CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
SIMULATION AND ANALYSIS OF A RADAR MODULATOR
A graduate project submitted in partial satisfaction of the
requirements for the degree of Master of Science in
Engineering
by
Arnoldo Silva
May, 1987
The graduate Project of Arnoldo Silva is approved:
Prof. Tarek Shraibati
Chair
California State University, Northridge
ii
ACKNOWLEDGMENTS
I wish to express my gratitude to the professors who
served on my graduate committee, with special thanks to my
advisor, Professor Nagwa Bekir for her guidance in this
project.
I
also wish to thank Professor Sembian Rangarajan
for his advice and friendship and Professor Tarek Shraibati
for his contributions.
To Mr. Thayer Shearin, I express heartfelt thanks
for all his valuable contributions and friendship.
Finally, I
thank my wife, Dolores, for her patience
in seeing me along and my parents, Arnalda and Guadalupe,
who were there to start me off a long time ago.
.
d
iv
TABLE OF CONTENTS
Page
Dedication
iii
Acknowledgment
iv
Abstract
ix
Chapter
Chapter
Chapter
Chapter
1.1
1.2
1.3
Introduction
Scope
Limitations
Objectives
1
1
1
2
2
2.1
2.2
2.2.1
2.2.2
2.2.3
2.2.4
The Radar Modulator
General Discussion
Modulator Systems Considerations
General Modulator Considerations
Transmitter Power
Bandwidth
Pulse Shape
3
3
3
3.1
3.2
3.2.1
The Project Modulator
Requirements
Modulator Description
Modulator Block Diagrams
10
10
4
Device Modeling
Microwave High-Power Devices
Cross-Field Amplifiers
General Description
Amplitron Operation Theory
The CFA Model
Project CFA Model Parameters
Pulse Transformers
General Discussion
PT Equivalent Circuit
PT Parameters
Stray Reactances
Load Side Strays
Primary Side Strays
Pulse Generators and Snubbers
The Current Source Generator
Snubbers
17
17
17
19
20
23
25
28
28
1
4.1
4.2
4.2.1
4.2.2
4.2.3
4.3
4.4
4.4.1
4.4.2
4.4.3
4.5
4.5.1
4.5.2
4.6
4.6.1
4.6.2
f}
v
3
3
4
5
7
11
11
30
38
39
39
40
41
41
44
Page
Chapter
5
5.1
5.2
5.3
5.4
Simulation of Modulator
Basic Modulator Schematic
Computer Model
Computer Results
The z Match
0
46
46
46
50
53
Chapter
6
6.1
6.2
Conclusions
General Discussion
Application
59
59
60
61
References
vi
LIST OF FIGURES
Page
1.
Pulse Waveform Definition
2.
Simplified Block Diagram
12
3.
Detailed Block Diagram
14
4.
Family Tree of Crossed-Field Amplifiers
18
5.
Backward Wave CFA Interaction
21
6.
Typical CFA Mode Boundaries
24
7.
CFA Voltage Current Relationship
26
8.
Biased-Diode Model
27
9.
Biased-Diode Model with Parameters
29
10.
Ideal Transformer
31
11.
PT With L
33
12.
PT With Non-Idealizing Elements
35
13.
PT Model
37
14.
Modulator Schematic
47
15.
Computer Model
48
16.
Computer Run of CFA Voltage/Current
51
17.
CFA Voltage and Current Rise Times
52
18.
CFA Voltage and Current with Lr = ro
54
19.
2:1
z0
1
and Winding Resistance
8
57
Mismatch
vii
LIST OF TABLES
Page
1.
Current Source Pulse Generator Parameters
42
2.
CFA Diode Parameters
49
viii
ABSTRACT
SIMULATION AND ANALYSIS
OF A RADAR MODULATOR
by
Arnoldo Silva
Master of Science in Electrical Engineering
A computer aided modeling method is described in
which important modulator pulse parameters such as
bandwidth and pulse droop are controlled.
The modulator is
examined from the high power video switching circuits to
the microwave RF amplifier.
By using an accurate model and
analyzing output numerical results, the attendant design
risks are reduced.
ix
Chapter 1
INTRODUCTION
1.1 Scope
The "Simulation and Analysis of a Radar Modulator"
hereinafter referred to as the "Project", was used to
satisfy the requirements for the Masters Degree in
Electrical Engineering at the California State University
at Northridge, Ca. June, 1986.
The work was performed by the author at ITT Gilfillan,
Van Nuys, Ca. in conjunction with this writing.
The
numerical results presented are applicable only to the
specific example used.
1.2 Limitations
Since the goal here is to focus on the modulator, we
will not treat other parts of a transmitter sub-system that
are necessarily required.
Therefore, treatment will be
limited to the following:
A) Power
B) Bandwidth
C) Pulse shape
In effect, the modulator will be examined as a
"pulser", where the desired pulse is the common rectangular
pulse.
This by far is the most common of pulse shapes
found in actual practice.
1
2
Modeling shall be limited to the following devices:
D) Crossed-Field Amplifiers {CFA's)
E) Pulse Transformers {PT's)
F) Stray reactive elements {Inductive and Capacitive)
The limitations will serve to help sharpen the focus on
the modulator at hand.
1.3 Objectives
The objective of the Project is to demonstrate how
system requirements can be translated into hardware design
requirements.
This would minimize then, the problems
associated with a "trial and error" approach.
very costly to redesign a modulator.
It can be
For instance, it
might take 3-6 months to redesign and fabricate a PT.
It
would be much simpler and more efficient to design the PT
and modulator by computer and then correct or adjust any
parameters that might be "off."
The benefits should be
obvious.
The objective of the Project is to show how this
modeling approach can be done in a specific case, and, as a
corollary, serve as a springboard to different cases •
."
Chapter 2
RADAR MODULATORS
2.1 General Discussion
A radar system is composed of many sub-systems and a
major sub-system is the transmitter group.
transmitter are many functional sub-groups.
Within the
We will be
examining the modulator sub-group along with its associated
RF amplifier.
The modulator provides the high power video
pulse which modulates or pulses the RF amplifier.
The RF
amplifier then serves as the load for the modulator.
The
RF amplifier amplifies the RF to be transmitted at the
antenna.
The power transmitted PT seen in the radar
equation is the power output at the antenna.
This is not
generally equal to the modulator power P mo d used to pulse
the RF amplifier.
Section 2.2 shows in a simplified manner
how some basic parameters are related to system objectives.
2.2 Modulator Systems Considerations
2.2.1 General Modulator Considerations
Modulator requirements along with associated RF
amplifier requirements interact intimately to meet the
transmitter requirements to in turn meet system
specifications.
We will only be concerned with those
factors that directly affect the output pulse.
For our
purposes, these factors are Power, Bandwidth and Pulse
shape.
3
f)
4
2.2 Transmitter Power
There are practical limits to how much power can be
made available for transmission.
up, so do cost and complexity.
