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1965-06
A high-power one-millisecond pulse-forming network
Walker, William George
http://hdl.handle.net/10945/12290
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1965.06
WALKER, W.
A HIGH-POWER ONE-MILLirECOND
PULSE -FORMING NETWORK
WILLIAM GEORGE WALKER
/^©©©LPLrSLl©©'
GENUINE PRESSBOARD BINDER
no.
BF 2507 EMB
ACCO
OGDENSBURG.
LONDON.
MEXICO.
CHICAGO.
N.Y.
TORONTO.
D. F.
A HIGH-POWER ONE-MILLISECOND
PULSE -FORMING NETWORK
by
WILLIAM GEORGE WALKER
S.
B.
,
United States Coast Guard
Academy
(1959)
SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June, 1965
Library
U-
S.
Naval Postgraduate School
Monterey. California
Z^R^ Y KN0X
{.
IBRARY
A HIGH-POWER ONE -MILLISECOND
PULSE-FORMING NETWORK
by
William George Walker
Submitted to the Department of Electrical Engineering on May 21, 1965
in partial fulfillment of the requirements for the degree of Master of
Science.
ABSTRACT
Design and construction of a breadboard model of a pulse-forming network
to be used in a line-type generator for a space vehicle radar system
is described. The
is unique in that it produces a one-millisecond,
PFN
high-power pulse and uses linear, ferrite-core inductors. It is designed
to be space-flight worthy, reliable, efficient, and most important, the
smallest and lightest weight unit that is compatible with the other pulsegenerator components. A study of a pulse generator is made to determine
the parameters that describe the optimum PFN. A pulse transformer
and a charging reactor are discussed in detail and a description is given
of the operation of the pulse
generator using silicon-controlled rectifiers
as switching elements.
Thesis Supervisor: J. Francis Reintjes
Title: Professor of Electrical Engineering
-2-
ACKNOWLEDGEMENT
wish to thank James R. Sandison and Joseph A. Bosco for suggestion
of this topic as a thesis subject and for the encouragement and assistance
I
freely given and gratefully received.
-3-
TABLE OF CONTENTS
TITLE PAGE
page
1
ABSTRACT
2
ACKNOWLEDGEMENT
3
TABLE OF CONTENTS
LIST OF FIGURES
CHAPTER
I
CHAPTER
II
A.
B.
III
A.
5
INTRODUCTION
7
THE PULSE FORMING NETWORK
DESIGN PARAMETERS
SELECTION OF MATERIALS
C.
D.
E.
CHAPTER
A.
B.
18
18
2.
Inductors
18
a.
Description of Requirements
18
b.
Choosing the Proper Core
and Wire Size
24
Typical Inductor Design Procedures
28
TESTING THE PULSE FORMING NETWORK
MEASUREMENT OF INDUCTOR CORE
SATURATION VOLTAGE LEVEL
CONSTRUCTION OF THE PFN TESTING CIRCUIT
CORRECTION OF THE PFN OUTPUT
PULSE WAVEFORM
MEASUREMENT OF PFN EFFICIENCY
ENVIRONMENTAL TESTING
SUMMARY
IV
APPENDIX A
13
Capacitors
.
B.
13
1.
c.
CHAPTER
4
30
35
35
42
46
47
A PARAMETRIC STUDY OF THE
OPTIMUM PULSE GENERATOR
THE PULSE TRANSFORMER
THE CHARGING REACTOR
APPENDIX B
30
SILICON-CONTROL-RECTIFIER SWITCHING
DEVICES AND TIMING CIRCUIT
BIBLIOGRAPHY
52
52
59
65
69
-4-
LIST
OF FIGURES
1.
Radar Transmitted Pulse Train
2.
Original Ten-Section
PFN
3.
Block Diagram
Pulse Generator
4a.
Odd Periodic Rectangular Waveform
15
4b.
Approximation
15
5.
Five Section, Type-C, Guillemin Network
16
6.
Inductor Construction
20
7.
B-H Curve
8a.
C-type Cut Core
25
8b.
Uncut Toroidal Core
25
9.
Circuit for Displaying Inductor Core Saturation Voltage Level
31
10.
Core Hysteresis Loop
31
11a.
Five
lib.
Breadboard Model
12.
Dummy Load
13.
Output Pulse Waveform from the First
14.
Output Pulse Waveform from the Second
15a.
Output Pulse Waveform from the Final
15b.
Leading Edge
16.
Graph
17.
Relation Between Power Supply Voltage,
Output Pulse Voltage
PFN
of
of the
page
and Charging Reactors
for Z-type
Hyper sil
21
Inductors
of the
9
II
Rectangular Pulse
to a
9
32
PFN
for Testing
of the Final
and the Charging Reactor
PFN
32
36
PFN Version
PFN Version
PFN
Version
Output Pulse Waveform
Voltage-Squared Versus Time for an Output Pulse
PFN
39
39
41
41
43
Voltage, and
44
18.
Simplified Pulse Transformer Model
54
19.
Equivalent Charging Network
54
-5-
LIST
20.
OF FIGURES
Power Supply Level and
of the
(Continued)
the d-c Resonant Charging
PFN
page
61
21.
PFN
22.
Pulse Generator Timing Circuit
66
23.
Timing Pulses
68
Oscillations after an Output Pulse
-6-
61
CHAPTER
I
INTRODUCTION
Microwave radar has resulted
capable of producing
in the
need for pulse generators
The convention
a rapid series of pulses.
is to
use essentially rectangular pulses of high power and short duration.
The
length of the pulses are from a few nanoseconds to several microseconds,
1*
more depending on
or
However, there have been
the specific application.
some iong duration pulse generators developed primarily
astronomy and space communication radar systems.
microwave research
application is the Haystack
Lincoln Laboratory.
A
for use in radio
An example
facility of
of this
M.I.T.
pulse generator that will produce a series of
long duration (one millisecond) pulses for use in a specific space vehicle
radar system presents some unique problems.
Rigid restrictions on size
and weight require new construction techniques to minimize these quantities.
The Electronic Systems Laboratory (ESL)
model
of a space vehicle
M.I.T. has
the vehicle would be shot at
of the
with bursts of rf energy at X-band.
a
near-miss trajectory.
to-noise calculations were
made
at
As
it
flies
surface of Venus will be illuminated
Comparison
of the reflected to
transmitted energy will give a measure of surface reflectivity.
of 20, 000
breadboard
Should the experiment be formally scheduled,
Venus on
successive small portions
approach
a
radar system for making measurements of the
reflectivity of the surface of Venus.
by,
at
ESL based
kilometers plus elognation
3
Signal-
on the closest point of
of the
returned echo due to
curvature of the surface of Venus and relative velocity between the planet
and spacecraft.
These calculations resulted
TT—
in
peak-power and pulse -duration
Superscripts refer to numbered items in the Bibliography.
-7-
—
transmission requirements
respectively.
one kilowatt and one millisecond,
of
4
This radar system uses a klystron which requires an input pulse
of
8-kv at 0.60 ampere for one millisecond to produce a one kw output
pulse, or a pulse generator output of
P
The pulse train
is
shown
=
3e
Eq
I
=
q
that this radar
in Fig.
(8,
000) (0. 60) = 4. 8
system will transmit
Four one-millisecond pulses
1.
portion of the surface.
A twenty-millisecond
is
(1)
normal operation
will be directed at each
delay between pulses is
required to prevent overlap of the echoes which
second period between bursts
in
kw per pulse
may
be elongated.
A
fifteen-
required to insure reception of the entire
burst echo and change the antenna position prior to transmission of the next
By reference
burst.
to Fig.
1,
the average pulse generator output
power
is
seen to be
P average
"
=
When considering
(total power output)
(total period)
(4x 10
of
it is
)(4,
800)
15.0
1.28 watts
(2)
a line-type pulse generator for use in this
application, the pulse -forming network (PFN) is the
since
_3
the bulkiest and heaviest.
most
critical item
Analytical procedures for the design
pulse-forming networks are well established, but the physical realization
of these
networks for high-power application usually results in units
considerable size and weight.
constructed by
ESL
for the
Figure
2
shows the original
breadboard model
of this
PFN
of
that
radar system.
was
It is
22 inches long, has a volume of about 800 cubic inches and weighs 15 pounds
-9-
•/&—
SMC
«
*
«"
10.m%
I
Ml
-Sf-
-tf-
FIG. I
RADAR TRANSMITTED PULSE TRAIN
'-fM
FIG. 2
- -f-
T~T~
"
^
ORIGINAL TEN SECTION PFN
AND CHARGING REACTOR
-10-
The reduction
obtained.
and weight was highly desired but not too
of size
Commerical manufacturers
of
easily-
pulse-forming networks
declined to undertake the problem.
