close

Вход

Забыли?

вход по аккаунту

?

Патент USA US2115826

код для вставки
May 3, 1'938.
E. |_. NORTON ET Al.
2,115,826
IMPEDANCE TRÁNSFORMERFiled Sept. 30, 1936
2 Sheets-Sheet 1
ATTORA/Eff
Patented May 3, 1938
v
UNITED STATES PATENT OFFICE
2,115,826
IMPEDANCE TRANSFORMER
Edward L. Norton, Summit, N. J., and Ronald F.
yWick, St. George, N. Y., assignors to Bell Tele
phone Laboratories, Incorporated, New York,
N. Y., a. corporation of New York
Application September 30, 1936, Serial No. 103,316
'
1s claims.
(o1. 17a-44)
'I'his invention relates to impedance transform-
rents induced in it by the coil. While this effect
ers for coupling lines or electrical devices of un-
could be eliminated or reduced to a small value
equal impedance and has for an object to provide
an impedance transformer which will be substan5 tially independent of the frequency over a Wide
range of high frequencies.
In the preferred embodiment the coupling de-
by slitting the sheath, it is desirable because it
permits a much greater rate of change in e than
would otherwise obtain, and also because it acts 5
as an electromagnetic shield for the coil. The
tapering effect can be controlled by varying the
vice takes the form of a tapered transmission
line comprising a long cylindrical coil of a large
lo number of turns surrounded by a concentric metallic sheath of circular cross-section in which
the sheath or the coil is tapered in radius. The
diameter- of sheath or of coil or both, or by vary
ing the number of turns per unit length of the
coil. This latter could be accomplished by vary- 10
ing the pitch of the winding or by using a multi
layer winding and varying the number of layers.
dimensions of the coil and sheath and the rate
of taper have values dependent upon certain fac16 tors such as the ratio of the two impedances to
In the embodiments hereinafter described, single
layer coils of constant pitch have been used, with
either the coil diameter uniform and sheath di- l5
be connected by the device and the minimum frequency to be transmitted as will be explained
hereinafter. In employing such> a properly de-
ameter variable, or vice versa. When a tapered
line is so constructed that its impedance varies
from some value, 21, at one end to a different
signed device as ahigh frequency transformer between a low impedance line and a high impedance
value, 22, at the other, it behaves like a trans
former at suiiiciently high frequencies. It is this
line one terminal of the low impedance line is
property with which We» are here concerned.
connected to the low impedance end of the coil,
Nl 0
Referring to the drawings,
one terminal of the high impedance line is conFig. i represents a longitudinal section and Fig.
nected to the high impedance end of the coil, » 2 a cross-section of an impedance transformer in
o5 and the other two terminals of the two lines are which the coil is of constant radius and the sur- 2,
connected to opposite ends of the surrounding metallic sheath. The parameters of such a tapered
line may be readily computed in order that its
rounding sheath is tapered;
Fig. 3 represents the manner of connecting the
impedance transformer of Fig. l in a transmis
impedance at each end will be substantially equal
sion circuit;
30 to the impedance of the line connected thereto.
The device constructed in this manner will act
efficiently as a step-up transformer over a wide
range of frequencies and the device is of particular interest in the frequency range above one
Figs. 4 and 5 represent another type of im- 30
pedance transformer in which the coll is of ta
pered diameter and the surrounding sheath is of
constant radius;
Fig. 6 is an enlarged longitudinal section of the
35 million cycles per second.
tapered line of Fig. 4;
_
A uniform transmission line is characterized by
an impedance, f-
35
Fig. '7 represents the frequency transmission
characteristic of the tapered line of Fig. l;
/f
1=\ ë
¿o
Fig. 8 represents the contour of the tapered coil
line of Fig. 4; and
Fig. 9 represents the contour of the tapered 40
and a, velocity constant,
1
a :w/_L-ö
45 where L and C are the inductance and capacity
per unit length of the line. It is possible so to
construct aline thatLand C vary along its length,
giving thus a tapered line. A flexible and practical arrangement consists of a solenoid enclosed
50 in a conducting sheath. The ratio of sheath diame-ter to coil diameter at any point then deter-
mines C, while L is determined by this ratio, the
number of turns per unit length, and the diameter of the coil, at that point. The sheath af5 fects the inductance, of course, because of cur-
Sheath line 0f Fig, 1_
v
In determining the parameters of such tapered
line used as an impedance transformer advantage
is taken of the observation that when the dif
ferential equations are expressed in terms of the 45
time required fOr a Wave t0 Travel along the
line, instead of in terms of the distance, the ve
locity function drops out. That is, the electrical
characteristics of a tapered line depend solely on
the Way in which the impedance varies with the 50
time of transmission. Thus all the electrical
characteristics obtainable with tapered lines can
be studied by considering different functions for
this one parameter. A particular function for
the impedance having been chosen, the actual 55
2
2,115,826
shape of the line, for any desired type of con
struction can be found by direct means.