In general, as power goes
A major cost item of a
radar is the transmitter and so it is essential to be
designed properly (i.e., efficiently and reliably).
The
peak power can be defined as the instantaneous power
averaged over the pulsewidth t. for a train of rectangular
pulses, an average power may be defined as
P ave
=
PT X du
(1)
where du represents the duty cycle of the radar.
Duty
cycle is defined as the ratio of pulse width to interpulse
period.
The peak energy transmitted is
ET
=
PT X t
where energy is in Joules.
(2)
An important point here that
can be overlooked is that is is the Energy transmitted per
pulse regardless of pulse shape) that is important in
establishing radar performance in the Radar Equation with
respect to detectability.
For instance, it is easy to see
that transmitting a pulse of high peak power and low pulsewidth is equivalent, in energy, to transmitting a pulse of
half the peak power at twice the pulsewidth.
What is
5
important for detection then is the ratio of signal energy
noise power per unit of bandwidth [2].
Other
considerations will determine pulsewidths, rise/fall times
and shape.
Modulator power requirements are primarily dictated by
the load.
In the case of a CFA, the peak power required
may be arrived at by using the specified values of voltage
and current.
If the nominal peak operating voltage of the
CFA is say, 29 KV, and the nominal pulse current is 2 A
then the peak power required is 20 KV x 2 A
=
40 KW.
In
words, the peak power required at the tube is simply the
product of its operating voltage and current.
The average
power is the peak power multiplied by the duty cycle.
In an actual design, the modulator would have to be
able to deliver more energy than called out by the above.
This is to ensure adequate design margin due to any
variations in modulator circuit performance, tube variances
line losses and other factors.
2.2.3 Bandwidth
The output bandwidth of a radar system is an important
parameter that impacts the transmitter design directly.
This is because the reciprocal of bandwidth B can be
approximately equated to the rise time of the transmitted
pulse.
That is,
t
.
r1se
= B-1
(3)
6
The "ideal" rectangular pulse implies zero rise and
fall times thus requiring infinite B, a physical
impossibility.
times.
All realizable pulses have finite rise/fall
Range accuracy can be defined as the precision with
which a target is located.
Accuracy can be improved if the
error in time measured to and from a target is reduced.
This will give a more accurate measure of the distance
(range) to the target.
[
It can be stated that
(~;::::)] 1/2
where
--------2
(ATmeas)
t
=
.
r1se
-------( 2 S/N) 1/2
( 4)
is the RMS error in
the time delay measured to the target and back and S/N is
the signal-to-noise IF power ratio [2].
From a systems
point of view, EQ. 4 shows that to minimize the error of
~Tmeas'
the rise time needs to be reduced or the S/N
term increased.
In the limit, the rise time could approach
zero or the S/N term infinity thus assuring exact range
determination.
This is not realizable and even good range
determination may not be practical or desired depending on
system requirements.
In this simplified view, we have
shown that rise/fall is an important parameter.
with this criteria is pulse shape.
next.
Associated
This is considered
7
2.2.4 Pulse Shape
Pulse fidelity can be defined as the ability to control
and maintain the output waveform in the desired or required
condition (shape) to meet system objectives.
Fig. 1 shows
a realistic pulse waveform often seen in actual practice.
Judicious waveform design at the system level can impact
the overall cost and efficiency of a radar set because the
transmitter is often the major cost item.
Pulsewidth, for instance, can be directly related to
range resolution as
R
res
(5)
= ct/2
where t is the transmitted pulsewidth
and c is the speed of light
Resolution is the ability to resolve or distinguish two
targets by the distance given in EQ. 5.
In this simplified
view, pulse compression is not considered.
The pulse should be as flat in amplitude and phase as
possible.
controlled.
Thus, pulse droop should be carefully
If the droop were great enough it could affect
the radar's detection capabilities.
Likewise, pulse
overshoot should be controlled to minimize the occurrence
of spurious outputs by the tube.
These are a few simple
examples of how the output pulse can be related to system
objectives.
These will be explored more fully later.
In
8
b
TANGENT TO
/TRAILING EDGE
\
!
-- - ---
l
w
(.?
~
f-
_J
\
E
0
>
I
I
I
AXISOF,OSCILLATIONS
I 1
0.9 E
!
TIME
+
THE VARIOUS PORTIONS OF THE REPRESENTATIVE VOLTAGE PULSE SHOWN IN
FIGURE 1 ARE DEFINED AS FOLLOWS:
E- PULSE VOLTAGE (IN VOLTS)
e- BACKSWING (IN VOLTS)
a- RISE TIME (IN MICROSECONDS)
f - RETURN SWING (IN VOLTS)
b- OVERSHOOT (IN VOLTS)
g- START OF FALL TIME
c- DROOP (IN VOLTS)
t - PULSE DURATION (IN
d- FALL TIME (IN MICROSECONDS)
MICROSECONDS)
NOTE A:
PULSE CURRENT- IF THE CURVE OF FIGURE 1
IS ASSUMED TO BE OF CURRENT VS. TIME,
THE PULSE CURRENT WOULD BE REPRESENTED
BY E. A SHELF MAY APPEAR ON THE LEADING
EDGE OF A CURRENT PULSE, BUT IT IS TO BE
DISREGARDED IN THE MEASUREMENT OF RISE
TIME. LEADING EDGE SHOULD BE EXTRAPOLATED
TO TIME AXIS, AND RISE TIME MEASURED STARTING
WITH 0.1 E.
Figure 1.
Pulse Waveform Definition
0.9 E
[10]
9
the next chapter we examine the Project modulator
requirements.
'
t)
Chapter 3
THE PROJECT MODULATOR
3.1
Requirement~
To set the stage for simulating and analyzing the
performance of the modulator, we must first specify the
performance objectives.
and specified.
First, the RF amplifier is given
In this case it is to be a Crossed-Field
Amplifier (CFA) whose nominal power output is 140 KW at
S-band (approximately 3GHZ).
Its pulsed operating levels
are specified at 14KV and 22A.
values.
These are nominal peak
The modulator peak power requirement at the CFA is
then 14KV x 22A
=
308KW.
The nominal modulator
requirements are listed below.
Nominal Modulator Requirements
A)
Duty. • • . • . . . . . . . . • . . • . . . . . • . . . . . • . . . . . . . . . . . . . . .
. 002
B)
Pulsewidth......................................
6.5us
C)
Peak Power .••••••••.•.•••••••••••••••••••••••••.
308KW
D)
Rise/Fall time .•.•••.•.•••••.••••••.••..•..•••••
250ns
Additional pulse performance requirements are as
follows:
E)
Pulse Overshoot ••••••••...•••••.•..••.••...•••••
200V
F)
Current Pulse Droop •••••••••••••••••••••••••••••
2%
10
11
Again, note that the peak power to be delivered by the
modulator is at the 14KV level with 22 amperes of peak
current when pulsed.