The object
model
of an
of this thesis is to design, build
optimum PFN
for a one millisecond, 4.8
generator using as criteria for optimization:
2)
reliability,
kw peak power pulse
minimum
1)
"space flight worthiness,
efficiency, 4)
3)
and test a breadboard
"
size and weight,
and
compatibility
5)
with the other components of the pulse generator.
A PFN can
"optimum" only
be regarded as
use results in the
if its
smallest and lightest weight pulse generator of this type that can be built.
In order to determine the parameters that describe the
optimum PFN,
a
study was conducted of a hypothetical pulse generator, the details of which
may
be found in Appendix A.
The circuit
in
which the
PFN
is
used
shown
is
in Fig.
configuration meets the desire to reverse saturate, or "reset,
pulse transformer between pulses.
that the pulse
This
3.
"
the
This resetting feature reduces the chance
transformer will saturate during the long pulse.
pulse generators of this and other types
is
Operation of
described in detail in Reference
The pulse generator described here differs from conventional types
5.
in the use
of high voltage silicon-controlled rectifiers (SCR) as switching devices.
Operation begins with the
supply is
assumed
to
upon receipt
of a
initially
uncharged.
have a constant d-c output
system are small, the
2E
PFN
PFN
of
E
The power
volts.
If
will charge d-c resonantly to approximately
timing signal
at the gate
electrode of SCR-1.
current passes to ground through the pulse transformer causing
The resetting
Ri
is
losses in the
accomplished by
during the charging period.
a voltage appearing
The value
of R,
it
Charging
to reset.
across the resistance
is set to
supply just the
-11-
s
Uj
Uj
IA
-J
k
O
CD
O
00
«
-12-
necessary voltage required
to reset the
that charging current is flowing.
pulse transformer in the interval
This charging interval
is a
constant
value given by
where:
VL c
Tc
=
T
=
Charging interval
L.
=
Inductance of charging reactor
Cn
=
Total capacitance
of
r
U
|
3 is
the total
PFN
inductance.
L
A more
in
of 10
.
electrode
impedance
PFN
of
E
SCR-2.
If
PFN
the
much larger
than
JL
,
charging reactor
of the
upon receipt
impedance
of a
is
discussed.
timing signal at the gate
of the load
and the characteristic
are matched, the voltage appearing across the primary
transformer
and duration T.
is
L.
This establishes a practical lower limit on
will discharge
of the
of the pulse
PFN
detailed explanation of the charging process is given
Appendix A when design
The
(3)
x
'
based upon the assumption that
Equation
L.
Cn
is
an approximately rectangular pulse of amplitude
The pulse transformer secondary then sees N E
T
=
output pulse duration
N
=
pulse transformer turns ratio
E
=
DC power
where:
supply output level
At the end of the pulse there will be a small amount of residual magnetizing
current flowing in the primary winding
of the
pulse transformer.
cause a large negative voltage spike, called "fly-back voltage,
across the transformer primary.
the klystron
R,
from
The function
of the diode
D
"
This will
to
is to
from possible damage from the fly-back voltage and
the circuit during discharge of the
rate is set by a timing circuit to
meet
PFN.
appear
to
protect
remove
The pulse repetition
the requirements of the radar system.
CHAPTER
II
THE PULSE -FORMING NETWORK
A.
DESIGN PARAMETERS
Selection of parameters to be used in designing the
based on the results
is that pulse
of
Appendix A,
PFN was
the significant feature of which
transformer size and weight in
this application are
independent of other parameters for the three values of operating power
supply voltage assumed.
that
would simplify the
This result allowed selection of supply voltage
PFN
construction.
PFN must
The
be constructed
to operate at twice the supply voltage; therefore, the obvious choice,
in this case, is 300 volts.
'
from
available
the
pulse generator.
Table
This
power supply
A summary
that will actually be
of the
Es
lowest value of
is the
that will be
used
in the
important parameters
complete
is given in
1.
Table
Summary
of
1
Pulse Generator Design Parameters
E s = power supply voltage = 300 volts
N = pulse transformer turns ratio = 26.7
=
PFN
characteristic impedance
r
C
=
total
Ln
E
=
total
PFN
PFN
=
pulse transformer secondary voltage
I
=
pulse transformer secondary current = 0.6
T
=
output pulse duration = 1.0 millisecond
a
=
pulse rise time factor
L.
=
charging reactor inductance =130 millihenrys
Z
•
turns
n
capacitance
inductance
=
-13-
=
18.7
ohms
26.7 microfarads
=
9.35 millihenrys
J
= 5
= 8,
000 volts
amp
percent
-14-
The PFN design procedure
generator are small and the
is as follows:
PFN
If
losses in the pulse
considered to be matched
is
to the
load, the pulse transformer turns ratio is approximately
N
jf
=
(4)
s
The characteristic impedance
a
matched load condition
is
_
The
PFN was
chosen
pulse-forming network required for
of the
-
rrr"
n
<e /i
x
o'
;
o)
type-C, Guillemin network with
to be a five- section,
parameters:
The choice
of a periodic
of
PFN
waveform
T
cn
=
Ln
=
(6)
n
TZ n
(7)
2
configuration was based upon the Fourier analysis
of the type
shown
This
in Fig. 4a.
an odd
is
periodic function and can be used to calculate an approximation to the
desired output pulse.
A
rectangular pulse of current can be approximated
fairly well by a pulse that has parabolic leading and falling edges and a
flat top,
shown
as shown in Fi
in Fig.
g.
4b.
The odd periodic waveform
of this
shape
4a can be represented by a Fourier series in the form:
co
i(t)
=1
^
b
v
Sin
(
^
;
V =
5
3
l
>
'
'
•
*
'
(8)
-15-
Time
FIOT.
4a.
ODD PERIODIC RECTANGULAR Y/AVEFORM
A
}L
aT
H
aT
<£-
FIG. 4b.
APPROXIMATION TO A RECTANGULAR PULSE
Time
-16-
H
ismsu]
x>
o
»0
<sj
-J
K
UKXJOJ
O
-J
-4
3
ismor
<*%
-J
r>4
H
O
<LMM7
<m
<M
-J
H
10
iMoor
H
O
-17-
Only the odd harmonics will be present, the coefficients
of
which are given
by
m
sinvrra,
_4_
v
v
vir
=
I
p
A
five section,
v
'
v-rra
NI o
'
(10)
v
'
type-C, Guillemin network
is
shown
in Fig. 5.
The
element values are given by
sin
.ry
Ck
^TTZ n
v
where: k
=
1, 2, 3, 4,
5
=
v-rra
1
'-T
tt
Z T
Lk
1
-j
sin
— vua
Z
-j
^-f^1
v-rra
The
has shown
<
12 >
.corresponding to the appropriate network section.
in Table Z.
that the contribution to
rapidly.
?
>
The calculated element values and the current
network are given
^
?
>
PFN was
i(t)
Examination
from
the higher
i,
(t)
in
each section of the
of the values of
i,
(t)
shows
harmonic components decreases
limited to five sections primarily because experience
that addition of
more
sections would not improve the resulting
pulse waveform significantly to warrant the additional weight and space.
-18-
Table
2
Theoretical Coefficients and Parameters
Type-C, Guillemin Network
for a Five Section,
C
1
.
W)
L k (mh)
21.6
1
B.
k
i
4.69
k
(t)
20.3 sin
(^)
2
2.36
4.77
6.65 sin (1^-)
3
0.824
4.80
3.87 sin
(5zJ_)
0.399
4.82
2.67 sin
(ZljL)
0.226
4.85
1.9
sin (2Zj->
SELECTION OF MATERIALS
Capacitors
The capacitors used
in construction of the
breadboard model are
standard commerically available, high quality, 600v paper type.
a
Size and
weight are normally a consideration, but since the exact values of capacitance
needed had
weight
to be obtained by
of the
combinations
of
standard values, size and
experimental units are not too important.
single, light-weight units will be
manufactured
to
It is
expected that
meet space application
specifications and used in place of the experimental units.
2.
Inductors
Description of requirements
a.
was based upon
.
The selection
a high saturation flux density.
material of this type
is a
grain-oriented
tape-wound cores under the trade names
Table
2
3
of a
core material
The most readily available
/o silicon steel that comes in
of "Silectron, "
shows that the highest frequency harmonic
in
7
i(t)
and "Hypersil.
that will be
"
8
-19-
significant is the
to a
frequency
component 1.9
sin
(jut),
where
9lT
u)
At this frequency the
of 4, 500 cps.
= -m-
.
This corresponds
H and Z
type, 4-mil
cores will have reasonably small eddy current losses 7 and will be suitable
for this application.
The Z-type material
is
preferred over the H-type because
slightly higher saturation flux density
8
operation with fewer turns of wire than
which
if
may
it
has a
allow satisfactory
the H-type
were used.