We begin the mathematical discussion by writ
ing down the fundamental differential equation
for a non-dissipative transmission line with a
sinusoidal applied voltage of frequency
(d
is the value of the line impedance at the low im
pedance end, say the left-hand end. The phys
ical significance of t1 is explained as follows: Sup
pose the line were extended to the left until a
point was reached where the line impedance was
zero. Then t1 is the time required for a wave,
started at this end of the line, to reach that part
of the line where 2:::1 (the actual extremity of
the physical line).
Another type of characteristic is the exponen
tial:
10
x(t)=z1e"‘
(5)
in which the rate of taper is determined by a.
'I'his is a limiting case of (4) obtained by allow
ing m and t1 to approach infinity in such a way
that
i==current at same point
L=inductance per unit length at this point
C=capacity per unit length at this point
20
10
f1
remains constant,
j:«/îî
When the function (4) is used for zu), Equa
tion (3) becomes
Expressed in terms of the impedance,
.=\/ë
C
25 and the velocity,
25
1
8::
A
«l C
these equations are:
d'v
30
z
“ai-wal
d
_
1
"ai Jwza"
(l)
Then Equation (6) becomes
d‘W
(2)
35 The time required for a wave to travel to this
point from the end where X=0 is
clW
-1 2
ßLîsï-i-ad--l-[?-(E-r) :IW/:0 (7)
S
This is Bessel’s equation and the general solution
for the current in a tapered line having the type 35
of taper given by Equation (4) is thus
X
f= 0 «Qi
8
where
40 from which
40
@11m-Hol
and lf2-¿ammi
2
2
si _i
dX-_a
Since
are Bessel functions of ñrst and second kind, re
d
spectively, and of order
df d _ 1 d
äîf=üaît-îdt
m-l
Equations (1) and (2) can be written
l
2
and argument w(t+t1). Aand B are constants
which are to be determined by the boundary
conditions. The voltage can be found from the
50
current by Equation (2') .
When a tapered line is used as a transformer
'I'he velocity, a, has canceled out, showing that
the electrical characteristics of the line depend
only on the impedance 2 regarded as a function
of the time t.
Diiîerentiating Equation (2') once with respect
to t and using (1') and (2') to eliminate o and
the values of the line impedance z, at the ends oi'
the line are made equal to the terminal imped
ances at the respective ends. The measure of
the electrical performance we take to be the
“insertion gain ofthe line between the terminal
resistances”, which we deñne as
Insertion gaìnE 20 log). ä-,db
60
we get
df2+zdfdf+w F0
(3)
In order to study the various possible electrical
characteristics it is now necessary to assume a
particular functional form for ad). One of the
simplest is
'I‘he rate of taper is fixed by the pure number m.
This function leads to solutions of (3) which,
for general values of m, contain Bessel functions.
60
>where I2 is the current in the receiving resistance
when an E. M. F. is applied to the other end of
the line through the terminal resistance appro
priate to that end, and I2' is the current which
would iiow in the receiving resistance if the ta
pered line were removed and the input connected
directly to the receiving termination.
The boundary conditions are:
At the low impedance end,
70
t=0 and E=z|i(0)-{-v(0);
at the high impedance end,
(9)
V(fz)_
t = t3, say, and i( t2) ,-z,
When m is an even integer, the solutions are in
75 terms of sines and cosines. In Equation (4), 21
E is the generator E. M. F.; tz is the time re
75
2,115,826
quired for a wave to travel the length oi' the line;
i(0), 11(0) are the current'l and voltage at the low
impedance end of the line; i(tz), v(tz) are the
current and voltage at the high impedance end;
and 21, z2 are the values of the terminal imped
ances. The constant t2 is determined in terms
of zi, zz, t1, and m by Equation (4) :
In the ilrst two cases when
à
f1
is fixed the insertion gain may be plotted as a
function of mtl. The ratio
-
.a
t’i
is found from the impedance ratio by Equation
(4):
10
wier-1l
-t-z=í7--1,
for linear line,
Z1
Equations (9) thus permit the determination of
16 the constants A and B, and ñnally the insertion
gain.
