I
APPENDIX
C
AUTOTRANSFORMERS
The autotransformer
atically
in Figs.
designed by J. C. Martin
C. 1 a, b, c, d.
and I. Smith’ is shown schem-
It consists of 0.002- to 0.005~inch copper foil
cut to the shape indicated in Fig. C. la and attached to a sheet of polyethylene
mylar insulation.
As indicated in Fig. C. lb
absorbent
or
(toilet) paper of about the
same thickness as the copper is inserted around the edges of the copper to fill the
remaining
cylinder
space. The sandwich is then wound on an insulating
cylinder
(e. g. , a
made of lucite) which has an outer radius and length appropriate
particular
transformer
a second insulating
cylinders
being constructed.
cylinder
As indicated in Figs.
C. lc and C. Id,
is added after the winding is completed,
are sealed at the bottom by an insulating
important
function of distributing
The arrangement
The primary
the field smoothly at the edges of the copper wind-
used for generating
C
prim
sheets does not occur.
the flux linkage from primary
inputs of the transformer
across a capacitor
Vin by closing a switch
S. The outputs of
be a Blumlein.
Alternate
of Fig. C. 2b is constructed
C. 2a.
C. la-d) are connected
A and B, are applied to the load Csec, which might,
arrangements
- --
to secondary.
a high voltage pulse is shown in Fig.
(C and D of Figs.
at a voltage
The tapered
the secondary,
transformer
with copper
been outgassed. The copper sulfate* has the
ing so that breakdown through the insulating
windings are intended to optimize
and the two
plate. The result is put into an
evacuated chamber for several hours and is then vacuum impregnated
sulfate solution which has previously
for the
are shown in Figs.
for example,
C. 2b and C. 2~. The
by cutting off the pattern of Fig. C. la
just left of the point C and by using C as one of the secondary as well as one of
the primary
original
a primary
*
leads. The transformer
of Fig. C. 2c is constructed
by winding the
sandwich back upon itself just after the point D and by using D as both
and a secondary lead.
The resistivity
of the copper sulfate solution should be of the order
- 134 -
lo4 ohm-cm.
I
\lNSULATING
SHEET
C
D
COPPER FOI L7
b min
a.
/
COPPER FOIL
/MYLAR
INSULATING
SHEET
:n-n
,~.~::.;.
.;;
.,.
..:.._
i.1
;.::
.i:::
.‘
:.,...
;:.‘
:../ )
-VACUUM
IMPREGNATED
WITH Cu SO4
SOLUTION
B
d.
C.
757~26
FIG. C. l--Layout
and construction details for the autotransformer
by J. C. Martin and I. Smith of AWRE.
- 135 -
developed
FIG. C. 2--Three
A
different
a.
circuit
configurations
csec
b.
for the autotransformer
B
..
B
developed by J. C. Martin
PD
set
A=B
An equivalent circuit
age inductance
windings
for the autotransformer
in nH can be calculated from the total thickness of the
Lleak
A, the minimum
and maximum widths of the windings
and the radius of the transformer
of Fig. C. 2a, 2.0 for the cir-
of Fig. C. 2~. All dimensions are in cm.
L,,, /N2,
40 r2
= r+b IllaX
nH
N is the turns ratio.
+ L-]
The final factor,
hl
inductances.
(
=
where
gap
l
%a1
+L
)
Csec),
is the
for the loss in voltage due to
nsec
cap + Lleads + Lleak
L is expressed in nH and C in nF.
is greater
+ ’
fC-lc)
The rise time of the output pulse in nsec is given by
l/2
T = 7r Ltotal
[cpri::gsec]
2 C prim/(Cprim
~Wnging efficiency It; the first factor is an expression
the various
(C-lb)
.
the ratio of output to input voltages is given by
L .
+PL’,, - 2.f:p
prim
leads
where
l
inductance is given by
L prim
Neglecting
:C -la)
nH
p has a value of l/2 for the circuit
cuit of Fig. C. 2b, and 1.0 for the circuit
The primary
bmin and bmx,
r:
36 Ar
= ’ (2bmax + bmin)
Lleak
The parameter
is shown in Fig. C. 3. The leak-
It is assumed throughout that 2r
than bmax and that r is much greater
-
137 -
than A.