Otherwise
either material is completely equivalent and the final choice is based upon
availability.
The characteristics
the
B-H curve
in Fig.
7.
of
Z-type Hypersil are given approximately by
This curve shows that the permeability of the
core remains essentially constant throughout most of the range of flux
density and changes radically only at the extremes where saturation occurs.
Pulse shape depends upon maintaining a constant value of inductance throughout
Therefore,
the pulse period.
it is
essential that operating points near
saturation flux densities be avoided.
The range
of flux
density (AB)
taken as 1.45 webers per square meter which
is just
where saturation begins as shown
the flux density is
in Fig.
7.
If
was
short of the point
assumed
to be constant over the core cross section, then the change in flux density
is
given by the general relationship
T
AB
=
NA J
e(t) dt
where:
A
N
=
core cross-section area
=
number
e(t)
=
applied voltage
t
=
time duration of applied voltage
of turns in coil
<
13)
-20-
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ta^a^ts^vnts/JGCGii -^^i^thct^p"^
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z:
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'
i
-22-
Assuming constant inductance,
T
L[i(T)
e(t) dt =
S
Substituting Eqs. 8 and 14 into 13 and solving for
NA
where
'
=
b
J
"SB"
P
v
- i(0)]
NA
(14)
for the k-th inductor,
^F
sin
<
in this case:
K =
ex.
v
=
C, J
1 t L,3,
L
,
,
,
.
.
,
.
k + n for
In
s 0, 1,2, ...
The cores must not saturate during the time the applied voltage
or for one-half the pulse interval.
t
T/2 and Eq.
=
15 reduces to
L,
At this point,
adequately specified.
It
I
b
J^l
(16 ,
on the right of Eq. 16 are known and
all the quantities
will essentially
is positive,
Therefore, for this particular case,
NA=
is
15 >
NA
has been shown that minimizing core volume
minimize losses
in the inductor.
There are additional
relationships that can be written, but there is a danger of over-specifying
the core resulting in conflicting
requirements and confusion.
of core and wire size selection is simplified
method
is
used instead
if
The procedure
a modified cut-and-try
of attempting to constrain all the variables.
procedure described here does minimize the core volume and
The
is straight-
forward and practical.
Coil resistance is usually determined by the allowable temperature
rise.
In this application, the
peak power from Eq.
1
that
must be passed
-23-
by the
PFN
is 4. 8
kw.
If
power dissipated
in the
PFN
is
limited to
less than five percent of the peak power, then
P dissipated
Most
of this
most
of the total
= (°-0 5 )( 4 . 80 °) =
power would be dissipated
A
energy.
24 ° watts/pulse
in inductor L,
reasonable figure
is to
since
(17)
it
is
supplying
allow Li to consume
ninety percent of the total loss.
PL
T
(0.90)(240) = 216 watts per pulse
=
(18)
l
Average power can be calculated from
T
P avg
The pulse current
-r
=
in
JL.
2
(t)
i
dt
(19)
x
taken from Table
(t)
i
R
\
U
=
2 is
20.3 sin (^t)
(20)
x
Let t
=
T and
substitute Eq. 20 into Eq. 19
R.
P
(20.3)'
-X.
=
=
^1
is a
good figure
will be shown,
it
2
(^)
dt
(21)
and using Eq. 18 gives the result
Solving Eq. 21 for Rt
This
sin
J
to
(2)
(216)
=
1<05ohms
(22)
(20.3)^
use for all of the
PFN
inductor coils since, as
will result in reasonable coil sizes.
-24-
A completed
by
must yield
coil
the
proper value of inductance given
1
Aug
N
Lk
1|—
=
(»>
Figure 8a shows the standard type-C core that will be used with air gaps
The number
adjusted to satisfy Eq. 23.
of turns of
wire on each core
large, requiring the air gap to be relatively large.
most
of the
magnetic energy will be stored
is
can be assumed that
It
in the air gap.
In this case
fringing cannot be neglected and the terms are defined as:
=
\i
p,
the permeability of air
i
=
length of air gap
A
=
effective cross section of the air gap
The effective cross section
but
is difficult to calculate,
it
can be estimated
by the empirical approximation
i
i
A
where D and E are
give an
answer
=
8)
(D +
the dimensions
(E + -J-)
shown
in Fig.
(24)
8a.
Use
of
Eq. 24 will
for inductance correct only to within a factor of 2 or 3
.
By
adjusting the length of air gap and measuring inductance with an impedance
bridge, each inductor can be set to any required value.
b.
The correct wire
Choosing the proper core and wire size.
size can be found
from reference
1,000
to
wire tables
R^
w
=
w
R
=
=
coil resistance in
i
=
average length in feet
r
r
T
entering the table with
NT^
(25)
wire resistance in "ohms rper
1,
000 feet"
ohms as given by Eq.
of a turn of
wire
22
—
8
-25-
STRIP
WIDTH
WINDOW
LENGTH
CUT HERE
G
BUILD UP
r
-I
FIG.
a.
F
kwiNDOW
WIDTH
C-TYPE CUT CORE
STRIP
INSIDE DIAMETER
WIDTH
BUILD UP
•+•
OUTSIDE DIAMETER
F/G.SL UNCUT TOROIDAL CORE
26-
From
the
entire
window area
is
geometry
shown
of the core,
in Fig. 8a,
and assuming the
will be used, the average length of a turn of wire
given approximately as
i
F
=
2E + 2D
+
(26)
Nyclad magnet wire was used primarily because
sizes and easy to
work
with.
mately as shown in Fig.
wire (size given by Eq.
6.
25)
same
The required core window area
was found with
Formvar which
The insulation thickness
is
is slightly
much
less than the rated value and
between layers.
to insulate
lighter core with smaller
N
for
turns of
it
rated
at
860 volts
greater than one
The
operating voltage any core will be subjected to is 600 v.
is
many
the aid of a table of turns per
mil and there are several layers of wire on each core.
volts-per-turn
in
Nyclad insulation has approximately
11.
insulating characteristics as
per mil at 25 C.
was available
The coils were hand wound on a lathe approxi.
square inch found in Reference
the
it
maximum
Therefore, the
was not necessary
This provided a more compact coil and a
window area was required than
if
an unnecessary
insulating layer had been used.
The smallest core
given by the product
that can be
FG
used
in Fig. 8a,
is
one that has the window area,
completely
filled with
wire.
For
each inductor, calculations were carried out for several core sizes and
the results
and
coil.
compared
in
order to determine the best combination of core
The choice usually came down
to
two cores, one had a larger
cross section and was also usually heavier than the other.
In each case,
calculations showed the smaller core required a larger coil in order not
to saturate at a given voltage level.
Resistance
of the
two coils was the
-27-
same, about one ohm, and therefore the choice seemed easy to make-select the smaller core to minimize core losses.
to be the best choice.
When
these two inductors were assembled and
tested, as discussed in Chapter
III,
cross section invariably saturated
the inductor with the smaller core
at a
lower voltage level than was
Whereas, the inductor with a larger core cross
indicated by the calculations.
section saturated at about the calculated level.
is that the
This did not prove
A
simple explanation for this
larger number of turns of wire required by the core with the
smaller cross section resulted in weak linkage of flux with the core from
For
the turns in the outermost layers.
a criteria for choosing
this reason,
between two theoretically equivalent cores for a given inductor
is to select
the core with the larger cross section.
The cores and wire sizes
that
were selected
and the charging reactor are summarized
in
Table
3.
PFN
inductor
The figures
in
are the result of calculations similar to the sample calculations
this table
shown
in
for the
Part C of this chapter.
Table
3
List of Inductor Construction
Material Characteristics
L.
L,
L
Inductor
1
8
7
Core number
Dimension (in.)
'
D
E
F
G
Weight (lbs.)
Cross sec. (sq. in)
Window area (sq. in.)
i
c
(feet)
Wire size (AWG)" LI
r
w (ohms/1000 ft .)
*
2
3
•
^4
L
5
^L6
Z-216
H-41
Z-1
Z-4
Z-2
Z-5
0.750
0.375
0.500
1.500
0.354
0.281
0.750
0.229
0.625
0.250
0.500
1.312
0.500
0.250
0.500
1.125
0.375
0.375
0. 187
0. 187
0. 170
0. 156
0. 122
0. 114
0.250
0.625
0.038
0.063
0.656
0.562
0.375
1.000
0.056
0.063
0.375
0. 187
0. 167
0.
0.750
0.375
0.625
1.250
0.334
0.253
0.780
0.240
19
8.051;
125
0. 156
0. 135
22
16. 14
24
25.67
24
25.67
24
25.67
16. 14
952
1,596
1.596
1,596
952
22
'
Winding density
(turns/sq. in.)
