46

Seite 53


amplitude

Frequency spectrum echoes
Each echo is within an envelope curve of frequencies

frequency

Fig 4.4 FM - CW frequency spectrum after Fast Fourier transform. The Fast Fourier
transform algorithm converts the signals from the time domain into the frequency
domain. The result is a frequency spectrum of the difference frequencies. The
relative amplitude of each frequency component in the spectrum is proportional to
the size of the echo and the difference frequency itself is proportional to the
distance from the transmitter. The echoes are not single frequencies but a span
of frequencies within an envelope curve

Complex process vessels and solids
applications can prove too difficult for
some FM - CW radar transmitters.
Even a simple horizontal cylindrical
tank can pose a serious problem. This
is because a horizontal tank produces
many large multiple echoes that are
caused by the parabolic effect of the
cylindrical tank roof. Sometimes the
amplitudes of the multiple echoes are

higher than the real echo. The processors that carry out the FFT analysis are
swamped by different amplitude signals across the dynamic range all at the
same time. As a result, the FM - CW
radar cannot identify the correct echo.
As we shall see, this problem does
not affect the alternative pulse radar
technique.

53


15.01.2007

18:46

Seite 54

PULSE radar level transmitters
Pulse radar level transmitters provide distance measurement based on
the direct measurement of the running
time of microwave pulses transmitted
to and reflected from the surface of the
product being measured.
Pulse radar operates in the time
domain and therefore it does not
require the Fast Fourier transform
(FFT) analysis that characterizes FM CW radar.
As already discussed, the running
time for a distance of a few metres is
measured in nanoseconds. For this reason, a special time transformation pro-

cedure is required to enable these short
time periods to be measured accurately.
The requirement is for a ‘slow motion’
picture of the transit time of the
microwave pulses with an expanded
time axis. By slow motion we mean
milliseconds instead of nanoseconds.
Pulse radar has a regular and periodically repeating signal with a high pulse
repetition frequency (PRF). Using a
method of sequential sampling, the
extremely fast and regular transit times
can be readily transformed into an
expanded time signal.

Fig 4.5 Pulse radar operates purely within the time domain. Millions of pulses are
transmitted every second and a special sampling technique is used to produce a
‘time expanded’ output signal

54


15.01.2007

18:46

Seite 55


To illustrate this principle, consider
the sine wave signal in Fig 4.6. It is a
regular repeating signal with a period
of T1. If the amplitude (voltage value)
of the output of the sine wave is sampled into a memory at a time period T2

which is slightly longer than T1, then a
time expanded version of the original
sine wave is produced as an output.
The time scale of the expanded output
depends on the difference between the
two time periods T1 and T2.

T1
Periodic
Signal
(sine wave)
Sampling
signal

T2

Expanded
time signal

Fig 4.6 The principle of sequential sampling with a sine wave as an example.
The sampling period, T2, is very slightly longer than the signal period, T1. The
output is a time expanded image of the original signal

A common example of this principle
is the use of a stroboscope to slow
down the fast periodic movements of
rotating or reciprocating machinery.
Fig 4.7 shows how the principle of
Periodic
Signal
(radar echoes)

sequential sampling is applied to
pulse radar level measurement. The
example shown is a VEGAPULS transmitter with a microwave frequency of
5.8 GHz.

T1
Emission
pulse

Echo
pulse

T2
Sampling
signal

Fig 4.7 Sequential sampling of a pulse radar echo curve. Millions of pulses per second
produce a periodically repeating signal. A sampling signal with a slightly longer
periodic time produces a time expanded image of the entire echo curve
55


15.01.2007

18:46

This periodically repeating signal
consists of the regular emission pulse
and one or more received echo pulses.
These are the level surface and any
false echoes or multiple echoes. The
transmitted pulses and therefore the
received pulses have a sine wave form
depending upon the pulse duration. A
5.8 GHz pulse of 0.8 nanosecond duration is shown in Fig 4.8.
The period of the pulse repetition is
shown as T1 in Fig 4.7. Period T1 is

Seite 56

the same for the emission pulse repetition as for any echo pulse repetition as
shown.
However, the sampling signal
repeats at period of T2 which is slightly longer in duration than T1. This is
the same time expansion procedure by
sequential sampling that has already
been described for a sine wave. The
factor of the time expansion is determined by T1 / (T2-T1).