~-
I
I
!i
LGAP
--
1
I
I
I
1
I
I
L LEADS
FIG. C. 3--Equivalent
I
CPRIM I
circuit
1
T 1
I
I
L~----.-l
I
r- -I
I
I
I
I
I
for the autotransformer
LGAP
LLEAK
developed by J. C. Martin
1
1
and I. Smith of AWRE.
757A28
Z N2 csec
Some calculations
based upon Eqs. (C-la-d)
are plotted in Figs. C. 4 and C. 5.
In Fig, C. 4, the rise time T is given as a function of bmax for various values of r
and for all three transformer
configurations.
The turns ratio
16-20, was adjusted to satisfy the requirement
V
was the required
out
output voltage assumed for the two-meter
this case was to minimize
=
v.
=
in
cap
=
gap
=
L
is inconvenient
500 nF ,
C
The fixed
= 0.9nF,
set
= 1.5cm,
l.OnH,
A
4.OnH,
Input energy
transformer
= 624 joules .
is preferred;
The rise time decreases slowly with transformer
close to minimum
In Fig. C. 5, we have plotted
for
Vout versus
in the center top configuration
C
prim
with four
ESC 295 capacitors
The fixed parameters
= 250nF,
were:
Lleads
= 6.OnH,
C set
= 0.9nF,
L
= 2.OnH,
A
= 3.0 cm ,
gap
= 4.OnH,
Input energy
Tobe Deutschmann Laboratories,
= 1240 joules.
Canton, Massachusetts
- 139 -
in series.
Vout; the resulting
= 100 kV ,
L
radius (as long as
T for various values of r and
V.in
cap
it
bmax 1 20 cm.
this case, the number of turns was chosen to maximize
was N =- 16 at every point.
however,
since the input leads attain roughly half the output voltage
2 7~Nr << TC), and it is fairly
*
Our mtention in
= 6.OnH,
Lleads
50 kV ,
in practice
during the pulse.
max
in series.
the rise time for the given output voltage.
As indicated in Fig. C .4 , the center-tap
b
chamber and where
values were:
Cprim
L
in the range
Vout /Vin = 800 kV/50 kV = 16, where
V.in was the voltage rating of two ESC 259* capacitors
parameter
N, typically
In
value
I
I
!G
0
a
I
20
l.
l.
‘.
l.
-.
l.
I
--..
30
l.
I
l -..
I
I
I
40
I
50
Y;r,“,“,m,
r=7cm
I
60
-v
--
-
I
70
----a
-----
r=9cm
I
r=llcm
80
I
757A.29
r=8cm
_ _
r=lOcm
r=ll cm
r =12cm
-----...- --------........_.__...............--.--------0-
l -.. ----
I
FIG. C. 4--Calculated rise time in nsec for V o~t/Vin = 800 kV/50 kV versus bmax, the maximum width of the tapered
autotransformer
winding. Calculations were made for the three circuit configurations indicated and for the
transformer radii shown with each curve. Additional parameter values are included in the text.
10
01
t
I 3.
‘1
-i
I
L
l.
1400
z
P
1300
6
ii
z
a:
1200
E
3
E
1100
5
57
g
1000
3
z5
900
P
800
I
0
1
I
I
I
I
I
I
I
100
RISETIME
T
IN
1
200
NSEC
I
I
I
I
300
757E.O
FIG. C. 5--Calculated output voltage maximized with respect to the number of
turns in a center-tap autotransformer
versus the output rise time
in psec. The maximum width b
of the tapered winding, and
the radius r identify the differe%%rves.
Additional parameter
values are included in the text.
- 141 -
Figure C. 5 illustrates
that the output voltage has a maximum as a function of T
and N, and that ultimately the rise time can be shortened only
max
by sacrificing output voltage. Since the transformer would be followed in our ap-
as well as b
plication
by a pulse-shaping
network,
the rise time is important
adds to the delay in applying the final pulse to the streamer
REFERENCE
1.
J. C. Martin and I. Smith, private
communication.
- 142 -
only in that it
chamber.