473
-28-
Typical inductor design procedures
c.
methods used
sample
in constructing the inductors
initial calculations for
.
The procedures and
are shown by a set o£
one inductor.
Then
it is
shown how
these figures had to be changed after the inductor had been tested.
The sample calculations are shown
Chapter
of the inductor is the subject of
the initial ones
made
to
in this part, whereas.the testing
determine
if
III.
The following calculations are
the particular core and wire size are
adequate for the element under consideration, in this case L,.
value of the element
The
shown
in
is
given in Chapter
first step is to select a
Table
Z-216 core,
from Eq.
3.
The
III.
core and tabulate
its
characteristics as
With the core cross section area from Table
the required
number
final
of turns of
3 for
the
wire for L, can be calculated
16
N
(4.69xl0-
=
3
)(l6 0)(1.27)
(1.81x 10
=
362 turns
(2?)
)(1.45)
where:
69 millihenrys
Li,
=
4.
I
=
16.0 amperes
P
1.27
b,
=
AB
=
1
A
=
4
(0.281)(6.45 x 10"
.
45 webers/square meter
)
=
4
1.81 x 10" square meters
The wire size can now be determined from Eq. 25 and a wire
r
w
~
(1.05)(1,000)
(362) (0.229)
"
table
,
.
/, Q00 £teett
2 * 7 ohrns /
000
1Z
1
'
(2.8)
—
-29-
This corresponds directly to number 21 wire, but number 20 wire was
selected because of
its
lower resistivity.
The Z-216 core has
a
would be adequate for
The required
=
362
0.583 square inch
j-jt- -
window area
of
air gap
2
T
L..
=
(362)
1
'
is
it
this inductor.
can be estimated with the aid
= (1.750)(1.375)(6.
and the inductance
(29)
0.750 square inch, therefore
an air gap of one inch on each side of the core
A
to
the coil winding is
Window area
If
20 wire has a winding
The window area required
density of 621 turns per square inch.
accommodate
Number
4
45 x 10"
)
=
of
Eqs. 23 and 24.
assumed, Eq. 23 becomes
is
4
15.5 x 10" sq. meters
(30)
approximately
4
7
(15.5 x 10~ )—(4ir x 10~ )—
-j
(2) (2.54 x 10)
•
=
...
n
.....
5.03 millihenry s
,
w(31)
,„
(_ _}
Equation 31 shows that a total air gap of two inches will give approximately
the required inductance for
L>,
.
Exactly the required value
of
inductance
can be obtained by shimming the air gap and measuring inductance with an
impedance bridge.
This is the extent of the
PFN
inductor.
initial calculations that
Based upon these calculations
were made
the five
PFN
constructed and assembled for tests as shown in Fig. 11a.
the
completed breadboard model which
is the final
for each
inductors were
Figure lib shows
version of the PFN.
Preliminary versions differed from
this photo only in that capacitance
decade boxes, which were easier
manipulate during tests, replaced the
capacitors shown.
PFN
to
The exact nature and extent
are described in Chapter
III.
of the tests
performed on
the
CHAPTER
III
TESTING THE PULSE FORMING NETWORK
A.
MEASUREMENT OF INDUCTOR CORE SATURATION VOLTAGE
LEVEL
It
was desirable
satisfactorily under
determine
to
if
the individual inductors
would perform
normal operating conditions without having
and test the complete PFN.
to
assemble
Equation (13) states that the flux density in a
ferrite core inductor is proportional to the time integral of the voltage
This assumes that the resistance of the
applied across the coil terminals.
coil is zero, or at least
very small compared
to the coil
When
reactance.
the coil resistance cannot be ignored, the circuit of Fig. 9
can be used
to
subtract the voltage drop caused by the coil resistance and display a picture
of the hysteresis loop,
which in
this
case would be more accurately
described as a plot of coil flux versus coil current.
The operation
at point
the currents
Y
l
Which
By summing
of this circuit is as follows:
c '
»R
+
%
<
32 >
is
vR.
dv
V
R
v
-
v
v
c-*--itf--^-V
+
where:
v = vT + v
i
= coil voltage in volts
= inductor
current in amperes
r =
inductor coil resistance in
R=
10
C
one microfarad
=
R.
—
<R
ohms
ohm, 50 watt potentiometer
'
?
=
one megohm
-30-
-
v
V-
(33)
-31-
L
R,
I
*
.T-i*
-\
C
* Y
-
V
R2
':> R
X
R
FIG. 9
l
>V
R,
Rpt
CIRCUIT FOR DISPLAYING INDUCTOR
CORE SATURATION VOLTAGE LEVEL
20 volts/cm
20 volts/cm
FIG. 10
CORE HYSTERESIS LOOP
-32-
FIG.
FIG.
lib
11a
FIVE PFN INDUCTORS
BREADBOARD MODEL OF THE PFN
AND THE CHARGING REACTOR
-33-
The resistance
of the parallel
than the reactance of
and
if
we measure
in the coil,
and in
C
R } and R
£
combination of
The reactance
at 60 cps.
the coil resistance and set
R
much
will be
larger than
R
to this value,
or i_
i
.
On
v
small
the current
this basis
2
R
= -ir
v
c -
c - n
R^-R-;(33)
larger
can be made:
v
Then equation
much
of the coil is also
1
the following approximations
will be
(34)
can be written
v
=
cry J
c
vdt
-
dq J idt
<
35 )
But
RR
c
r
therefore
V
The hysteresis loop
c onnecting the
=
C
ciq
I
<
v
- ir
of the inductor core
>
dt
06)
can be viewed directly by
horizontal and vertical amplifiers of an oscilloscope to
points x and y, respectively.
This circuit
is
used by first calculating the flux density level
that the
inductor must absorb under operating conditions and relating
this level to
an rms voltage reading across the
here for
L,
coil.
Sample calculations are given
.
The voltage drop across an inductor
e(t)
=
I^-
coil is
'
(37)
-34-
Coil current in
L under
operating conditions
=
i(t)
o
sin^-
(38)
LI o i
T cos^TT
e(t)=
The flux density level
I
is
(39)
u
is
T
B
=
LI
f e(t) dt =
(40)
Or
This corresponds
to
one-half the total change in flux density that a
inductor will experience during a discharge pulse.
It is
PFN
required that the
inductance remain constant during this interval or that the flux density
remain
in the linear region of the hysteresis curve
T
2
J
at 60 cps this
e(t)dt = (2)(4. 69
corresponds
-,
3
x 10" )(20.
to a
—
= (0. 190)(0.707)
of Fig.
minimum
volt-seconds
(41)
voltage across the inductor of
00833
This must be the
3) = 0. 190
=
w
.
,,,.
l4
0>/ro
volts
RMS
.
(
4
*
*
voltage reading at the point where the curve
10 begins to change slope in order to
insure a constant value of
inductance during a pulse.
Figure 10 shows the hysteresis loop obtained for L, by
The voltage level corresponding
saturate: is 19.0 volts
perform satisfactorily
RMS.
in the
to the point
where
this
method.
the core begins to
This result indicates that this inductor should
PFN
under normal operating conditions.
-35-
CONSTRUCTION OF THE PFN TESTING CIRCUIT
B.
The
to
do this
For
PFN was
tested by observing
was necessary
it
testing the
to
assemble
dummy
network a
its
output pulse waveform.
shown
the pulse generator
shown
load, as
in Fig.
12, was
is
made variable
to
provide an exact matched load for the PFN.
pulse waveform referred
to is the voltage
The function
discharges.
while charging the
PFN
appearing across
of the diode is to
in Fig. 3.
used in
R
R
place of the pulse transformer, klystron, and elements D, and
order
In
The output
R T when PFN
remove R_ from
the circuit
improve charging efficiency.
to
The power supply used was a large nonregulated d-c unit that was available in the laboratory.
It
was arranged with
voltage to be varied from
arrangement
to
protect
500 volts and a current limiting circuit breaker
to
from overloads during
it
The charging reactor for
tests.
the test circuit could have
been any reactor
had low coil resistance, provided a satisfactory charging interval and
that
The one
did not saturate.
that
was used throughout
reactor described in detail in Appendix
and
a variac to allow the output
A
all the tests is the
and referred
to in
1,
3,
7.
The timing circuit and switching SCR's are discussed in
Appendix B.
ator.
PFN
However,
and
is
detail in
This part of the test circuit requires a lengthy discussion to
properly emphasize
C.
Tables
its
this
deferred
importance in the design of
discussion
is
this type of
pulse gener-
not pertinent to the actual testing of the
to a later part.
CORRECTION OF THE PFN OUTPUT PULSE WAVEFORM
Requirements
summarized
that the output pulse
as follows:
than 50 microseconds,
1)
2)
rise time
waveform must meet can
from
the
to
oe
90 percent level less
overshoot and ripple less than 10 percent,
-36-
Oroo a
Fig. 12
Dummy
Load for Testing
PFN
-37-
3)
approximately one millisecond in duration,
energy.