Fig 4.8 Emission pulse (packet).
The wave form of the 5.8
GHz pulse with a pulse
duration of 0.8
nanoseconds

Example
The 5.8 GHz, VEGAPULS radar level transmitter has the following pulse repetition rates.
Transmit pulse 3.58 MHz
Reference pulse 3.58 MHz - 43.7 Hz
Therefore the time expansion factor
is 81920 giving a time expanded pulse
repetition period of 22.88 milliseconds.
There is a practical problem in sampling the emission / echo pulse signals
of a short (0.8 nanosecond) pulse at 5.8
GHz. An electronic switch would need
to open and close within a few picoseconds if a sufficiently short value of the
5.8 GHz sine wave is to be sampled.
These would have to be very special
and expensive components.

56

T1 = 279.32961 nanoseconds
T2 = 279.33302 nanoseconds
The solution is to combine sequential sampling with a ‘cross correlation’
procedure.
Instead of very rapid switch sampling, a sample signal of exactly the
same profile is generated but with a
slightly longer time period between the
pulses.
Fig 4.9 compares sequential sampling by rapid switching with sequential sampling by cross correlation with
a sample pulse.


15.01.2007

18:46

Seite 57


Emission / Echo pulse

Sample signal

Sampling with picosecond switching

Sampling by cross correlation with a
sample pulse

Fig 4.9 Comparison of switch sampling with ‘cross correlation’ sampling. The pulse
radar uses cross correlation with a sample pulse. This means that rapid ‘picosecond’ switching is not required

Instead of taking a short voltage
sample, cross correlation involves multiplying a point on the emission or echo
signal by the corresponding point on
the sample pulse. The multiplication
leads to a point on the resultant signal.
All of these multiplication results, one
after the other, lead to the formation of
the complete multiplication signal.
Fig 4.10 shows a short sequence of
multiplications between the received
signal (E) and the sampling pulse
signal (M). The resultant E x M curves
are shown on page 58.
Then the E x M curve is integrated
and represented on the expanded curve
as a dot. The sign and amplitude of the

signal on the time expanded curve
depends on the sum of the area of the
E x M curve above and below the zero
line. The final integrated value corresponds directly to the time position of
the received pulse E relative to the
sample pulse M.
The received signal E and sample
signal M in Fig 4.10 are equivalent to
the periodic signal (sine wave) and
sample signal in Fig 4.6. The result of
the integration of E x M in Fig 4.10 is
directly analogous to the expanded
time signal in Fig 4.6.

57


15.01.2007

18:46

Seite 58

E
M
ExM

max
Integral
ExM

0
min

Fig 4.10 Cross correlation of the received signal E and the sampling M.
The product E x M is then integrated to produce the expanded time curve. The
technique builds a complete picture of the echo curve

The pulse radar sampling procedure
is mathematically complicated but a
technically simple transformation to
achieve. Generating a reference signal
with a slightly different periodic time,
multiplying it by the echo signal and
integration of the resultant product are
all operations that can be handled easily within analogue circuits. Simple, but
good quality components such as diode
mixers for multiplication and capacitors for integration are used.
58

This method transforms the high
frequency received signal into an accurate picture with a considerably
expanded time axis. The raw value
output from the microwave module is
an intermediate frequency that is similar to an ultrasonic signal. For example
the 5.8 GHz microwave pulse becomes
an intermediate frequency of 70 kHz.
The pulse repetition frequency (PRF)
of 3.58 GHz becomes about 44 Hz.


15.01.2007

18:46

Seite 59


amplitude

Pulse echoes in a process vessel are separated in time

t1 t 2

t3

t4

t5

time
transmit pulse

Fig 4.12 With a pulse radar, all echoes (real and false) are separated in time. This allows
multiple echoes caused by reflections from a parabolic tank roof to be easily
separated and analysed

Pulse radar operates entirely within
the time domain and does not need the
fast and expensive processors that
enable the FM - CW radar to function.
There are no Fast Fourier Transform
(FFT) algorithms to calculate. All of
the pulse radar processing is dedicated
to echo analysis only.
Part of the pulse radar transmission
pulse is used as a reference pulse that
provides automatic temperature compensation within the microwave module circuits.
The echoes derived from a pulse
radar are discrete and separated in time.
This means that pulse radar is better
equipped to handle multiple echoes and
false echoes that are common in
process vessels and solids silos.