3.2 Modulator Description
The type of modulator being examined here is the so
called "hard-tube" modulator although using the term
"active-switch" would probably be more appropriate since
the actual switching elements are active solid-state FET
devices.
These devices are paralleled to switch the high
energy video pulse required by the CFA.
Older modulators
would often use gas-thyratron switches or similar devices
to gate the pulses and hence the name "hard-tube" [1],[2].
The general trend in current radar technology is toward the
solid-state active switching technology.
Active-switch
type modulators offer the advantages of pulsewidth agility
and reliability by redundancy (many devices in parallel).
The disadvantages are that the modulator becomes more
complex and costly.
3.2.1 Modulator Block Diagrams
The block diagram of the modulator is as shown in Fig.
2 where major components are shown.
These major components
are the active switching circuits, pulse transformer, high
voltage cable and the CFA tube.
In this configuration, one
side of the PT secondary is grounded so that the pulse
return is through the anode of the tube (which is at the
.Lno :::ll:l
3l8'V~
l
Nl:::ll:l
.ld
l:IO.l'Vl:I3N3E>
13
ground potential).
negative.
Consequently, the CFA cathode is pulsed
Also shown is the high voltage power supply
which provides the energy required for pulsing.
Although
we will not examine the high voltage power supply per se,
we will be looking at the energy storage devices
(capacitors) as they can play a major role in the modulator
performance.
We will take note of the DC operating level
of the power supply since this is required to be known in
establishing modulator operating points.
Fig. 3 is a more
detailed block diagram of the modulator.
As configured,
such switching module contains 16 MosFet switching
devices.
Quick calculations show that the peak power
switched per MosFet is (14KV x 22A)/(4 modules X 16 MosFets
per module)= 4.8KW and the average power is then 4.8KW X
Duty which is equal to 9.6W with a Duty = .002.
the primary reason to parallel.
This is
Even with using 64
MosFets, the peak power that is switched per MosFet is
still 4800 Watts.
The PT provides the required voltage transformation
(usually a step-up transformation) and impedance
transformation to drive the load.
Between the PT and CFA
is a cable that electrically connects the two.
It is
included in the block diagram because it can become a
modeling factor.
The cable introduces inductance and capacitance to the
modulator circuit as stray reactances.
It should be
14
RF IN
>--~I
I
I
I
I
COMMAND
GATE
---------....1 PWR
I
-
-
::L
-
PT
CABLE
n
-=c
I
I
CFA
-
I
I
I
I
I
I
l..-
I
_J
R
I
I
I
r--1---
1-
FET
I
-
FET
:::r::
-
::::L
I
,---------~---~--
1
I
L
'-FET
l-----=r:
FET
:.:L
Figure 3.
:L
Detailed Block Diagram
RF OUT
15
stressed that it is the reactances of the entire modulator
circuit that must be accounted for to be able to accurately
model the system.
The reactances, then, play a major role
in determining overall pulse performance.
The CFA is the modulator load.
The function of the CFA
is to accept RF input and amplify it when pulsed.
is then output for transmission.
The RF
In our case the RF
frequency is at S-band (about 3GHZ) and the power output is
140KW nominal.
CFAs are characterized by modest gains
around the 10-25 db range.
5KW nominal.
In this case the RF input is
Upon receipt of a pulse command then, the Fet
switching modules are simultaneously switched into
conduction and a high-energy video pulse is created at the
primary of the PT.
By transformer action this induces a
stepped-up voltage pulse at the PT secondary which then
pulses the CFA.
The goal is to pulse the CFA at the
required power level and desired pulse shape.
Pulsing with
the desired pulse shape implies pulsing at the correct
impedance level and within the limits specified for rise
time and fall time.
The reasons for this will be discussed
further in the next chapter.
Because pulsing the tube
under all probable combinations of operational conditions
will have to be anticipated, it is important the system be
properly modeled.
There are analytical expressions in the literature that
provide insight but they lack the ability to provide an
adequate overview of pulse waveform performance because
'
'
16
they often require separating the pulse into its turn-on,
intrapulse and turn-off phases for analysis [1], [4].
now turn our attention to device modeling •
•
f}
We
Chapter 4
DEVICE MODELING
4.1 Microwave High-Power Devices
Currently, there are many types of microwave
high-power devices on the market.
fall into three classes.
These devices generally
Linear-beam devices (Klystrons,
TWTs), crossed-field devices (magnetrons, crossed-field
amplifiers) and solid-state devices (high frequency
diodes/transistors).
disadvantages.
Each has their advantages and
Solid-state microwave devices still cannot
compete in the high-power arena that linear-beam devices
and crossed-field devices are in although advances are
being made in this area.
And crossed-field devices,
generally speaking, do not have the high gain capabilities
that linear-beam tubes can be capable of although they do
enjoy greater efficiencies.
It is not the scope of this
paper to treat these devices in great depth so the reader
is directed to references {1]-{3].
However, it would seem
fruitful to examine the case of the crossed-field amplifier
(CFA) since system requirements have dictated the use of
it.
Also, examining the tube in a little more detail will
help in gaining some appreciation for the modeling of the
CFA.
4.2 Cross-Field Amplifiers
The CFA of interest goes by the Raytheon tradename
of Amplitron.
Fig. 4 shows where it lies in the category
17
NON-REENTRANT
ELECTRON STREAM
NON-REENTRANT
ELECTRON STREAM
BITERMITRON
CARCINATRON
IOSCILLATORI
CARCINATRON
(OSCILLATOR I
TPOM
BIMATRON
TPOM
BIMATRON
Figure 4.
AMPLITRON
PROPOSED
DEMATRON
DEMATRON
Family Tree of Crossed-Field Amplifiers [3)
~
00
19
of cross-field devices.
We shall briefly examine the tube
noting that references (1]-[3] and [5] describe the device
in more detail.
The CFA is an offshoot of the magnetron.
A prime distinction between the two is that the magnetron
is an oscillator and the CFA is an amplifying device.
4.2.1 General Description
The CFA derives its name from the fact that its
static magnetic field is oriented so that it is cross-wise
to the static electric field imposed upon it.
Also
oriented cross-wise is the RF electric field due to input
RF.
The tube is capable of very good efficiencies upwards
of 50% and is high as 90%.
The gain of the tube though is
usually a little more modest (10-20 db).
The tubes are
attractive because they are relatively lightweight and can
handle high peak powers.
Their phase stability is good and
relatively predictable for changes in operating conditions
and thus are suitable for coherent applications.
Two
general types of CFAs are the distributed emission type and
the injected beam type.
the former.
We shall only be concerned with
From here we can further classify the
distributed emission type by its form of RF interaction on
the slow-wave circuit.
It can either be of linear format
or circular format as in Fig. 4.
In the linear format, the
tube can only be of the nonreentrant type.