Item number 4
until the final
The
waveform was obtained and
first three
The
first
but
is significant,
items are covered in
PFN
version of the
it
4) contain
was not actually measured
the
PFN
efficiency
that
was tested had approximately
The actual measured element values differed
it
was
glas stock and
air gap.
slightly
of
from
the
Chapter
II.
the theoretical
inductor air gaps precisely using plexi-
diff icult to adjust the
mylar shims which was
The element values for
was calculated.
this section.
element values calculated from the theoretical discussion
because
4.8 joules of
the
method used
to
the first
PFN version
are listed in Table
The resulting output pulse waveform
is
shown
in Fig.
13.
obtain the required
4.
This pulse meets
rise time and duration requirements, but the ripple is about 25 percent and
gets
worse toward
the end of the pulse.
Table 4
Element Values
for the First
Version of the
Measured
PFN
Measure :d
C (M<f)
k
^(mh)
1
4.70
21. 5
2
4.80
3.
1
3
4.97
0.
775
4
4.80
0.
370
5
5.05
0.
180
Reference
1
indicated that an increase of sixteen percent over the theo-
retical values of inductance resulted in substantially
In order to
k
determine the amount
following approximations
of
improved waveform.
increase required in this case, the
were made:
-38-
TO
T/
-
=
z
"V
Z
T
= 18
(43)
TT
(44)
n
ohms (approximately)
= one millisecond
Solving these equations yields
This
is
L, = 5.75
mh
C1
n,f
= 17.5
(45)
an increase of twenty-three percent over the theoretical value of
The second version
of the
PFN was made
by increasing the inductance
values all by approximately twenty-three percent.
are listed in Table
L.,
These element values
5.
Table
Element Values
for the
5
Second Version
of the
PFN
Measured
C (M.f)
k
Measured
Calculated
L (mh)
L^mh)
k
15.0
1
5.75
5.75
2
5.85
5.85
1.512
3
5.88
6.05
0.495
4
5.90
6.00
0.241
5
5.95
6.20
0.
The resulting output pulse waveform
an undesirable overshoot
is
shown
of about twenty-five
in Fig.
14.
percent and
130
This pulse has
is
also too narrow.
In order to reduce the overshoot, the amplitudes of the higher harmonics
-39-
100
0.20
Fig. 13
msec
cm.
PFN
Version
30
Fig. 14
msec
cm.
cm.
Time
Output Pulse Waveform from the First
0.20
volts
Time
Output Pulse Waveform from the Second
PFN
Version
volts
cm.
-40-
were decreased by successively increasing
The
ments
final
of
version of the
PFN
was arrived
at
by trial-and-error adjust-
element values until a satisfactory pulse waveform was obtained.
This waveform
in Table 6.
shown
is
in Fig. 15a and the element values are
summarized
This waveform meets the first three requirerre nts verywell.
Figure 15b shows the rise time
than fifty microseconds.
to the ninty
Table
Element
percent voltage level
Figure 15a shows the pulse duration
one millisecond, and the overshoot and
rippj.e
is
is
approximately
6
L^mh)
PFN
C k (^f)
1
5.80
2
6.25
1.60
Z3
7.40
0.464
4
8.30
0.194
5
9.35
0.103
The adjustment
19.7
of inductance values for the final
was carried out with E
= 100 volts.
When
number
version of the
the supply voltage
give a 300 volt output pulse, the pulse shape
core saturation was beginning.
less
are less than ten percent.
"Values for the Final "Version of the
k
to
the values of inductance.
PFN
was increased
became distorted
indicating
This was remedied by recalculating the
required on each inductor, as shown here for L,, and
of turns
making the additions.
XT
N
=
—5.80
3
x 10" x
2
1.81 x 10
r
w
=
445
xO^
16.
x 1.27
=
..-
.
445 turns
,.,.
(46)
x 1.45
=
9.8 ohms/1,000
ft.
(47)
-41-
^—
Nj
-L
X
+
i
!
J
J.
X
J.
*
i
i
i
i.i
i
TW
\i
•
T";
;
x
I
+
X
\/'
L 1 1
Ml
J
volts
100
1
cm.
:
0.20
Fig. 15a
msec
Time
cm.
PFN
Output Pulse Waveform from the Final
Version
j.
X
X
X.
X
I
j
/
/
1
/
I
/
/
1
Li
J.
I
III!
Ml!
MM
I
1
II
Ml'
100
X
1
X
50
Fig. 15b
i-
sec
cm.
Time
Leading Edge of the Final Output Pulse Waveform
volts
cm.
-42-
This corresponds
to
number
wire which has a winding density
19
of 473
turns per square meter.
445
Window required
This
is
= -r^pr
the effective
window area
to
of the large air
gap which increased
approximately one square inch.
MEASUREMENT OF PFN EFFICIENCY
The efficiency
of the
PFN
effects of the charging reactor
for the
the
(48)
larger than the window of the Z-216 core, but the additional wire
was accommodated by taking advantage
D.
0.94 square inch
-
PFN.
PFN
of the
Figure
charges
PFN
is
to
is difficult to
must also be included
shows
17
describe independently.
that for a d-c
in the efficiency figure
power supply
450 volts in about five milliseconds.
about 0.2
ohm and
The
level of 240 volts,
The d-c resistance
the charging reactor resistance is 3.84
ohms,
Substituting this value of resistance into Eq. 78 gives
v(T
The attenuation
of the
)
= 1.925
PFN
x E
=
462 volts
(49)
voltage could be reduced but only by making a
larger reactor coil winding to reduce coil resistance resulting in a heavier
element.
When
the
The resulting pulse voltage level
PFN
of about
was tested with
20 msec between pulses.
from
the
in Fig.
17 as
200 volts.
full
power
if
the
PFN were
lossless.
at a continuous repitition rate of
The average power input
power supply was measured as
to its
This loss shows up as a lower
one ohm.
level output pulse than would be expected
PFN
shown
discharges, each inductor dissipates some power due
own winding resistance
The
is
to the
pulse generator
-43l
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:
-45=
P~
in
I
E
E
I
s
s
0.75 x 380 = 285 watts
=
power supply output current
=
=
power supply output voltage
The average power per pulse
is
in
(50)
v
'
amperes
in volts
given as
P— .IJ^d*
R
pulse
t J
(51)
T
wher e
t = 10
-3
seconds
PFN
e(t) =
output pulse voltage in volts
R T =1.75 ohms
The integration for Eq.
was carried out graphically as shown in Fig.
51
The resulting pulse power
is
P pulse
.
The average power output
n
P
out
=
—
=£Hr
17. 5
is
kw
(
v
52
)
'
defined as
4.53 x 10
ot;
Z0
t~
pulse repetition rate
s^rri
The resulting efficiency
3
00 , watts
= 226
/c _.
(53)
v
is
"-y^-MI
in
It is
= 4 - 53
power
r—pulse
c
16.
"
°-
794
(54)
not sufficient to discuss efficiency just in terms of power transfer.
In this case, it
may
be
more meaningful
to
describe the requirements of the
pulse generator in terms of energy transfer and output pulse shape.
The
pulse generator must deliver, to the klystron, 4.8 joules of energy in one
millisecond.
The pulse shown
output requirement.
required
4. 8 joules.
in Fig.
15 does not quite
The energy output
is
meet
the energy
only 4. 53 joules instead of the
-46-
The voltage level cannot be increased because
would adversely
Therefore, the only thing that can be done
effect the klystron.
the
this
energy in the pulse
is to
it
will reduce the
a poorer match with the load (Re:
values can only be
made
PFN
Eq.
One adverse
effect
characteristic impedance causing
A
5).
increase
This could be accomplished
increase its duration.
by increasing the capacitance values some small amount.
of doing this is that
to
final
determination of element
with the pulse generator actually driving the klystron
under operating conditions.
In
any case, the adjustments would be minor
and we can assume that the power requirement can be met without too much
difficulty.
E.
ENVIRONMENTAL TESTING
In order to insure a degree of space flight worthiness, the
PFN
inductors and the charging reactor were tested in a hot-cold chamber.
inductors alone were tested because
cal items since they
the
were
all
it
was
handmade.
felt that they
The capacitors
breadboard model would not be usedin a
final
were the most
that
version of
The
criti-
were used
this
PFN
in
and
there was no point in testing them.
The inductors were enclosed
generator was operated with
full
in the hot-cold
perceived.
the test pulse
operating voltage levels at -25 C for two
hours and at +50 C for two additional hours.
was monitored
chamber and
The output pulse waveform
for this entire period and no change in shape or level
was
CHAPTER
IV
SUMMARY AND CONCLUSIONS
SUMMARY
A.