Z
The insertion gain will now be given for
different rates of taper of the impedance by ñrst,
making m=1 (so-called linear line) ; second,
making m=2 (so-called conical line); and third,
making m as well as t1 approach inñnity in such
a Way that
2
fl
sertion gain may be plotted as a function oi' `
z_w
a
The parameter atz is determined from the im
pedance ratio by Equation (5) :
dl
25
‘E
2\/í’
30
.
In the exponential case, when at: is fixed the in
25 remains constant (so-called exponential line).
' For the linear line (m=1) :
Insertion gain=20 log",
.
;2l for conical line.
l
The quantity t1, in the case of linear and conical
lines, or a, in the case oi’. exponential lines, is 30
IV
_- 20 lOgm
L
85
wtl'l' D00 N 1
in which
(10)
fx
determined in any speciñc case by the lowest
40
40
45
The J- and Y-functions are Bessel functions of
the ñrst and second kind, respectively, and vsatis
iy the same recurrence formulae.
`
For the conical line (m=2) :
14,--’1
Insertion gain=20 logm--É
zz
Zi
frequency it is desired to transmit. The “cut-oft`
frequency” of a tapered line is not, in general, 50
sharply defined. Consequently, one should plot
the insertion gain for the impedance ratio de
sired before deciding upon the value of t1 ( or a).
The above discussion was concerned with the
study of possible electrical characteristics of ‘
tapered lines without regard to the mechanical
cos 2 graff-«2 -wtl sin 2
t1
60
For the exponential line
(m and t1= œ y2=a>
l‘1
Insertion gain=20 loglu
fl
(u)
construction. We shall now show how to deter
mine the shape, size, and number of turns of wire
for two particular kinds of mechanical construc 65
tion, first, where a tapered sheath and a constant
radius coil are employed and, second, where a
tapered coil and a constant radius sheath are
employed.
70
I-Development of equations for transformer ,
70
with. tapered sheath
First, let the tapered line be made up of a long
cylindrical coil of circular cross-section having a
constant radius ro and N turns per unit length, 75
2,115,826
4
surrounded by a shield with a variable radius r.
Now
g
The inductance per unit length is:
dy
is found from (19):
dx
1
l-e-U-i-ye‘”
This is substituted into (23), Ygiving the differ
ential equation
10
where c=3><101° centimeters per second, the
velocity of light.
The factor
2
15
in the inductance formula takes account of the
"short-circuiting” effect of the sheath which per
mits taper in the inductance. The impedance
and velocity are given by
X=
(24)
20
The appearance of a function of t in the inte
grand may be confusing, since integration is to
be performed with respect to y. 'I'he way this is
to be handled will be made clear in the speciñc
cases now to be discussed.
25
Let the function f(t) be that determined by
Equation (4):
f(f)=(1 + 2)"
30
30
Differentiating :
and let the subscripts 1, 2 reier to the low and
high impedance ends of the tapered line, respec
tively. Then
2
-9
z=c E: #yO-ew)
(18)
But
what)
lll-l
35
l
and from (19)
or
1+i-7mm"
f(f)= „_-yë
el?)
1_
,qw/¿(1151).
y1(1 -- e’f’i)
40
(19)
(20)
We want a relation between X, the axial distance,
and y.
By deñnition of t,
'
_gg y(1-e“”) î
tl
1(lg-_e-Ul)
The possibility of expressing f’(t) explicitly in
terms of f(t) was necessary to the solution of the
present problem, the determination of a usable
relation between X and y to arrive at the shape of 50
_din
dX '_ a
and from (20)
ï =~----1d
y
avv m
Hence we have
m-l
y
a=8n 11;;
40
.Y1 1_8
(21)
the tapered sheath.