That is, once
the electrons have interacted on the slow-wave structure,
they are "spent"
(energy transferred to the RF circuit) and
20
pass to the anode.
It can now be seen that CFA tubes that
are of the reentrant variety would appear to be capable of
higher efficiencies.
In the circular format, spent
electrons may be able to reenter the interaction space if
the tube is so designed.
The Amplitron is a reentrant type
CFA with the added distinction that is of the backward wave
variety.
4.2.2 Amplitron Operation Theory
The Amplitron can be described as a backward wave,
reentrant, non-resonant, distributed emission crossed-field
device.
Although the model of the CFA is relatively simple
and can be derived from analysis of the magnetron it is
important to gain insight into the Amplitron.
In Fig. 5,
it can be seen that the magnetic field is into the paper.
The tube is turned on when a DC electric field is imposed
across the cathode and anode.
As the electric field
assumes full strength electrons will leave the cathode
toward the anode slow wave structure but they will be
deflected in a circular manner because of the crossed
magnetic field.
At some point these electrons will form
into spoked bunches of charge whose velocity will approach
synchronism with the RF field.
They then interact with the
RF and give up their potential energy thus amplifying the
RF.
See Fig. 5.
An important attribute of these tubes is
that cathode emission can occur without resorting to
thermal heating of the cathode.
Secondary emission of the
21
INPUT-OUTPUT SEPARATOR
AND DRIFT SPACE
RF OUTPUT
I
CATHODE
Q9
SLOW WAVE
DELAY LINE
CIRCUIT
ENERGY
DIRECTION
Figure 5.
ELECTRON FLOW AND
MAGNETIC FIELD DIRECTION,
ACCORDING TO FORWARD
OR BACKWARD WAVE
INTERACTION
Backward Wave CFA Interaction [~
22
cathode occurs because not all electrons become part of the
rotating space charge and are returned to the cathode.
This back bombardment of the cathode is responsible for
heating the cathode in a sufficient manner to induce
thermionic emission.
The kinetic energy of these returning
electrons can amount to as much as 5% of the input DC power
[3),[5].
Because of this back bombardment and the
reentrant configuration, the CFA can enjoy quite high
efficencies as noted.
The Amplitron operates as a backward wave device.
This means that the phase velocity of the RF (as it appears
to the electrons) is in a direction opposite to the group
velocity of the space charge (electrons}.
This implies
that the tube is sensitive to frequency so that for a
constant power output, the applied DC voltage would have to
change for a change in RF input frequency.
By using a
constant current modulator, the power output could be held
within reasonable limits.
The modeling and design of the
project modulator is based on using a constant current
modulator.
An important benefit of constant current
modulation is that the phase shift is relatively constant
for an anode current level.
A typical value of phase shift
change for anode current change is about .5 deg/1%.
Because of this CFAs are useful in coherent radar systems.
Another advantage to controlling the operating
current is that this reduces the chance of operating the
tube in an undesirable mode, when a CFA "modes", it's not
23
operating at the intended frequency and is subject to
spurious output of signal as well as noise power.
Moding
happens because the tube can support other modes of
operation much like other microwave devices.
Tubes can
mode if the applied voltage rate is too fast or not fast
enough.
This applies to the end of pulse as well (although
it is usually not as critical).
Also, if the anode current
were too high or low then a competing mode might set in.
Fig. 6 shows a typical CFA mode boundary performance
curve.
It should be apparent that the best way to modulate
a CFA would require the use of a constant current modulator
especially when noting that some CPA's have slim boundary
limits.
4.2.3 The CFA Model
The CFA acts as a non-linear saturated amplifier
which conducts current after a certain voltage is exceeded.
Upon reaching this threshold voltage the CFA is on and can
be viewed as a two-port device with a static impedance and
a dynamic impedance called Rd.
represent the CFA.
A diode can be used to
The CFA has a cathode and anode and
operates in a non-linear fashion much like a zener.
The
difference between the two is that the CFA has a bias
associated with it.
In magnetron terminology this is
called the "magnetron firing voltage" or "Hartree" voltage.
The CFA model must account for this by introducing a diode
voltage bias.
•
c>
Magnetrons have been modeled this way for
24
4.5
~
I-
•. 0
~ 3.5
UPPER MODE REGION
I
~
r-
OPERATING CURRENT
-
FOR SPECIFIED BAND AND
FIXED POWER SUPPLY SETTING
a:
a:
::>
(.)
::..!
''
3.0
~
w
0...
/
2.5 I
LOWER MODE REGION
2.0
1.5
2.90
2.95
3.0
3.05
FREQUENCY (GHz)
Figure 6.
Typical CFA Mode Boundaries (3)
3.10
25
some time and the "biased-diode" model is applicable to the
CFA [1].
Fig. 7 shows the voltage current relationship for
a CFA and Fig. 8 shows the biased-diode equivalent circuit
for the CFA.
4.3 Project CFA Model Parameters
The capacitance shown in the CFA model represents
the total stray capacity of the tube and the resistor Rd
represents the dynamic resistance of the tube.
The battery
is just the bias voltage to fire the tube and the diode is
the non-linear element.
Each element in the model is
"ideal" for purposes of simulation.
complete.
That is, the model is
If stray capacity is not specified then the
model must be used to determine what value of stray
capacity is tolerable given all other factors.
must be made if other designs are not yet known.
Trade-offs
If the
tube to be used already exists then its stray capacity can
be measured if it is not specified in its data sheet.
This
will provide a value of stray capacity to use in the model.
Measured values for the tube were found to be in the
vicinity of 70pF.
A dynamic impedance can be defined for
the tube in the following manner.
Dynamic impedance is
usually defined as the change in voltage slope divided by
the change in current slope (in the region of interest).
It has been our experience at ITT Gilfillan in working with
CFA's that a very good estimate of Rd can be made by
taking 10% of the CFA static resistance as the value for
I·
26
fh = 9.5 GHz
30
f
m
= 9.3 GHz
>
.X
t 1= 9.0 GHz
w
(.!)
;::
...J
0
> 20
~
<!
w
0..
10 ~--------~--------~--------~----------~--------~------0
10
20
50
40
30
PEAK CURRENT (A)
Figure 7.
CFA Voltage Current Relationship [3]
27
CATHODE
DIODE
DYNAMIC RESISTANCE
BIAS VOLTAGE
STRAY CAPACITANCE
ANODE
Figure 8.
Biased-Diode Model
28
Rd.
In fact, experimental data in the lab has been taken
for CFA's plotting pulse voltages against pulse current to
measure Rd.
With good correlation, it can be stated that
(7}
Rd=lO% X Ep/Ib
where Ep is the pulse voltage across the tube and the Ib
term is the operating current of the tube.
suitable dynamic impedance for the model.
This defines a
A nominal value
for Rd can then be calculated by using nominal values of
14KV for Ep and 22A for Ib in EQ. 7.