Pulse radar takes literally millions of
‘shots’ every second. The return echoes
from the product surface are sampled
using the method described above. This
technique provides the pulse radar with
excellent averaging which is particularly important in difficult applications
where small amounts of energy are
being received from low dielectric and
agitated product surfaces.
The averaging of the pulse technique
reduces the noise curve to allow smaller echoes to be detected. If the pulse
radar is manufactured with well
designed circuits containing good quality electronic components they can
detect echoes over a wide dynamic
range of about 80 dB. This can make
the difference between reliable and
unreliable measurement.

59

15.01.2007

18:46

Seite 60

Fig 4.11 Block diagram of PULSE radar microwave module


60


15.01.2007

18:46

Seite 61


Pulse block diagram - (Fig 4.11)
The raw pulse output signal (intermediate frequency) from the pulse
radar microwave module is similar, in
frequency and repetition rate, to an
ultrasonic signal.
This pulse radar signal is derived in
hardware. Unlike FM - CW radar,
PULSE does not use FFT analysis.
Therefore, pulse radar does not need
expensive and power consuming
processors.
The pulse radar microwave module
generates two sets of identical pulses
with very slightly different periodic
times. A fixed oscillator and pulse former generates pulses with a frequency
of 3.58 MHz. A second variable oscillator and pulse former is tuned to a

frequency of 3.58 MHz minus 43.7 Hz
and hence a slightly longer periodic
time. GaAs FET oscillators are used to
produce the microwave carrier frequency of the two sets of pulses.
The first set of pulses are directed
to the antenna and the product being
measured. The second set of pulses are
the sample pulses as discussed in the
preceding text.
The echoes that return to the antenna are amplified and mixed with the
sample pulses to produce the raw, time
expanded, intermediate frequency.
Part of the measurement pulse signal is used as a reference pulse that
provides automatic temperature compensation of the microwave module
electronics.

Pic 3 Two wire pulse radar level transmitter mounted in a process reactor vessel

61


15.01.2007

18:46

Seite 62

Choice of frequency
Process radar level transmitters
operate at microwave frequencies
between 5.8 GHz and about 26 GHz.
Manufacturers have chosen frequencies
for different reasons ranging from
licensing considerations, availability of
microwave components and perceived
technical advantages.
There are arguments extolling the
virtues of high frequency radar, low

frequency radar and every frequency
radar in between.
In reality, no single frequency is
ideally suited for every radar level
measurement application. If we compare 5.8 GHz radar with 26 GHz radar,
we can see the relevant benefits of high
frequency and low frequency radar.

2.6 GHz

5.8 GHz

Fig 4.14 Comparison of 5.8 GHz and 26 GHz radar antenna sizes. These instruments
have almost identical beam angles. However this is not the full picture when it
comes to choosing radar frequencies

62


15.01.2007

18:46

Seite 63

Antenna size - beam angle
The higher the frequency of a radar
level transmitter, the more focused the
beam angle for the equivalent size
antenna.
With horn antennas, this allows
smaller nozzles to be used with a more
focused beam angle.
For example, a 1½" (40 mm) horn
antenna radar at 26 GHz has approximately the same beam angle as a 6"
(150 mm) horn antenna at 5.8 GHz.
However, this is not the complete
picture. Antenna gain is dependent on
the square of the diameter of the antenna as well as being inversely proportional to the square of the wavelength.

Antenna gain is proportional to:2
diameter
wavelength 2
Antenna gain also depends on the aperture efficiency of the antenna.
Therefore the beam angle of a small
antenna at a high frequency is not
necessarily as efficient as the equivalent beam angle of a larger, lower frequency radar. A 4" horn antenna radar
at 6 GHz gives excellent beam focusing.
A full explanation of antenna gain
and beam angles at different frequencies is given in Chapter 5 on radar
antennas.