Finally, substituting this expression for f'(t)
into (24) we get the desired equation
55
Suppose We consider a perfectly general variation
of z with respect to t and write it
(25)
z=z1f(t)
Later, the speciñc forms of f(t) given by Equa
tions (4) and (5) will be taken up. Diiîerentiat
ing (22) we have
dz__
,
'd-t-Ilf (t)
Where
This integral of Equation (25) can be expressed
in series form, the ñrst few terms of which will
be given for certain values of m. These give
suflìcient accuracy for practical design purposes.
If greater accuracy is desired, more terms must
be computed. But it should be noted that when
ever a series is diillcult to compute one can al
f'm-f f'ïf
ways resort to graphical integration.
For the linear line (m=1, (25) becomes
But
70
75
«Langres
dt dydXdt
and using (21) we get
70
(26)
75
«wat
TIT-1
:a Mg M2,7. 1
t* (1_0-"luf,"
For the exponential line
15
and nnauy
13
`
2Xm
Sat1
20
20
l1
or expressed in the series form
25
au _210gyl
(36)
__96 -l-“V + . . .
II-Development of equations ,for transformer
with tapered coil
Equations (25), (26), (27.) and (28) refer to
which corresponds to Equation (25).
25
The equations corresponding to (26), (27) and
(28) are then:
For the linear line:
30 the case of a line with uniform coil and tapered
30
sheath as in Fig. 1. The corresponding equations
for a line with tapered coil and uniform sheath
as in Fig. 4 are derived in a similar fashion.
35
Let
r :radius of coil
Tozradius of sheath
N=number turns per unit length
r1=radius of coil at low impedance end
r2=radius of coil at high impedance end
35
40
y=2 10g ç fram which
Si)
_
_K__gê z__
2 _l
a .__
--llosyx
960' y1)
960'“ _ y1)
- --
In ¿A
III-Calculations for specific case involving ta
pered coil
z=z1
(
(34)
1
(3 5)
It will now be shown how the design is to be
carried out for the case where the coil is tapered 60
and the sheath has a constant radius for which
the equations are given in Section II. We shall
assume a given problem in which the lowest fre
quency fc which the tapered line is required to
pass is 5.2 X106 cycles per second, that the im
pedance a1 at the small end of the tapered line
should be 70 ohms and the impedance z2 at the
large end of the tapered line should be '700 ohms.
One must first decide upon the desired taper oi
the sheath whether it should be linear, conical or 70
exponential. From the standpoint of electrical
characteristics the exponential taper is prefer
able and will be chosen for the following discus
sion.
Certain preliminary steps are involved before
6
2,115,826
one can directly ñnd the parameters of the ta
pered line for the given values of zi, zz and fc.
Assuming we desire the exponential type of
taper we must ñrst find the value of ata, in order
that this value may be used in Equation (12) for
the insertion gain of the device.
From Equation (5)
700
at: =10g É1 =10g
10
(40)
the impedance of the tapered line will not vary
monotonically from one end to the other. Fur
thermore if we took
59== 2.06
l'
the shape of the coil form would have an iniìnite
slope at the high impedance end which would be
undesirable in practice. Therefore we have the
requirement that
It is now necessary to consider the insertion
fo
gain characteristic of the exponential tapered
line and for this purpose a curve should be
plotted with various assigned values of
must be less than 2.06 and since
15
15
_
as abscissae, and as ordinates the resulting in
sertion gains as given by Equation (12). For our
assumed problem, the resulting curve will take
the form shown in Fig. 7. It will now be neces
sary to choose some “cut«olï” point for
TT
beyond which the insertion gain is at a satisfac
tory high level, and assume that We choose this
cut-off point as the point A on the curve of Fig.
7 for which the insertion gain is 4.5 decibels. It
30
will be noted that for the point A the value of
is 2.43 for our speciiìc example. Designate this
value of
Q
.Y2-2 10E r2
T
this means that y2 should be less than 1.44 in the
case of the tapered coil-uniform sheath line. At
the same time it must be noted that the smaller 20
y2 is chosen the smaller will be y1 and if y1 is
made very small the separation between the
sheath and the coil at the low impedance end
will also be very small. A study of these factors
indicates that y2==1 is a reasonable value.
25
Assuming this value of 112:1, we now solve for
the values of y1 and ao.
The value of y1 is to
be obtained from Equation (34) letting 2:22 and
¿1:11a in that equation from which
30
This is a transcendental equation in y1 and its
exact solution cannot be obtained algebraically.