This problem originated when the Electronic Systems Laboratory
at
M.I.T. constructed a breadboard model
system
for
making measurements
radar
of a space vehicle
This breadboard model had a line-type pulse generator which used a
that
to
was 22 inches long and weighed about
minimize
fifteen pounds.
It
it
was
felt that if it
PFN
was desired
the size and weight of the entire pulse generator.
the largest and heaviest item and
Venus.
of the reflectivity of the surface of
The
PFN was
could be optimized,
then the entire pulse generator would also be optimized.
Subsequent in-
vestigations verified this assumption.
The
problem was
first step in the investigation of the
to
make
a
study of the proposed line-type modulator to determine the parameters
that described the
A
optimum PFN and hence
guiding factor in the determination of the
the
optimum pulse generator.
PFN was
that the associated
components, such as the pulse transformer and the charging reactor,
had
to be physically realizable.. It
the combination of these
was assumed
that the study
components that resulted in
lightest weight complete pulse generator.
This
is
the details of which are in Appendix A, but there
would reveal
the smallest and
what the study revealed,
was the unexpected
additional result that the physical size and weight of the pulse transformer
was independent
of other
parameters
for the three values of
power supply
voltage that were assumed.
The power supply that would be used
in the
capable of operation at any fixed level between
this reason, the
3
complete system
00 and 500 volts.
is
For
values of power supply voltage taken for the study were
-47-
-48-
300, 400, and 500
volts.
For each
of
these three operating values, the
pulse transformer had a calculated weight figure of about 2.5 pounds.
This
is less
than the complete transformer would actually weigh because
the weight of insulation and packaging
was not considered.
figure indicated that any of the supply voltage levels
This weight
was satisfactory and
that final determination rested on the value that optimized the
was
PFN, which
the original assumption.
Two
chosen.
factors indicated that the lowest power supply level should be
First, the higher voltage levels would require heavier insulation
in the inductor coil construction, and second, the higher voltage levels
would require more turns in each
factor
was
coil to
prevent saturation.
the relative ease in obtaining 600 volt
A
final
SCR's as compared
to
1,000 volt SCR's for use as the switching devices.
There were two factors
this
PFN
It
was
made
the design and construction of
These are the high power and long pulse
a difficult problem.
duration.
that
felt that the size
and weight
of the
considerably by using ferrite core inductors.
PFN
The inductors had
linear, however, to obtain a satisfactory output pulse
meant
had
that the core material
throughout
its
to
could be reduced
to be
waveform.
made
This
be one that had a linear permeability
range of flux density.
This led to the examination of the
"square loop" materials and Z-type "Hypersil" was selected because
it
has a higher saturation flux density than the other materials considered.
One small problem with
this
in certain standard sizes.
material was that
it
was readily available only
The manufacturer's delivery time on these
"stock" sizes was two-to-three weeks, and the non-standard items had to be
specifically
made and took up
to nine
weeks
for delivery.
For
this
reason
-49-
one of the
more
readily available H-type Hypersil cores was used in the
construction and testing of the
The completed
PFN
inductors are shown in Fig. 11a with a reference
scale to indicate their size.
inductors
was used
compares
is listed in
PFN.
Table
The important characteristics
The
7.
of these
statistics for the charging reactor that
in the tests is also included in the table to indicate
to the
one used with the original
Table
Summary
of
PFN
PFN
how
it
which weighed 5.8 pounds.
7
Inductor Characteristics
Total
Number
Wire
Size(AWG)
Resistance
(ohms)
Weight
Inductor
Core
Li
Z-216
19
442
1.
11
0.917
L2
H-41
22
280
1.04
0.312
L3
Z-1
24
230
1.
L4
Z-4
24
290
1.24
0.129
H
Z-2
24
253
1.22
0.
of
Turns
10
N Inductors
Lc
Z-5
3.84
Total Weight of All Inductors
The small size and weight
of the
PFN
capacitors used in the final version of this
the total
PFN
weight
to
5.6 pounds.
inductors
Consideration was given
187
099
0.790
2.434
is significant.
PFN weighed
lbs
The
four pounds bringing
This weight can be reduced considerably
by having capacitors specially manufactured
ments.
0.
1.644 lbs
500
22
(lbs)
to
meet space application
to the fact that the
require'
highest operating voltage
-50-
required the smallest amount of capacitance.
considerable weight
to the
PFN
the capacitors will be lighter
This
voltage.
may
if
Since these items contribute
a superficial examination
the
PFN
is
would indicate
that
designed to operate at the highest
not true, however, because although less capacitance
is
be required, the units are larger and heavier than for a similar
lower voltage rating and no net savings can be realized.
The original PFN, shown in Fig.
twenty-two inches long.
about one-third as
2,
weighs fifteen pounds and
is
This new PFN, shown in Fig. 11a, weighs only
much and
could be packaged in about six inches by
four inches by four inches depending upon the capacitors and the arrange-
ment used.
The efficiency figure for
the
PFN, given
reasonable considering that a certain amount
PFN
in order to
make
it
compact.
by reducing the resistance
Although
larger.
above
it still
would have
may
be
may
to
this
of the
Some
in Chapter
of loss
III
as 79.4 /o, is
was designed
into the
saving in power could be realized
charging reactor by making the coil
would certainly improve the efficiency figure given
not be a desirable thing to do.
Any increase in
coil size
be accompanied by a larger core and the additional weight
more undesirable.
This efficiency figure also does not include
any loss that would be incurred by resetting a pulse transformer by the
method described
in
Appendix A.
In conclusion, the
a satisfactory
efficient,
It
answer
PFN
to the
that
was constructed and tested provides
problem
of size
and weight.
and operates satisfactorily over a wide range
produces a pulse waveform that meets
all the
It is
of
reliable,
temperatures.
requirements but energy
-51-
content.
This deficiency
is
small, however, and can be easily corrected
by making the pulse duration a
little
longer by increasing the capacitance
a small amount.
The circuit that was used
to test the
PFN
is
a complete pulse generator
with the exceptions of a pulse transformer and proper power supply.
also the
optimum pulse generator
of this type for this application.
refinements in the timing circuitry
to
It is
With
meet environmental requirements
would be ready for further application in
the
complete radar system.
it
APPENDIX A
A PARAMETRIC STUDY OF THE OPTIMUM PULSE GENERATOR
The object
The
of this thesis is
initial step in the
an optimum
PFN
PFN
construction of this
voltage at which the system will be operated.
as described in Chapter
is to
II.
determine the supply-
The power supply voltage
be used in the pulse generator can be any level from 300
to
500 volts.
that
would
This
appendix studies the effect of power supply voltage on the components of the
pulse generator.
All calculations are based upon three values of
E
as
shown
in Table 8.
A.
THE PULSE TRANSFORMER
The elementary theory
transformers
of pulse
is sufficient for the
purpose of describing the smallest possible transformer that will work in
this
pulse generator.
must consider
and ease
The actual construction design
details of
of construction.
minimum
transformer
distortion of the pulse shape, efficiency,
These items will not be evaluated here since they
are not too important in the determination
A
of this
simplified model of a transformer
of size
is
and operating voltage.
given in Fig. 18.
The relation-
ships between primary and secondary quantities are
E
I
=
I
p p
=
I
p
E
Es
(55)
NI s
(56)
E
-^
N
(57)
=
p
s
E
E /I
_£.= _£*.
X
N^
p
(58)
The transformer being considered here will drive a klystron with an
input pulse of 4. 8
kw
at 8, 000 volts.
-52-
-53-
so'
E
E
=
= 8, 000 volts
=1
I
= 0. 60
(59)'
K
amps.
(60)
E
~-
13,300 ohms
=
(61)
s
This pulse transformer must meet the following specifications:
not saturate during a pulse,
must not store
2)
magnetic energy during a pulse,
4)
must be compact and
If
3)
a large
must have low
amount
1)
must
of residual
resistive losses, and
light weight.
the voltage input to the
primary
is in
the
form
of a rectangular pulse,
T
e(t)dt =
:
ET
(62)
Because the transformer will be reset between pulses,
core, as shown in Fig. 8b, can be used.
but
it
does not
during a pulse
make
if
This
may
transformer unfeasible.
the
a gapless toroidal
complicate construction,
The
cc::e will not saturate
the turns-cross section product satisfies
NA = ||.
The number
of turns in the
(63)
primary winding must be
the residual magnetizing current to a
minimum
reasonable figure that gives good results
is that
sufficient to keep
at the end of a pulse.
magnetizing current should
be less than five, percent of load current.