Focusing at different frequencies

5 GHz

10 GHz

15 GHz

20 GHz

25 GHz

Fig 4.13 For a given size of antenna, a higher frequency gives a more focused beam

63


15.01.2007

18:46

Seite 64

Antenna focusing and false echoes
A 26 GHz beam angle is more
focused but, in some ways, it has to be.
The wavelength of a 26 GHz radar is
only 1.15 centimetres compared with a
wavelength of 5.2 centimetres for a
5.8 GHz radar.
The short wavelength of the 26 GHz
radar means that it will reflect off many

small objects that may be effectively
ignored by the 5.8 GHz radar. Without
the focusing of the beam, the high frequency radar would have to cope with
more false echoes than an equivalent
lower frequency radar.

Fig 4.15 a Low frequency radar has a wider beam
angle and therefore, if the installation
is not optimum, it will see more false
echoes. Low frequencies such as
5.8 GHz or 6.3 GHz tend to be more
forgiving when it come to false echoes
from the internal structure of a vessel
or silo

Fig 4.15 b High frequency radar has a much
narrower beam angle for a given
antenna size. The narrower beam angle
is important because the short
wavelength of the higher frequencies,
such as 26 GHz, reflect more readily
from the internal structures such as
welds, baffles, and agitators.
The sharper focusing avoids this
problem

64


15.01.2007

18:46

Seite 65

Agitated liquids and solid measurement
High frequency radar transmitters
are susceptible to signal scatter from
agitated surfaces. This is due to the signal wavelength in comparison to the
size of the surface disturbance.
The high frequency radar will
receive considerably less signal than an
equivalent 5.8 GHz radar when the liq-

uid surface is agitated. The lower
frequency transmitters are less affected
by agitated surfaces.
It is important that, whatever the frequency, the radar electronics and echo
processing software can cope with very
small amplitude echo signals. As discussed, pulse radar has an advantage in
this area no matter what the frequency.

Fig 4.16 High frequency radar transmitters are
susceptible to signal scatter from
agitated surfaces. This is due to the
signal wavelength in comparison to the
size of the surface disturbance. It is
important that radar electronics and
echo processing software can cope with
very small amplitude echo signals.
By comparison, 5.8 GHz radar is not as
adversely affected by agitated liquid
surfaces. Lower frequency radar is
generally better suited to solid level
applications

Condensation and build up

Steam and dust

High frequency radar level transmitters are more susceptible to condensation and product build up on the antenna. There is more signal attenuation at
the higher frequencies, such as 26 GHz.
Also, the same level of coating or condensation on a smaller antenna naturally has a greater effect on the performance.
A 6" horn antenna with 5.8 GHz frequency is virtually unaffected by condensation. Also, it is more forgiving of
product build up.

Lower frequencies such as 5.8 GHz
and 6.3 GHz are not adversely affected
by high levels of dust or steam. These
frequencies have been very successful
in applications ranging from cement,
flyash and blast furnace levels to steam
boiler level measurement.
In steamy and dusty environments,
higher frequency radar will suffer from
increased signal attenuation.

65


15.01.2007

Foam
The effect of foam on radar signals
is a grey area. It depends a great deal
on the type of foam including the foam
density, dielectric constant and conductivity. However, low frequencies such
as 5.8 GHz and 6.3 GHz cope with low
density foam better than higher frequencies such as 26 GHz.
For example, a 26 GHz radar signal
will be totally attenuated by a very thin
detergent foam on a water surface. A
5.8 GHz radar signal will see through
this type of foam and continue to see
the liquid surface as the foam thickness
increases to 150 mm or even 250 mm.

18:46

Seite 66

However, the thickness of foam will
cause a small measurement error
because the microwaves slow down
slightly as they pass through the foam.
When foam is present, it is important to provide the radar manufacturer
with as much information as possible
on the application.

Minimum distance
Higher frequency radar sensors have
a reduced minimum distance when
compared with the lower frequencies.
This can be an additional benefit when
measuring in small vessels and stilling
tubes.

Summary of the effects of radar frequency
Better focusing at higher emitting frequency means:
higher antenna gain (directivity)
less false echoes
reduced antenna size

focusing

.
.
.

5 GHz

10 GHz

15 GHz
frequency range

Fig 4.17 Focusing and radar frequency

66

20 GHz

25 GHz


15.01.2007

18:46

Seite 67


reduced signal caused by damping

Reduced signal strength caused by
damping at higher emitting frequency
caused by:

.
.
.

5 GHz

10 GHz

condensation
build - up
steam and dust

15 GHz

20 GHz

25 GHz

frequency range
Fig 4.18 Signal damping and radar frequency
Higher damping caused by agitated
product surface

reflection from medium

.
.
.