Although a graphical solution is generally advis 35
able, we can use the first few terms in the power
series for an approximate formula for y1 in terms
of y2 and
El
providing
Z2
40
Up to the present point the calculations apply
to either a tapered sheath or a tapered coil. Ii.'
we wish a tapered coil and uniform sheath we
El
45 have by deñnition from Equation (30) the follow
ing expressions for
y1 (the value of y at the low impedance end of
the line) and
'J2 (the value of y at the high impedance end .of
50 the line):
50
the radical
1/yze_"”(1-e-U2)
55
Where To is the radius of the sheath, r1 theA radius
of the small end of the coil and r2 the radius of
the large end of the coil. As an expression in
volving N, the number of turns per centimeter of
is equal to 0.483. Thus, from the above equation
1li-10.050
Nòw from Equation (33) mung 2:22 and 11:11:
60 the winding surrounded by the sheath, we also
have by definition from Equation (29) ,
60
9X 1020>( 10ng X 0.483
One is free to specify any one of the quanti
85 ties y1, y2 or au, after which the others may be
65
uniquely determined. But it is preferable to as
sign a deñnite value to yz for it can be shown from
Equation (31) that the largest value which can
be used for
l'
is 2.06 and that for a larger value of
75
70
We can now choose N and ro in any way as
long as their product equals '7.71. If, for exam
ple, we make ro=1 inch, then N becomes 7.71
turns per inch, a reasonable value.
75
'aliases Y
rv.-'cazenlmmm> fer meme we involving ta
'or x where y=m and hence rmmnquauon (so)
`
pered sheath
after_aiviainqhothmiedery
’l‘helengthLofthe-taperedcoilisthatvalue
It 'wm now be shown how the design‘is to be
4 carried out for the case where the sheath is ta--
pered and the coil is >of constant radius, the
a. Í `
`y '
2sy v
.
1
L-F-:Dog¿jmoe-ym-mw-m]- p
>
.
'
es.: cm.=25.7 inches
The value oi' X corresponding to each value of
y chosen between w=0.050 and m=1 can be com
puted in the same way. l'br example, ten values
ci' y intermediate thesetwo values may be chosen.
The shape oi'- the form which supports the ta
pered coil may be found by plotting
'
lo'
'
III that 21 the low impedance» is 70 ohms, zz
the high impedance is 700 ohms, and the cut-oil'
frequency fs is 5.2x10‘ cycles per second. The 10
notations employed are similar to those -em
ployed for the tapered coil except that in the
present case r is the variable radius o! the
sheath and n is the radius of the coil. ~
The expression for the value oi' the insertion 15
gain for the tapered sheath device is the same as
that used for the tapered coil, namely, Equation
(12), so that the curve oi insertion gain plotted
_ against
elk
the value ot
equations for which are given in Section I. ` We
shall assume as in the other example in Section ’
20
l’
will be that of Fig. 7 and we will utilize the same
fo
cut-oi! point where
being »computed for each
chosen value of y by v
the Formula (30)
'
'
25
@was
-
a
from which a=26.9X10° as in previous example.
Again let yz=1 as in previous case, although it 30
may be pointed out that the restriction that 1l:
for the tapered coil line should be less than 2.06
does not apply to the tapered sheath construc
tion. We have by deiìnitlon from Equation (17)
For these assigned values of y between
y1=0.050 and m=1
we can ilnd not only the ratio
'
35
a»
f
but also .the distance that ratio holds from the
small impedance end ot the line by means of
Equation (39) and hence can plot
fo
'
t
against
L
as has been done for our example in Fig. 81'` f-'I'he`
curve of Fig. 8, therefore. sives the coil shape for
our' speciñc example.
-
'
'
'I'he radii of the two ends‘of the 'coil canfrbe
where ri is the radius of small impedance end
of sheath; ra is radius of large impedance end of
sheath; ro is radius of coil; and N is the number 45
of turnsoi' coil per unit length.
Equation` (i9) gives an expression for m in
terms ofk the knownquantities ya, zi and zz or
readily determined since rq=1 inch and since rr '
is the value oi' r where `11=y1=0.050 and rz is the
value of r where y=yn= 1. That is
50
and as in the case of the tapered coil we will
use the nrst i'ew terms of the power series of e
and obtain an approximate solution for y1, 55
namely
`ell-0.606 inch
e
2
e
î
That is, for our typical example the tapered
i coil ywill be 25.7 inches long, will have a radius of
0.975 inch at its low impedance end, will have a
radius of 0.606 inch at‘its high impedance end
and will have the Vcontour prescribed by the
curve of Fig. 8.