63.6 Ohms.
The value for Rd is
Fig. 9 shows the Project CFA model.
4.4 Pulse Transformers
4.4.1 General Discussion
Pulse transformers (PT's} arose from the developing
radar requirements of the second-world war for being able
to transmit rectangular pulses at high power levels.
PT's
are now used extensively in radar transmitters because they
provide many desirable features of interest to the designer
of a transmitter.
The primary function of the PT is to
provide an impedance match for the pulse generator and its
load (usually a microwave device).
The PT is most often a
step-up type and may or may not be phase-inverting.
It can
be said then that the PT couples pulse energy from a source
to a load.
By their very nature, they have to be
relatively wide-band devices.
It is of more practical use
:!dOL
1\>!l L
9"£9
30010
6~
30
to circuit designers to be able to describe the PT in
time-domain terminology.
Parameters such as rise/fall
times and pulse droop are as easily specified or visualized
in frequency domain terminology.
Although PT's can be
examined from an analytical standpoint, it is more
instructive to develop a circuit model that is "complete"
in the sense that it can be used in a circuit analysis
program to aid in the design process.
In this way, a
designer might be able to more intelligently specify
magnetics design requirements to the magnetics designer.
In any event, this procedure would at least allow for a
more informational dialogue to occur.
Because of this, an equivalent PT circuit based on a
common terminology understandable to both groups is a very
desirable thing to have.
The next section explores the
development of such an equivalent circuit.
4.4.2 PT Equivalent Circuit
In beginning to develop the PT model it must be
recognized that the PT (or any transformer) is a passive
device that utilizes magnetic flux coupling for energy
transfer.
An "ideal" transformer would have perfect
magnetic coupling and no losses or stray elements
(capacitive and inductive) to effect a departure from the
ideal.
The only equation that would describe such a
transformer would be the simple turns-ratio equation.
10 shows the schematic representation of the ideal
•
<)
Fig.
31
PRI
]
[
SEC
1: A
1: A= TURNS RATIO
VSEC = VPRI x A
1SEC = 1PRI/ A
VPRI x 1PRI = VSEC x 1SEC
NO LOSSES
Figure 10.
Ideal Transformer
32
transformer with the turns-ratio given as Nl/N2 = a where
Nl and N2 are the number of turns for the primary and
secondary windings, respectively.
Of course no transformer
is ideal so now it is necessary to add elements to the
model which represent the departure from the ideal.
Since
the PT is a magnetic coupling device it is easy to
visualize and accept that not all the input flux will be
coupled to the output.
leakage flux.
That is to say, there will be some
The leakage flux is due to the real fact
that transformers cannot be physically built so that all
other possible flux paths are completely eliminated.
In
almost all cases the leakage flux paths involve air as part
of the closed path along with some iron.
To make the
transition to circuit terminology it is noted that leakage
flux induces a voltage equal to N d¢/dt which is equal to
the inductance voltage described by L di/dt.
It can then
be written that
L=N d¢/di
where d¢ is the change in magnetic flux.
(8)
In this way we
can thus allow a "leakage inductance" to be used in the
model.
Fig. 11 now shows the PT with its associated
primary and secondary leakage inductances and winding
resistances.
components I
To this model we must add the magnetizing
0
and Ic.
I 0 is the reactive component
of current that would if there were no core losses in the
33
R1
R2
JX1
-
JX2
-
+
+
T
----------
1:A
Figure 11.
PT With L1 and Winding Resistance
34
PT.
Ic is that component of current that would be
attributed to core losses.
Both are ficticious quantities
in that they are not measurable but can be used
analytically.
They are easily represented in phasor
diagram form.
It now must be recognized that the
transformer along with its associated pulse generator and
load introduce stray shunt and distributed capacitances
that must be accounted for.
Accordingly, we add to the
model a primary capacitance and a secondary distributed
capacitance.
This distributed capacitance takes into
account any primary to secondary capacitance as well as the
secondary shunt capacitance.
Fig. 12 now shows the
transformer with all its non-idealizing elements around it
and the actual transformer itself can now be considered an
ideal one.
It is now desirable to formulate a single-line
equivalent circuit model.
This is easily done by either
"referring to the primary" or "referring to the secondary"
any elements one may desire to move.
Before this operation
is invoked, we should simplify our "complete" equivalent
circuit to reduce the amount of element manipulation.
The
winding resistances are so small that they may safely be
omitted from the model along with any core losses so this
removes r
1
,r 2 and rc from the model.
Also, since the
magnetizing current is typically 2-5% of the pulse current
it too may be neglected [4],[6],[8].
The percent current
droop is about equal to the percent magnetizing current
under these conditions and can be further controlled by a
35
R1
I
JX1
-R~
_J!~-
~TTT~
+
T
1
co .J...
'c
PRIT
Rc
'm
&
t I I
+
Figure 12.
'.P _
1 :A
I
+ +-< JX1
PT with Non-Idealizing Elements
::;:: Co SEc
36
reset winding inductance if one is used.
A reset winding
is used for resetting of the PT core to insure that the PT
is pulsed at the zero flux point.
This insures that the PT
does not creep up its B-H curve toward eventual saturation
and inability to be pulsed.
In this case, the reset is
used and appears as a shunt inductance at the primary.
Note here that the reset inductance is typically much lower
than the magnetizing inductance and so for most cases the
reset is the controlling factor for pulse current droop.
This is because a high inductance in parallel with a low
inductance is essentially dominated by the low value
inductance, similar to the parallel resistor case.
The
primary leakage inductance can also be omitted since its
measured value is very small.
In this way now, all that
needs to be referred to the secondary is the reset
inductance on the primary.
Referring to the secondary requires dividing an
elemental value by the turns ratio squared (capacitive
elements) or multiplying by the turns ratio squared
(resistive and inductive elements).
This applies to the
step-up case and is reversed in the step-down case.
Therefore, the model appears as shown in Fig. 13 and
is seen to be the secondary leakage inductance in series
with a shunt distributed capacitance.
It should be noted
here that the reason for referring to the secondary is that
the secondary is the load side and that is where the pulse
•
tl
_.._
a J-r-
+
L£
38
waveforms are to be examined.
Other primary side strays
shall be referred to the secondary as they are discussed.
4.4.3 PT Parameters
The parameters of interest in our PT model will be
the secondary leakage inductance L , the distributed
1
capacitance Cd and reset inductance Lr.
In
establishing a PT specification base for a PT, it is
necessary to see the entire system as a whole entity
because the PT does not operate alone but as an integral
part of that system.
For now it will suffice to say that
for the Project modulator the measured values of leakage
inductance and distributed capacitance were 80 microhenries
45 picofarads respectively and the design value for Lr
was 1.0 millihenries.
The next chapter will show how basic guide numbers
are arrived at to begin a PT specification.
Its design is
predicated on how it is to "fit" into the system for proper
system operation.