5 GHz

10 GHz

wave movement
material cones with solids
signal scattered

15 GHz

20 GHz

25 GHz

frequency range
Fig 4.19 Signal strength from agitated and undulating surfaces and radar frequency
67


15.01.2007

18:46

Seite 68

Accuracy

Pulse radar bandwidth

There is no inherent difference in
accuracy between the FM - CW and
PULSE radar level measurement techniques.
In this book, we are concerned
specifically with process level measurement where ‘process accurate’ and
cost effective solutions are required.
The achievable accuracy of a
process radar depends heavily on the
type of application, the antenna design,
the quality of the electronics and echo
processing software employed.
The niche market for custody transfer level measurement applications is
outside the scope of this book. These
custody transfer radar ‘systems’ are
used in bulk petrochemical storage
tanks. Large parabolic or planar array
antennas are used to create a finely
focused signal. A lot of processing
power and on site calibration time is
used to achieve the high accuracy.
Temperature and pressure compensation are also used.

The carrier frequency of a pulse
radar varies from 5.8 GHz to about
26 GHz.
The pulse duration is important
when it comes to resolving two adjacent echoes. For example, a one
nanosecond pulse has a length of about
300 mm. Therefore, it would be difficult for the radar to distinguish between
two echoes that are less than 300 mm
apart. Clearly a shorter pulse duration
provides better range resolution.
An effect of a shorter pulse duration
is a wider bandwidth or spectrum of
frequencies.
For example, if the carrier frequency
of a pulse is 5.8 GHz and the duration
is only 1 nanosecond, then there is a
spectrum of frequencies above and
below the nominal carrier frequency.
The amplitude of the pulse spectrum of
frequencies changes according to a

Range resolution and
bandwidth
In process level applications, both
FM - CW and PULSE radar work with
an ‘envelope curve’. The length of this
envelope curve depends on the bandwidth of the radar transmitter. A wider
bandwidth leads to a shorter envelope
curve and therefore improved range
resolution. Range resolution is one of a
number of factors that influence the
accuracy of process radar level transmitters.

68

sin x
x
curve.
The shape of this curve is shown in
Fig 4.21.
The null to null bandwidth BWnn of
a pulse radar is equal to

2

τ

where τ is the pulse duration.
It is clear from the curve that the
amplitude of frequencies reduces significantly away from the main pulse
frequency.


15.01.2007

18:46

Seite 69

pulse frequency
5.8 GHz

4.8 GHz

shorter pulse
better range resolution

Fig 4.20 Pulse radar range resolution.
The guaranteed range
resolution is the length of the
pulse. A shorter pulse has a
wider bandwidth and better
range resolution

6.8 GHz

bandwidth BW nn,
2
equal to τ

Fig 4.21 The null to null bandwidth
BWnn of a radar pulse is equal
to 2 / τ where τ is the pulse
duration. Example a 5.8 GHz
radar with a pulse duration of
one nanosecond has a null to
null bandwidth of 2 GHz

Pulse radar envelope curve
Fig 4.22 shows how a pulse radar
echo curve is used in process level
measurement.
A higher frequency pulse with a
shorter pulse duration will allow better
range resolution and also better accuracy because the leading edge of the
envelope curve is steeper.

Fig 4.22 Envelope curve with pulse radar

High frequency, short
duration pulse

Lower frequency pulse with
longer duration

Fig 4.23 A shorter pulse duration gives better range resolution. The combination of
shorter pulse duaration and higher frequency allows better accuracy because the
leading edge of the envelope curve is steeper

69


15.01.2007

18:46

FM-CW radar bandwidth
The bandwidth of an FM - CW radar is
the difference between the start and
finish frequency of the linear frequency
modulation sweep.
Unlike pulse radar, the amplitude of the
FM - CW signal is constant across the
range of frequencies.