I
m =0.05x1p
The primary inductance
is
(64)
given by
T
I
m Lp =
I
tJ
e(t) dt
A
(65)
-54-
>
Cn—^sr
/»
R
,-rm
rv^_
L
<r
/V~A°
R
Ls
:
S^
v
/;/v
SIMPLIFIED
PULSE
o
TRANSFORMER MODEL
AAA
C*
^
V
¥
*
FIG. 19
EQUIVALENT
—.J
.J
CHARGING
NETWORK
-55-
E T
L =-=E-
In addition, the
(66)
primary inductance
is
related to the core material by
N 2 Aia
L
——
pi
m
=
A
= core cross section
=
M.
m=
1
(67)
v
'
T
^
core permeability
magnetic
path length
to
r
°
Z-type Hypersil has an incremental permeability
of
approximately
o
8,
000 over the operating range of flux density.
able answers but
This figure gives reason-
probably lower than the actual permeability.
is
of permeability taken as the average slope of the
operating limits
is
about 44, 000.
7
because the frequency components
This value
is
of the pulse
lower of these two values of permeability
is
The value
d-c.B-H curve between
higher than can be expected
are at least 500 CPS.
used for
The
all calculations to
allow for the higher frequency components.
Calculations were
made
for several toroidal cores before a choice
reached.
However, only the calculations for the Z-361 core are shown
since this
is the
one finally selected.
1
Volume
Core
Z-361
A(in
(in3)
7.85
Assume source
Primary
2
1.00
)
m
Window
Weight
(in)
(in 2 )
(lbs)
7.85
3.14
1.95
voltage of 300 volts.
turns:
N
=
P
300 x *°
_3
4
(6.45 x 10" )(2.9)
=
160 turns
(68)
was
-56-
Secondary turns:
Turns ratio
Ns
lj°°2
=
= (26.7)(160) =
The winding resistance
is
= 26. 7
(69)
4,275 turns
determined by limiting
it
to five
percent of the
load impedance.
R primary
= (°- 05 >< 18 - 7
Secondary
The average length
is
=
<
>
= °- 97 oh
™s
05 >< 13 300 > = 665 oh
'
'
turn
of a winding
™s
calculated from the core geometry
approximately
i
c
=
F
+
2E
+
2D
= 0. 583 feet
(70)
Primary winding resistance
r
This corresponds
w
to
= (l oQKQ^si) = 10 5
-
ohms /^
00 °
ft '
(
?1
)
number 20 wire.
Secondary winding resistance
r
w=
This corresponds to
|i&=
2ttohWM00ft.
(72)
number 34 wire.
The winding stacking factor was determined by examining a pulse trans-
former
of
in the laboratory.
This transformer has a primary widning consisting
400 turns of number 24 wire and a secondary winding consisting
turns of
and
8,
which
number 32 wire.
4,200
The primary and secondary voltages are 300 volts
000 volts, respectively.
is
of
The core window area
is 2. 06
square inches
completely filled with wire and insulation. By taking the total
wire area and dividing by the window area a stacking factor was determined
for use in further calculations.
-57-
X
(Number primary turns)(Area
=
+
20 wire)
of no.
(Number secondary turns)(Area
/window area
32 wire)
of no.
(73)
X
Stacking factor
=
0.163 turns
=
In addition, a hole large enough to pass a winding shuttle
Most
the center of the window.
inch diameter hole.
shuttles can be
must be
left in
accommodated by
a one-
Therefore, an area of 0.785 square inches must be
subtracted from the core window area.
The window area required
to
accommodate
the windings can
now be
obtained from Eq. 73.
w
Window
area required
.
.
.
.
000802)— +
(160)(0.
—
= -
.
.
=
1.6 square inches
=
3.14
Available window area
If
275)(0.
— 000031)L
163
(4.
A -s
,
0.785 =2.36 square inches
-
the weight of insulating materials and other attachments such as
terminals
is ignored,
measure
a
of the total
transformer weight can be
calculated for comparision purposes.
Weight
of
winding
(Number
=
Primary winding
(4,
Total coil weight
=
0.588
=
1.950
=
2.538
Primary inductance
=
p
gfe0>
(74)
.
(75)
is
2
L
)
275)(0. 00012)(0 583) = 0.300 lbs.
Secondary winding=
Transformer weight
turns)(Weight of wire)(i
(160)(0. 00309)(0. 583) = 0. 288 lbs.
=
Core weight
of
(6.45xl0-
4
)(8
.
OOOH^xlO- 7
£0
)
= Q
g32 he
-58-
The minimum primary inductance required
.
L
=
p
is
3
300 x 10"
.__
= n
0.375 henry'
n—
0.
,
These calculations show
that the
Z-361 core
(77)
is
adequate in
respects.
all
Similar calculations for supply voltages of 400 volts and 500 volts show that
the
same core can be used.
The results shown in Table
pulse transformer size
is
are interesting because they show that
8
independent of the supply voltage.
This means
PFN
that the size of the
optimum pulse generator depends solely on
charging reactor.
All other elements are fixed in size by the power
the
and
handling requirements.
Table
8
Summary
of Pulse Generator Parameters
and Pulse Transformer Characteristics
Supply voltage
E
Char, impedance
Z
Total
PFN
cap.
C
Total
PFN
ind.
Ln
Load current
I
Load voltage
E
Primary current
I
Pri.
mag. current
n
n
o
I
o
m
N
No. pri. turns
N
400.0
500.0
Ohms
18.7
33. 3
52.0
V*
26.7
15.0
9.6
,16.7
26.0
0.6
mh
9.35
Amps
0.6
0.6
Volts
8000.0
8000.0
Amps
116.0
12.0
8000.
9.6
Amps
0.80
0.48
0.60
Turns
26.7
20.0
16.0
Turns
160.0
214.0
267.0
20.0
21.0
22.0
4275.0
4275.0
34.0
34.0
P
Number
Pri. wire size
Sec. wire size
300.0
P
Trans, turns ratio
No. sec. turns
Volts
s
Ns
Turns
Number
'
4275.
34.0
-59-
Table
Max.
8
(Continued)
pri. resistance
R
Ohms
1.0
Max. sec. resistance
R
Ohms
665.0
2.60
1.67
665.0
665.
Min. pri. induct.
Henry
0.3
0.667
1.
Calc. pri. induct.
Henry-
0.832
1.49
2.32
Pri. coil weight
lbs.
0.288
0.305
0.340
Sec. coil weight
lbs.
0.300
0.300
0.300
Core weight
lbs.
1.950
1.950
1.950
Total weight
lbs.
2.538
2.555
2.590
B.
THE CHARGING REACTOR
The principle
of resonant charging
5
is
used
to
charge the
PFN
This method works best
approximately twice the supply voltage.
to
when
the
resistive losses in the charging network are small and the value of charging
inductance
large with respect to the total inductance of the
is
PFN.
If
these
conditions are met, the equivalent charging circuit is shown in Fig. 19.
assumed zero
Solution of this network, with
v
n
(t)
=
Es[
L
1
- e
-at
E
.
...
l
(t)
s
—r—
=
e
(cos
-at
cot
sin
+
—
w
sin
initial conditions, is
cot)]J
(78)
.
(79)
cot
c
where:
R
(80)
2T7
R
= total
L
° =
Cn
network resistance
= inductance of charging reactor
(
trrr
c n
= total
~
1/2
R
1
"
4L.
PFN
capacitance
(81)
04
-60-
If
losses are small, the solutions reduce to the approximations
v
(t)
=
E
(1-cos
(82)
cot)
E
i
The
PFN voltage
n
(t)
=-r~
coi-<
will reach a
sin
(83)
cot
c
maximum
2E when
s
of
t
=
tT\I L>
*
c
C~
n
At
.
this
time network current will be zero.
The normal method
of applying this principle is to trigger the
discharge at the resonant frequency
completely and then allowed
to
Tr
It is
with the original
Figure
PFN
2
=
by using
much
it
Lc
made
ma
is
about ten times
L
Secondly, an
L.
is too
large, the
to
be satisfactory.
are similar
to
must be used
SCR
13.
of a charging
L.
n
.
SCR
In this
Any value
'
A
value
generally requires about 30 to
microseconds,
q
to
turn
it
on;
will not fire because the timing
A
value of
L
= 130
for this reactor using a
those for L, given previously.
in place of e(t) in Eq.
was required
First, the charging period will
SCR
The calculations
that
in the calculations.
pulses are only about ten microseconds long.
found
The use
of gate current, sustained for several
the reactance of
discharged
would require a very large
as small as desired.
larger will cause two complications.
long.
is
(84)
this principle.
this will not justify ignoring
become excessively
PFN
n-\flTC n
shows the charging reactor
case the c
practical lower limit on
smaller than
which case the
charge again with the repetition rate
allows the charging inductance to be
if
in
not disirable to do this here because
charging reactor.