This is because an impedance match needs
to be effected between the load (CFA) and modulator (power
pulse generator, PT's, cables and stray reactances).
is often called the
z0
match [7].
Before that
discussion, cables and other reactances are examined.
This
39
4.5 Stray Reactances
4.5.1 Load Side Strays
On the secondary side of the PT there will usually
be a cable to take the pulse power to the RF tube.
In the
case of the Project Modulator, there is approximately 3
feet of pulse cable.
The cable is modeled by a lumped
series inductance, lumped series resistance and lumped
shunt capacitance.
This is a very good approximation since
the frequencies are relatively low (4-5 Mhz).
The model
can be simplified by noting that the cable resistance is so
low as to be negligible for efficient performance.
The
lumped inductance and capacitance parameters were measured
to be approximately .075 microhenries/ft. and 30
picofarads/ft. for the cable of interest.
can be controlled up to certain limits.
These parameters
At 3 feet, the
inductance parameter is only .225 microhenries and so can
be neglected in comparison with the 80 microhenries term.
The cable capacitance parameter however, cannot be
neglected because at a cable length of 3 feet it is equal
to 90 picofarads and this is comparable to the 70
picofarads introduced by the CFA load as well as the 45
picofarads of distributed capacitance in the PT.
The cable therefore can be modeled as a shunt
capacitance with a value of 90 picofarads.
40
4.5.2 Primary Side Strays
Two items are considered here.
One is the primary
shunt wiring capacitance and the other is the equivalent
series inductance (ESL) of the energy storage capacitors.
The primary capacitance Cp is that capacitance measured due
to the wiring configuraton of the unit from the highpowered video switching circuits up to the primary side
bushings of the PT.
It is best measured in the
configuration to be used but if that is not possible then
design experience must be used.
The values obtained are
not usually large and in this case a similar configuration
yielded a value for Cp of 15 picofarads.
It must be noted
that this value is the value obtained "referred to the
secondary."
Its actual value on the primary side would be
the turns ratio squared times 15 picofarads or 31 X 31 X 15
picofards which is equal to .0137 microfarads.
Cp is
therefore modeled as a primary side shunt capacitance with
a value of 15 picofarads.
The ESL introduced by the storage capacitors can
become an important factor.
This inductance when referred
to the secondary is multiplied by the turns ratio squared
in contrast to the capacitance which is divided down.
For
the aluminum electrolytic capacitors to be used, measured
values of ESL were found to be approximately 49-50 nH.
This is a very small value but when multiplied by 916 (the
turns ratio squared) becomes 45 microhenries.
This is the
value referred to the secondary and cannot be ignored.
It
41
is comparable with the PT secondary leakage inductance
value of 80 microhenries.
Therefore, this term L
es 1
is
modeled as a primary side series stray.
4.6 Pulse Generators and Snubbers
4.6.1 The Current Source Generator
It has already been noted that a current source is
required for achieving the best pulse response and control
of the CFA.
For modeling purposes, it is sufficient to use
the modeling program's library of programmable current
sources (if available) or programmable voltage sources.
In
the Microcap II program, only voltage sources are available
for use.
An equivalent current source is made by putting a
resistor in series with the voltage source.
Now this
current source can be made as ideal as desired (within
limits) for pulsing the system.
Table 1 shows the current
source parameters input to the program.
Note that
pulsewidth, rise time and fall time can be controlled.
Zero rise/fall times are not allowed.
In this manner we
can almost check the actual impulse response of the system
without tedious hand calculations.
We can idealize or
degrade our actual video switching circuits to any degree
for analysis.
An important item to note is that
experimental data taken has shown that there is very good
tracking between actual data taken and computer data
derived using this method.
This tracking assumes we take
our current source pulser to be nominal in that it is not
42
PROGRAMMABLE WAVEFORMS TYPE O... ALIAS CFA GENERATOR
VALUE
0:
1:
2:
3:
4:
5:
6:
ZERO LEVEL VOLTAGE
ONE LEVEL VOLTAGE
TIME DELAY TO LEADING EDGE
TIME DELAY TO ONE LEVEL
TIME DELAY TO FALLING EDGE
TIME DELAY TO ZERO LEVEL
PERIOD OF WAVEFORM (1/F)
Table 1.
'
'
0
2200000
0.0000001
3.5E-07
6.85E-08
0.0000071
1
Current Source Pulse Generator Parameters
43
made to be too ideal or too poor.
This is a judgement call
based on the designer's experience.
Setting the value of the current source pulser is a
matter of adjusting the voltage source and resistor to
establish the correct operating conditions at the load.
To
establish a value for the resistor, first remember that a
current source is a device that outputs a constant current
without regard to output voltage (within limits) and has a
high output impedance.
impedance.
Ideally, it has an infinite output
In our practical case, we have to look at the
impedance we are to drive.
the system
z0 •
The system
of the CFA (load).
next chapter.
Essentially, the impedance is
z0
is the static impedance
This will be discussed further in the
Now, a high output impedance is a relative
term and as a rule-of-thumb, a 20:1 impedance ratio is
about enough to establish a current source approximation.
In the model we set the current generator resistor at
100,000 ohms to establish an impedance ratio of 100,000/636
= 157,
well in excess of that required for a 636 ohm load
but this will give an easy number to calculate with.
The
voltage source then becomes by Ohms Law 22A X 100,000 ohms
= 2.2
MV.
This is where the 22A is the nominal peak CFA
(load) current required.
The voltage source must now be
appropriately programmed for rise/fall times and pulsewidth
as mentioned above.
parameters in detail.
.
0
The next chapter will show the
44
4.6.2 Snubbers
Snubbers find their place in many applications in
power control.
They are sometimes called load-line shapers
because they are used to shape or control the waveform so
that the semiconductor's safe operating areas are not
exceeded and that other performance requirements are met,
such as damping.
The RC snubber is located at the solid-
state switching circuitry and is referred to the secondary.
Careful attention should be paid by the designer to insure
that the C is chosen to safely limit the maximum holdoff
voltage of the semiconductor in the particular circuit
configuration.
Also, the R should be large enough to
suppress undesirable ringing of the pulse while not so
large as to affect rise time.
desired objective.
Critical damping is the
A design guide to use is to set the RC
time constant equal to rise time/2.3.
control of the dv/dt in the pulse.
This allows adequate
See [9] for a more
detailed discussion.
The values selected for the R and C were 600 ohms
and 150 picofarads respectively.
referred to the secondary side.
These values are as
The primary side values
would be 600/(31X31)-.655 ohms and 150pf X (31X31)=150
nanofarads.
This means that in the solid-state switching
circuits, there should be effectively distributed .655 ohms
and 150 nanofarads.
This says that if 8 snubbers are to be
used for 16 Fet switch devices, there should be .655 X 8 =
5.24 ohms and 150 nf/8=.018 microfarad in each snubber.