Seite 70

A wider bandwidth produces narrower
difference frequency ranges for each
echo on the frequency spectrum. This
leads to better range resolution in the
same way as with shorter duration pulses with pulse radar.
This is explained in the following diagrams and equations.

frequency

fd =

∆F x 2R
Ts x c

fd

∆F
Ts
R
fd
c

∆F

[Eq. 4.1]

bandwidth
sweep time
distance
difference frequency
speed of light

time
Ts

Fast Fourier Transform
The FAST FOURIER
TRANSFORM produces a
frequency spectrum of all echoes
such as that at fd.
There is an ambiguity ∆fd for each
echo fd.

amplitude
fd

∆fd =

2
Ts
[Eq. 4.2]

∆fd

70

frequency


15.01.2007

18:46

Seite 71

The ambiguity of the distance R,
is ∆ R

∆fd
fd

∆R
R

=

2
Ts
∆F x 2 R
Ts x c

∆R
R

=

c
∆F x R

∆R

R

∆R

=

=

c
∆F

∆R
R

amplitude

distance

Fig 4.24 to 4.26 - FM - CW range resolution

[Eq. 4.3]

From equation 4.3, it can be seen
that with an FM - CW radar the range
resolution ∆R is equal to:-

c
∆F
Therefore, the wider the bandwidth, the
better the range resolution.
Examples:
A linear sweep of 2 GHz has a range
resolution of 150 mm whereas a 1 GHz
bandwidth has a range resolution of
300 mm.

In process radar applications, each
echo on the frequency spectrum is
processed with an envelope curve. The
above equations (Equations 4.1 to 4.3)
show that the Fast Fourier Transforms
(FFTs) in process radar applications do
not produce a single discrete difference
frequency for each echo in the vessel.
Instead they produce a difference frequency range ∆fd for each echo within
an envelope curve. This translates into
range ambiguity.

71


15.01.2007

18:46

Seite 72

FM - CW frequency spectrum - bandwidth and range resolution
Frequency spectrum - narrow bandwidth of linear sweep
amplitude
envelope curves
around echoes

frequency
Frequency spectrum - wide bandwidth of linear sweep
amplitude
envelope curves
around echoes

frequency
Fig 4.28 Illustration of envelope curve around the frequency spectram of FM - CW
radars. The same four echoes are shown for radar transmitters with different
bandwidths. An improvement in the range resolution is achieved with a wider
bandwidth of the linear sweep

Other influences on accuracy
As we have demonstrated, FM - CW
and PULSE process radar transmitters
use an envelope curve for measurement. A wider bandwidth produces better range resolution. The correspondingly short echo will have a steep slope
and therefore a more accurate measurement can be made. Other influences on
accuracy include signal to noise ratio
and interference.

72

A high signal to noise ratio allows
more accurate measurement while
interference effects can cause a disturbance of the real echo curve leading to
inaccuracies in the measurement.
Choice of antenna and mechanical
installation are important factors in
ensuring that the optimum accuracy is
achieved.


15.01.2007

18:46

Seite 73


High accuracy radar

FM - CW radar

High accuracy of the order of
+ 1 mm is generally meaningless in an
active process vessel or a solids silo.
For example, a typical chemical reactor
will have agitators, baffles and other
internal structures plus constantly
changing product characteristics.
Although custody transfer level
measurement applications are not in the
scope of this book, this section discusses how a higher accuracy can be
achieved.

The fundamental requirement for an
accurate FM - CW radar is an accurate
linear sweep of the frequency modulation.
As with the pulse radar, it is possible
to look inside the envelope curve of the
frequency spectrum if the application
has a simple single echo that is characteristic of a liquids storage tank. This is
achieved by measuring the phase angle
of the difference frequency. However,
this is only practical with custody
transfer applications where fast and
expensive processors are used with
temperature and pressure compensation.

Pulse radar
For most process applications, measurement relative to the pulse envelope
curve is sufficient. However, if the liquid level surface is flat calm and the
echo has a reasonable amplitude, it is
possible to look inside the envelope
curve wave packet at the phase of an
individual wave.
However, the envelope curve of a
high frequency radar with a short pulse
duration is sufficiently steep to produce
a very accurate and cost effective level
transmitter for storage vessel applications.

frequency error

f2

f2
t1
Fig 4.30 It is essential that the linear
sweep of the FM - CW radar is
accurately controlled

Fig 4.29 Higher accuracy of pulse radar
level transmitters can be
achieved by looking at the phase
of an individual wave within the
envelope curve. This is only
practical in slow moving storage
tanks
73

Vega radar book

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Vega radar book

Similar to Vega radar book (20)

Recently uploaded

Recently uploaded (20)

Vega radar book