This coil will, of course, be sur
although a graphical solution of Equation (19) 60
may be employed if desired.
65
we obtain from the above formula
rounded by a sheath of‘constant radius of 1 inch.
I'I'his construction, it will be recalled, is for cou
70 pling a line of 70 ohm impedance to a line of 700
ohm -impedance with a lower cut-ofi frequency
of 52x10“ cyclesper second, and as previously
stated thel amount of vinsertion gain in decibels
,. realized by the employment of this device is
75 shown by' Fig. 7.
n
Now for 112:1 and
111:0.081
Also from Equation (18) we obtain
70
from which
a0= 1.023 X 10“
76
9,115,926
inch. Surrounding the winding Il is a circum~
ferentially complete cylindrical sheath I3 of
conducting material such as copper, the shape of
the sheath being in conformity with the curve
of Fig. 9 previously described. The sheath Il
may be suitably supported about the coil II by
r0N'=4.68.
means of spaced washers I4 of insulating ma
terial. This tapered line oi Fig. 1 is shown in
cross-section in Fig. 2.
`
If we take ro (the radius of the coil) as equal
It has been assumed that the low impedance
to 1 inch then N=4.68, that is, the coil will have - end of the tapered line is to be connected to a
4.68 turns per inch.
line having an impedance of 70 ohms for the ire
For the length of the coil we have from Equa
quency range to be transmitted while the high
tion (28) (where L is the value of X where 1l=ilz>
impedance end is to be connected to a line hav
after dividing both sides of the equation by
ing an impedance of 700 ohms. The manner of
connection is shown in Fig. 3 where line I5 hav
gg
ing an impedance of 70 ohms has one terminal
B0
connected to the terminal I6 of coil II and has
20
and by substituting the known values.
L=95.5 cm.=37.6 inches.
The shape of the sheath is computed by solv
25 ing Equation (28) for X for several values of y
between 111:0.081 and :12:1 and then calculat
ing the ratio
.
its other terminal connected to the surrounding
sheath I 3, while line I8 having an impedance of 20
700 ohms has one terminal connected to ter
minal I1 of coil Il and has its other terminal
connected to sheath I3. 'I'he insertion gain
achieved by the use of this impedance trans
former for the transmission of current from the 25
frequency source I9 to line I8 is slightly more
than 4.5 decibels as shown by Fig. 7 and this
substantially constant insertion gain applies for
a frequency range of ten to one or greater.
30 for each of these values of y by the Formula (17)
l.'
e2
Finally a curve is plotted of
35
_1S
L
` Versus
40
to obtain the shape of the sheath and such a
curve is shown in Fig. 10.
If we wish the values of r1, the radius of the
sheath at the low impedance end, and n, the
45 radius of the sheath at the high impedance end,
we have from Equation (17), knowing that ro=1
inch,
¿L
0.081
2=e 2 =1.041 inches
50 and
EL '
.1.
n=e2=e2=1.649 inches
Therefore, when employing a tapered sheath
construction for coupling a 70 ohm impedance
55 line to a 700 ohm impedanceline and with a
y
The other type /of tapered line which has been 30
computed has a tapered coil with a surrounding
sheath of constant radius as described in Sec
tions II and III. Such a tapered line is shown
in Fig. 4 where the winding 20 is wound on a
tapered cylindrical form 2| of insulating ma 35
terial tapered in accordance with the curve of
Fig. 8 for the example specifically calculated in
order to give the proper taper to the winding.
'I'he winding as shown more clearly in Fig. 6
may comprise ribbon shaped wire fitting into a 40
helical groove in the external surface of the cyl
inder Z'I. Surrounding the winding 20 is a con
centric sheath 23 of conducting material such
as copper suitably supported by one or more in
termediate insulating washers 24. The core 2l 45
at the high impedance end of the winding may
have a collar 25 which supports the sheath at
that end while at the low impedance end oi’ the
transformer the sheath 23 may be in contact
with core 2I at a point beyond the termina 50
tion of the winding 20. The tapered line of Fig.