45
This results because parallel capacitors add and parallel
resistors divide.
The snubbers are in parallel because the
Fet devices are in parallel switching the primary pulse
current and the snubbers are across the Fets.
This discussion is included to show how the model
values are obtained.
As a designer, one may start analysis
with a "ballpark" figure for the snubber based on
experience and the switching configuration.
In this paper,
switching circuit topologies are out of scope and will not
be addressed except to say that current design practice
favors the use of either bipolar (transistor) switching
technology or Fet switching technology.
Chapter 5
SIMULATION OF MODULATION
5.1 Basic Modulator Schematic
Fig. 14 shows the basic modulator schematic.
Note
that the power supply is shown as a capacitor to emphasize
that energy stored is in capacitors and that the ESL
(equivalent series inductance) must be dealt with.
The RG
snubber shown is the total primary RC snubbing required to
be referred to the secondary.
Individual snubbing units
are not shown along with the individual Fet switching units
that they clamp.
5.2 Computer Model
Fig. 15 shows the computer model to be used for
running in the Microcap II program.
Note all values are
referred to the secondary (load) side.
The prime
parameters of interest are the load current and load
voltage.
Also note that the pulse generator and diode do
not have values associated with them except for the numbers
alongside them.
All this means is that these are library
programmable devices.
Table 1 showed the generator
parameters and Table 2 shows the parameters for the CFA
diode.
The generator is programmed as required for pulse
voltage levels, duration and rise/fall time.
The diode is
likewise programmed as required for use in the model.
46
It
47
+500
PT
c
I
I
ENERGY
STORAGE
I
I
I
I
I
I
-----L
II~
1 :A
RD
rI
I
I
I
I
CABLE
CFA
-
___ J
TO SWITCHING
ELEMENTS (AND RC SNUBBERS)
NOTE
THAT EACH AREA CONTRIBUTES ELEMENTS THAT MUST BE MODELED.
SEE CH. 4 AND CH. 5.
Figure 14.
Modulator Schematic
48
LESL
LL
45UH
80UH
-
+
-
CFA DIODE
+
150PF
SNUBBER
-
1H
+
LR
300 PF
CL +CD+CCAB
15PF
10
,
63.6 ~RD
-
E
12 kV~ PMIN
<(
600
<(
eSTRAY
GENERATOR
+
Figure 15.
Computer Model
49
DIODES TYPE O... ALIAS CFA DIODE
VALUE
0: SATURATION CURRENT (10)
1:
2:
3:
4:
5:
6:
- ----------·
--------
- - - - - - · - - - - -·--
Table 2.
'
I
1 E-14
1000000
10
0.1
2E-12
1 E+08
1.11
ZENER VOLTAGE
ZENER RESISTANCE
SERIES RESISTANCE (RF)
CAPACITANCE
PARALLEL RESISTANCE
ENERGY GAP (0.6 TO 1.3)
-----·---
CFA Diode Parameters
so
is usually best to make the diode as ideal as possible so
as not to interfere in its biased-diode capacity.
5.3 Computer Results
The program is set to plot the output voltage and
current waveforms vs. time.
voltage requests.
The program responds to nodal
The current is read as the voltage
across the dynamic impedance resistance divided by the
dynamic resistance.
when specified.
The program does this automatically
Also, the voltage is read as simply the
voltage at the specified node.
Fig. 16 shows the CFA voltage waveform vs. time and
CFA current waveform vs. time.
·In this manner, the
waveforms can be analyzed as required.
All basic pulse
information is located within these waveforms.
Rise and
fall times can be seen as well as pulse current droop and
ringing of the pulse voltage or current.
As designers, we
can now set about to optimize the modulator design.
In
Fig. 17 we see the CFA voltage and current rise time.
The
current rise time appears to be about 100 ns, well within
our 250 ns rise time requirement.
The rise time is usually
measured from the 10 to 90% points (Fig. 1).
In Fig. 16,
the pulse current droop appears to be very small (under
.5%) across the pulsewidth and it appears that there is no
problem with droop.
There is some current overshoot at the
leading edge of about .5 A (peaks at 22.5 then drops down
'
f)
51
1.00
>
-3.00
1\
..>:.
ui
(.9
~
r/
-7.00
1....l
3:
-11.00
~
u..
u -15.00
-19.00
2
4
6
8
10
8
10
. TIME IN MICROSECONDS
25.00
~
~
20.00
w
a:
a:
;:)
u
15.00
z
l
cI
I
I
4
6
J
10.00
~
u..
u
5.00
0.00
2
TIME IN MICROSECONDS
Figure 16.
Computer Run of CFA Voltage/Current
52
1.00 ,........
>
-3.00
~
w·
<.:J
<(
-7.00
-"'
I-
...J
0
> -11.00
"' '\
'-..
<(
u.
(.)
I
I
'
i
-15.00
-19.00
I
I
200
400
600
800
1000
800
1000
TIME IN NANOSECONDS
25.00
<(
20.00
(
~---
z
w
a:
a:
::>
(.)
15.00
10.00
-----~
c___j
/
-----
<(
u.
(.)
5.00
0.00
200
400
600
TIME IN NANOSECONDS
Figure 17.
CFA Voltage and Current Rise Times
53
to 22) but not enough to create CFA moding for this tube.
The upper mode boundary for this tube is about 24-25 A.
Fig. 18 shows the same waveforms as Fig. 16 except
that the run was made without the reset inductance in the
model circuit.
Comparison of the two figures show that
they are very similar and so it could be safe to assume
that the PT could have been designed without an additional
reset inductance.
We now have seen how the basic model waveforms have
been arrived at and analyzed.
It can be safely said at
this point that the modulator will probably meet its basic
requirements and that a system
been achieved.
z0
impedance match has
The next section will discuss the
z0
match and show a computer run of a mismatched system along
with a computer run of an actual operational system to
compare with an actual oscilloscope photograph of the same
point.
5.4 The
z0
The
Match
z0
match concept is used to good effect in the
design and analysis of the radar modulator.
It is
applicable to both line-type modulators and hard-tube
modulators.
The modulator system can be viewed as a
transmission line with a characteristic impedance with the
load having a certain impedance of its own.
The goal of
the designer is to put together a modulator that meets the
requirements for rise and fall time along with pulse
54
1.00
>
-3.00
~
w·
~
<(
-7.00
"
r/
1...J
0
> -11.00
<(
lL.
u
-15.00
-19.00
2
4
6
8
_1 0
B
10
TIME IN MICROSECONDS
25.00
<(
20.00
[ C__
I --- ----
'--- -
2
4
~--·
z
w
±__
t
15.00
0:
0:
:::>
u
10.00
<(
lL.
u
5.00
0.00
B
TIME IN MICROSECONDS
Figure 18.
CFA Voltage and Current with L
r
= oo
55
overshoot and undershoot.