150
co,
PFN
The value
of v(t)
mh was
Z-5 core
from Eq. 86
-61-
&
-H-t-
++++ +*++ M-H-
++H +«
100
VOitS
Cm.
-/
2.0
Fig. 20
msec
Time
cm.
Power Supply Level and DC Resonant Charging
of
PFN
T
4!•
•.•.I
'
i.i
i
'
-
i
i
j,'-'
100
2.0
Fig. 21
PFN
msec
cm.
Time
Oscillations After an Output Pulse
volts
cm.
-62-
The charging period
T
c
is
3
6
(130 x 10" x 19.7 x 10" })* = 5.05
=
PFN
Figure 20 shows the
clearly in Fig. 21.
the
PFN
mismatch
is
shown
mismatch
is
required
end
of a pulse.
SCR
PFN voltage
In this figure, the
the end of a pulse and the ripples
the result of the
in Fig. 20 are
matched
PFN
stops conducting, the
is
oscillation.
to the load.
small reflection
The
This
is
turned
This
off at the
not zero at the end of a pulse
losses are very small and
it
is
slight
of the load pulse.
SCR
insure that the discharge
PFN voltage
shown more
not allowed to recharge at
is
show up as a damped
15 as a
in Fig.
The
PFN
not being perfectly
to
(85)
voltage and-power supply voltage during the charging
The small ripples on
period.
ms
when
the
therefore
These oscillations in no way adversely
oscillates with little damping.
effect the pulse generator operation since they do not appear across the load.
The possibility
the
of eliminating the charging reactor
primary winding
of the pulse
The voltage across a reactor
v
L.,
L (t)
=
transformer in
its
completely by using
place has been considered.
as in Fig. 19, is
E
cos w t
(86)
The reactor must not saturate during the charging interval.
This corre-
-
sponds to satisfying the equation
T
AB NA
If L. is
=
f
v(t)dt =
E Y'Lc"
s
n
sin (ttL
CJ
(87)
taken as the calculated transformer primary winding inductance
from Table
8,
this
reduces
to
AB NA
whereas
the pulse transformer
= (E
s
)(208
x 10' 9
was designed
AB NA
=
E x
S
)
(88)
to satisfy
10" 3
(89)
-63-
The difference between Eq. 88 and Eq. 89 indicates
former would not be reset
in the charging process
it
would most
to this:
use a cut-core with an air gap, which would result in a much larger
transformer,
3)
and that
There are three solutions
likely saturate during the next pulse.
1)
that the pulse trans-
2)
reset the gapless core from an external source, or
use a separate charging reactor.
able since
it
The third solution
will lead to the lightest pulse generator.
former must be reset during
the charging period.
is
the
most accept-
But, the pulse trans-
This requires that a
large voltage appear across the transformer primary winding in order to
reverse saturate the core.
In order to protect the klystron
the series combination of D,
and
from large negative fly-back voltages,
R,
is
The diode protects the klystron
used.
while the resistor provides the necessary voltage to reset the pulse trans-
former.
The equivalent charging circuit becomes similar
The assumptions are
than R, and that R,
1c
k
primary winding reactance
that the
is
much
larger
than
&
Rn
.
is
to that of Fig.
much
The voltage across
to
19.
larger
R.
k
is
approximately
E
v(t) =
ft
*
Rk
s
j-2.
sin
(90)
cot
c
Substituting
to
-
(91)
C
ifL
c
n
\
yields
v
(t)dt =
2Rk E s
-^ =2R
Therefore, the value of R, required
the charging period is
to
k
E Cn
s
(92)
reset the pulse transformer during
-64-
r>
R,
=
N2
3
x 10"
Yn
the resistances
R
and
n
2
x E
,
to
to a
600 volts.
xl0" 3
7T
1Q nnn
000
~ 18»
,.
/Q
(93)
.
ohms
.
system will be reduced due
Instead of the
PFN
charging
to
to
damping by
approximately
k
the final value, found
s
corresponds
PFN
of the
R
2
39.4 x 10
n
The charging efficiency
= (26.7)
from Eq.
i
78,» will be about
1. 6
x E
required supply voltage of 375 volts in order
.
to
.
This
s
charge the
APPENDIX B
SILICON-CONTROLEED-RECTIFIER
SWITCHING DEVICES AND TIMING CIRCUIT
When
this thesis
first
proposed, one
questions that had
effectively be
used as
At the time, commerically available SCR's had a
switching devices.
peak-forward-voltage rating
at least one
of the
was whether or not SCR's could
to be investigated
maximum
was
of 850 volts.
9
There was, however,
manufactufef who indicated that an SCR with Ratings
volts and 110
amperes was available.
13
There was no indication
of
i,
of the
availability and cost of this higher rated unit nor of its performance.
was
when
a contributing factor
Once
the
power supply voltage had been determined as 300
and an unmarked SCR that was tested and found
of an
SCR
proper times.
by opening the circuit or
first
method
maximum
is
used
2)
for
SCR-1
have the proper voltage
for
to switch the
means;
1)
to
SCR
off
and on
non-conducting
interrupt the flow of current
to turn off
SCR-1.
When
the
PFN
voltage reaches
during charging, the charging current, through SCR-1,
SCR-2.
The
9.
apply a negative voltage from anode to cathode.
and the SCR stops conducting
used
to
The switching from conducting
states can be accomplished by two
a
A 2N-691 was used
are given in detail in reference
primary problems faced here were simply how
The
volts, the
was used as SCR-2.
The characteristics
at the
This
power supply voltage was selected.
the
SCR's were selected from the laboratory stock.
rating
200
until triggered again.
The mismatch between
is
zero
The second method
the load and
PFN
characteristic
impedance causes
a small negative step at the end of the pulse which is
sufficient to cause
SCR-2
to stop conducting.
-65-
is
.66-
o
o
<*
I
or
O
K
<r
8
UJ
-I
a
cvj
-67-
In order to trigger the SCR's on at the proper times, the circuit of
Fig. 22 was constructed.
Basically, this circuit produces two sets of timing
pulses as shown in Fig. 23.
In each set, the pulses are twenty milliseconds
apart and the two sets of pulses can be shifted with respect to one another.
One
set of pulses is
set is
used
to trigger
between the sets
the
PFN
used
to trigger
SCR-2
of pulses
and discharging
The timing circuit
is
SCR-1
for charging the
to discharge the
PFN
and the other
PFN. The amount
of the offset
merely determines the delay between charging
it.
capable of operating continuously
at a
pulse
repetition rate between five and twenty-five milliseconds or, by closing the
toggle switch, as a burst generator that will produce a four pulse burst at
intervals from one-half second to about five seconds.
rate
Fig.
was decreased from
1,
to
more
The burst-repetition
the required fifteen second interval, as
easily view the tests by oscilloscope.
shown
in
-68-
2E s
E
Time
PFN VOLTAGE
E.
Time
PFN OUTPUT PULSES
6 volts
k—
20.
i(
20
-5* -;
IT.S
ns
Tims
TIMING CIRCUIT CHARGING PULSES
6 volts
2017.3
H-«
20
ms
>
20
ras
i—
Time
TIMING CIRCUIT DISCHARGING PULSES
FIG. .23
TIMING PULSES
BIBLIOGRAPHY
1.
Glasoe, G.N. and Lebacqz, J.V.; "Pulse Generators",
Radiation Laboratory Series; McGraw-Hill, 1948..
2.
Weiss, H.G., "Haystack Microwave Facility", IEEE Spectrum,
February, 1965.
3.
Roberge, J.K., "Design
of Spacecraft
Radar Systems
for
Investigation of the Planet Venus", Electronic Systems
Laboratory, M.I.T., 1962.
4.
Dertouzos, M.L. and Bosco, J. A. "Design of a Radar System
for Measuring the Electromagnetic Reflection Characteristics
of the Earth's Surface from a Satellite", Electronic Systems
Laboratory, M.I.T., 9461-M5, September, 1963.
5.
Reintjes, J.F. and Coate, G.T., "Principles of Radar",
McGraw-Hill, 1950.
6.
Jordan, R.L., "Semi-Conductor Magnetic Pulse Generators",
S.M. Thesis, M.I.T., 1962.
7.
Arnold Engineering Company Bulletin SC
8.
Westinghouse Company Descriptive Bulletin 44
9.
General Electric Company, "Silicon-Controlled Rectifier Manual",
,
-
107A, March, 1963.
-
550,
December, I960
1961,
10.
M.I.T. Department of Electrical Engineering Notes for Experimental
Electronics Laboratory, 1963.
11.
Terman, F.E., "Radio Engineers Handbook", McGraw-Hill,
12.
International Telephone and Telegraph Corporation, "Reference
Data for Engineers", American Book - Stratford Press, 1956.
13.
Texas Instrument Newsletter, Volume
-69-
2,
Issue
3,
1943.
October, 1964.