4 may be employed in the transmission circuit
of Fig. 3 in the same manner as the tapered line
of Fig. 1, the low impedance end oi' winding 20
being connected to line I5 and the high imped 55
lower cut-off frequency of 5.2><10s cycles per - ance end of winding 20 being connected to line I8.
Although certain specific embodiments of this
second, the coil will have a radius of 1 inch.
will be 37.6 inches long, will have 4.68 turns invention have been described for illustrative
' per in'ch and this coil will be surrounded by a purposes it is to be understood that the inven
sheath having the shape shown by the curve of tion is not hunted thereto as other embodiments 60
Fig. l() with a radius of 1.041 inches at the low can be readily realized commensurate with the
>in_ipedance end and a radius of 1.649 inches at scope of the appended claims.
What is claimed is:
v . the high- impedance end.
(We will now refer more in detail to the tapered
l. In- combination, two circuits each having a
65 line constructions shown in the drawings.
fixed, predetermined impedance, and means con 65
In Fig. 1 the impedance transformer is of necting said circuits in energy transfer relation
the tapered sheath type the parameters of which comprising an impedance transformer, said im
are given generally in Section I above, and for pedance transformer comprising two elements.
a speciñc example in Section IV above. The first. a long cylindrical coil and. second. a con
70 coil I I is of constant radius being wound on a centric metallic sheath surrounding said coil, at 70
suitable cylinder I2 of insulating material. As least one of said elements being tapered in ra
explained under Section IV for use between im
dius'over substantially its entire length. the in
pedances of 70 and 700 ohms and with a lower put and output impedances of said transformer
cut-oil frequency of 5.2)(106 the coil Il would
be 37.6 inches long with a constant radius of one
being equal to the respective impedances of said
two circuits.
75
2,115,826
2. In combination, two circuits each having a
fixed, predetermined impedance, and means con
necting said circuits in energy transfer relation
comprising an impedance transformer, said im
pedance transformer comprising two elements,
ñrst, a long cylindrical coil, and second, a con
centric metallic sheath surrounding said coil, one
oi' said elements being tapered in radius over
substantially its entire length, the other of said
elements being of substantially constant radius
over its entire length, the input and output im
pedances of said transformer being equal to the
respective impedances of said two circuits.
3. In combination, two circuits each having a
15 fixed, predetermined impedance, and means con
necting said circuits in energy transferl relation
comprising an impedance transformer, said im
pedance transformer comprising a long single
layer solenoidal winding of substantially constant
20 radius throughout its length and a metallic
sheath of substantially circular cross-section sur
rounding said winding, said sheath being tapered
in radius over substantially its entire length, the
input and output impedances of said transformer
25 being equal to the respective impedances of said
two circuits.
4. In combination, two circuits each having a
fixed, predetermined impedance, and means con
necting said circuits in energy transfer relation
30 comprising an impedance transformer, said im
pedance transformer comprising a long single
-layer solenoidal winding and a metallic sheath of
substantially circular cross-section surrounding
9
having such parameters that the impedance of
said device tapers approximately exponentially
as the time of wave transmission along its length
whereby its terminals present impedances having
values which are substantially equal to the im
pedances to be faced.
8. A radio frequency impedance matching de
5
vice in accordance with claim 7 in which said
winding is tapered in radius along its length and
said sheath is of substantially constant radius.
9. A radio frequency impedance matching de
vice in accordance with claim 7 in which said
sheath is tapered substantially continuously
alongV its length and said winding is of substan
tially constant radius.
_
15
10. In combination, a pair of radio frequency
electrical circuits having different impedances,
an impedance matching device whose terminals
are adapted to connect together said pair of cir
cuits, each set of terminals of said device pre 20
senting an impedance substantially equal to the
impedance of the electric circuit which it faces,
said device comprising a long cylindrical coil and
a concentric conducting sheath surrounding said
coil, one set of terminals of said device compris~ 25
ing one end of said Winding and the adjacent end
of said sheath, the other set of terminals of said
device comprising the other end of said winding
and the adjacent end of said sheath, said device
having an impedance which tapers continuously
along its length substantially in accordance with
Equation (4).