In actuality, the design goal is
to achieve a critically damped system.
over/undershoot can be minimized.
In this way, pulse
It is well known that
obtaining an impedance match in a system will minimize
reflections, oscillations and other phenomena.
reason, a system z
0
For this
match is a primary design goal.
Refs [1], {4] for additional information.
See
From basic
transmission line theory, it is well known that for a
lossless system the characteristic impedance (actually a
characteristic resistance)
ZO
=
is given by
(L/C)l/2
where L
=
series inductance
C
=
shunt capacitance
z0 =
( 9)
characteristic impedance
For purposes of our modulator analysis, we assume the
lossless case and justify this by saying that for a well
designed high-powered radar modulator, resistive losses are
so minimized that any resistive losses can be neglected.
In our case then, the L and C values are the total values
from the model.
That is, the total lumped series
inductance becomes the L value and the total lumped shunt
capacitance becomes the C value.
Adding up our series
inductances (from Fig. 15) we obtain an L value of 125
microhenries and the C value is just the sum of the shunt
56
capacitances as shown in Fig. 15 which is 300 picofarads.
Dividing the L by the C and taking the square root we
obtain a value of 645.5 ohms.
We now compare this value
with that of the CFA which is the nominal operating voltage
divided by the operating current which can be defined as
the CFA static impedance.
The CFA static impedance is therefore given as
(10)
ZCFA = Ep/Ib
where Ep = nominal operating voltage
Ib = nominal operating current
In this case, ZCFA = 14KV/22A=636.4 ohms nominal.
The
difference between the system impedance and the CFA
impedance is less than 2% and we can consider our system to
be matched.
Mismatches of 5% or greater would require that
the design be reviewed.
In sunooary, we say then that a system is matched to
its intended load when its
z0
i within 5% of the CFAs
characteristic impedance (static impedance) ZCFA.
In a
normal design, of course, a design tolerance analysis would
have to be done to insure a proper match over all
conditions.
Fig. 19 shows the voltage and current
waveforms for a 2:1
z0
mismatch.
ringing in both waveforms.
match.
.
;
Note the overshoot and
This would be an unacceptable
To correct a mismatch, one can treat either the L
57
1.00
>
-3.00
..:.!.
w
(!)
<2::
-7.00
~
n\_rvf_ :
II
1_j
0
> -11.00
<2::
u..
(.)
-15.00
-19.00
2
4
6
8
10
8
10
TIME IN MICROSECONDS
25.00
<2::
20.00
I 1\r I
I
I ,
4
6
~---
zw
a:
a:
15.00
::::>
(.)
<2::
u..
10.00
(.)
5.00
0.00
2
TIME IN MICROSECONDS
Figure 19.
•
d
2:1
z0
Mismatch
58
term or the C term.
This is a design judgement call
because what can get fixed easily at the computer may not
be as easily implemented in the real design world.
Therefore, the modeling design approach is an iterative
one.
The goal being to find an acceptable and
implementable design.
Due to the fact that the actual modulator upon which
this paper is based on has not been assembled yet, no
actual waveform photographs are available for comparison.
However, in order to provide some degree of merit to the
modeling techniques outlined above it will be noted here
that previous systems have been successfully modeled using
these techniques at ITT Gilfillan.
The correlation between
actual waveform photographs and computer generated plots of
the same system are beyond coincidence and thus this
provides a good degree of confidence in the modeling
techniques described above.
Chapter 6
CONCLUSIONS
6.1 General Discussion
We have seen how the computer has helped in
designing the radar modulator.
This design tool has helped
in the actual design/debug cycle.
Whereas it used to take
months and even years to take a design from paper to
hardware, it can now take weeks.
The computer screen is
the oscilloscope where waveforms or other parameters can be
analyzed.
The only major uncertainty is knowing whether or
not the computer derived results will bear any resemblance
to reality.
In the case at hand, it can be said that the
computer model is accurate because its methodology was
proven on a similar project as previously mentioned.
For
designs or applications of this nature, we can use the
methodology outlined above (with modifications as required)
for the specification of major modulator components.
Design tradeoffs or feasibility studies can be made both at
the transmitter level and system level.
What is also
important to note is that once a model is put together for
a given design configuration, it can be used over and over
with little modification to the configuration.
The
configuration used in the case analyzed above was for a
solid-state based hard modulator with CFA load.
Other
types of modulators could be possibly analyzed using
appropriate models and computer programs as required.
59
60
6.2 Application
It has now been shown that the simulation and
analysis just described is accurate and can be used in
actual design applications.
The philosophy behind the
analysis is, in general, applicable to any circuit
analysis.
That is, model what is important to the actual
performance.
In our specific application, the circuit was
of an analog nature {as opposed to digital) and was a
high-powered circuit.
The circuit was also relatively e?SY
to model with basic electrical elements, diodes and a few
computer conveniences.
To accurately model other circuits
which are more digital in nature or more "electronic,"
other methods should be investigated.
For instance, the
SPICE program allows a more detailed modeling of
semiconductors which in turn could allow a more detailed
modeling and simulation of the actual solid-state switching
circuits and control circuits.
The drawback is that it can
be very difficult to obtain data from the semiconductor
manufacturers for proprietary reasons.
Fortunately,
programs such as the Microcap II {and others) can be used
for most applications.
Again, this will depend on the
designer's ability to accurately model his devices with
respect to their intended applications and his
resourcefulness in using these programs while knowing at
the same time what the program's strengths and limitations
are.
In the end, the computer program is only a tool.
is up to the designer to properly exercise it.
It
REFERENCES
1.
Ewell, G.W., Radar Transmitters, McGraw-Hill, New
York, 1981.
2.
Skolnik, M.I., Introduction to Radar Systems, McGrawHill, New York, 1980.
3.
Okress, E.C., Microwave Power Engineering, Volume 1,
Academic Press, New York, 1968.
4.
Lord, H.W., "Pulse Transformers," IEEE Trans.
Magnetics, Vol. 7, No. 1, March 1971.
5.
Skowron, J.F., "The Continuous Cathode (Emitting Sole)
Cross-Field Amplifier," IEEE Proc., Vol. 61, No. 3,
March 1973.
6.
Lord, H.W., "A Turns Index for Pulse Transformer
Design," AlEE Trans., Vol. 71, 1952.
7.
Lord, H.W., "The Design of Broad-Band Transformers for
Linear Electronic Circuits," AlEE Trans, Vol. 70,
1951.
8.
Del Taro, V., Electromechanical Devices for Energy
Conversion and Control Systems, Prentice-Hall Inc.,
New Jersey, 1968.
9.
Grafam, D.R., and Golden, F.B., eds., SCR Manual, 6th
ed., General Electric, Auburn, N.Y., 1979.
10.
EIA RS-176, "Pulse Transformers for Radar Equipment,"
Electronic Industries Assoc., Wash. D.C., Dec. 1956.
61