11. An impedance transformer comprising a
long cylindrical shaped winding and a concentric
metallic tapered sheath surrounding said winding
said winding, said sheath being of substantially
35 constant radius throughout its length, the radius
of said winding being tapered over substantially in which the parameters of the transformer are
its entire length, the input and output imped»` substantially deñned by the formula
ances of said transformer being equal to the re
spective impedances of said two circuits.
5. An impedance transformer comprising a
long cylindrical coil and aconcentric metallic
sheath surrounding said coil, said coil being ta
pered in radius over substantially its entire
length, said sheath being of substantially con
stant radius, the ratio of sheath radius to coil
radius at the high impedance end of said trans
former being less than 2.06.
U
1
.Y
l +eV-1
m-ldy
wlan-(5%)?? tryo-WNW
where X=axial length of winding
45
4
6. A radio frequency impedance matching de
vice Whose terminals are adapted to face different
impedances comprising two elements, ñrst, a
ro=radius of winding
solenoidal winding, and second, a conducting
sheath enclosing said winding, one set of termi
y-2 log t--c
N=number of turns of winding per unit length
r
nals for said device comprising one end of said
winding and the adjacent end of said sheath, the
other set of terminals for said device comprising
the other end of said Winding and the adjacent
end of said sheath, said elements having such
parameters that the impedance of said device ta
pers substantially -exponentially as the time of
Wave transmission along its length, whereby its
r=radius of sheath at any point along its length
r1=radius of sheath at low impedance end
t1 is the value obtained from the expression
t2
terminals present impedances having values
which are substantially equal to the impedances
to be faced.
’7. A radio frequency impedance matching de
65 vice whose terminals are adapted to face different
impedances comprising two elements, first, a
long cylindrical shaped winding, and second, a
conducting sheath enclosing said winding, the
radius of at least one of said elements varying
70 substantially continuously along its length, one
set of terminals for said device comprising one
end of said winding and the adjacent end of said
sheath, the other set of terminals for said device
comprising the other end of said winding and
the adjacent end of said sheath, said elements
l
[film-1
zl
tz--time required for a wave to travel the length
of the winding
z1=impedance at low impedance end
z2=impedance at high impedance end
m=a constant preferably one of the following
values: 1, 2, infinity
e=base of natural logarithms
70
12. An impedance transformer comprising a
long cylindrical shaped winding whose radius is
tapered along its axis and a concentric metallic
sheath surrounding said winding in which the 76
audace
10
parameters of the transformer are substantially
defined by the formula
1
X:
t
an l
i
y
l +----y
ev»- l
m-idy
10
matching device interconnecting them for the
transfer of radio frequency waves occupying a
wide range of radio frequencies such that the .
highest frequency of said range is at least several
times the lowest frequency, said device compris
ing a long cylindrical coil and a concentric me
tallic sheath surrounding said coil, at least one
of said elements being tapered in radius over sub
stantially its entire length in such manner that
the impedance varies with the time of transmis 10
sion of said waves in accordance with Equa
tion (4).
N=number of turns of coil per unit length
15
t1=value of expression
t) 1*- *__*-21
for the transfer of radio frequency waves com
prising a long cylindrical coil and a concentric
er
-1
11
conducting sheath surrounding said coil, the im
pedance of said line varying gradually along said
t
t2=time required for a wave to travel the length
of the winding
z2=impedance at high impedance end
z1=impedance at low impedance end
rozradîus of sheath
y=2 log L;
30
'
14. In combination, two electrical circuits hav
ing different impedances and an impedance
matching transmission line interconnecting them
"
line with the time of transmission in such man
20
ner that the insertion gain is substantially uni- ,
form over a frequency band the highest frequency
of which is at least several times the lowest.
15. A combination in accordance with claim 14
in which said sheath is of substantially constant
radius throughout its length and the ratio of
sheath radius to coil radius at the high impedance
end is less than 2.06.
16. A combination in accordance with claim 14
r=radîus of winding at any point along its axis ` in which. said line is tapered in impedance in ac
m=a constant preferably one of the following cordance with Equation (4), where m lies be
tween 2 and infinity.
values: 1, 2, infinity
e=base of natural logarithms
EDWARD L. NORTON.
13. In combination, two electrical circuits hav
RONALD F'. WICK.
ing different impedances and an impedance
30
Документ
Категория
Без категории
Просмотров
0
Размер файла
1 086 Кб
Теги
1/--страниц
Пожаловаться на содержимое документа