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Патент USA US3068339

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Dec. 1l, 1962 `
Filed April 28, 1959>
3 Sheets-Sheet 2
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TERM/NAL /MPEoA/vcE-z„2 Foi?
ssn/Es on @maal/v6 @RANCH
United êtates Èatent
Patented Dec. 11, 1962
must be seen looking in either direction from these ter
minals. For this condition,
Robert W. De Monte, Berkeiey Heights, NJ., and William
J. Kopp, Richmond Hiil, NX., assignors to Beil Tele
phone Laboratories, incorporated, New York, NX., a
ZI-i-‘Zg t’dlnh Ü
where 0 is the transfer constant of the repeater 1, and will
corporation of New York
be negative in sign, and Z1 is its image impedance. By
Filed Apr. 28, 1959, Ser. No. 809,421
6 Ciaims. (Ci. 179-170)
image impedance is meant one of the two equal iin
pedances which will simultaneously terminate the two
This invention relates to wave transmission and more
pairs of terminals 2_3 and 4_5 in such a way that, at
particularly to a two-way, negative~impedance repeater
each of these pairs of terminals, the impedances in both
adapted to operate between unequal impedances.
eliminate reflection at one end of a two-way repeater
directions are equal. Equation 1 is essentially the same
as Equation 48 on page 137 of the book by K. S. John
son, entitled “Transmission Circuits for Telephonie Com
operating between unequal terminal impedances, An
munication,” published by Van Nostrand Co., New York,
other object is to widen the band over which an im
1925. However, we have set the driving-point impedance
Z equal to the terminal impedance Z1 and -use the symbol
The principal object of the invention is to reduce or
pedance match is obtainable.
Z2 for the other terminal impedance ZR. As indicated by
the arrow in FIG. l, the driving-point impedance Z of
Two-way repeaters are often required in wave trans
mission systems such as loaded voice-frequency transmis
sion lines. These may be located at the end of the line 20 the repeater 1 is the impedance seen at the terminals 2_3
when the impedance Z2 is connected betweenthe terminals 4_5 and the impedance Z1 is removed.
ñection effects and singing in the system, it is important
or at an intermediate point: In order to reduce >re
»From Equation 1,
that the repeater should present a good match to the
terminal impedance, at least at one end, over a broad
band of frequencies. This is sometimes difficult when 25
the repeater operates between unequal terminal im~
pedances, especially if one or both of the impedances are
Zïmiiïa tana @ii/[2 man vii +2125] (3)
In accordance with the present invention, a good im
pedance match over a band of frequencies is obtained at 30
It is seen from Equation 3 that there are two choices of i
one end of the repeater by a special choice of its image
impedance. The required image impedance has one of
to be made in evaluating Z1. Therefore, Z1 may have
four values which are determined by the terminal im~
any one of four different values. These `are determined
by choosing both i signs as -|-, both as _, the first as -|--
pedances and the gain of the repeater. The repeater
may be built as a lattice, a bridged-T, or any other equiva
35 and the second as ---, or the first as -- and the second
lent structure, generally requiring two or more negative
impedance converters.
The nature of the invention and its various objects,
features, and advantages will appear more fully in the
following detailed description of the typical embodiments 4
illustrated in the accompanying drawing, of which:
FIG. 1 is a block diagram showing a negative-im
pedance repeater in accordance with the invention operat
ing between unequal impedances;
FIG. 2 is a set of graphs showing, the frequency char
acteristics of the resistance and reactance of terminal im
pedances assumed as an example;
FIG. 3 shows therresistance RIA and reactance X12 of
one image impedance ZIA suitable for the repeater;
FIG. 4 shows a symmetrical lattice network and FIG.
5 a balanced bridged-T network suitable for the repeater
of FIG. l;
FIGS. 6 and 7 show impedances suitable, respectively,
for the impedances _Z2 and -Zb of FIG. 4 to realize
as -|-. However, in order to facilitate the synthesis of
the network, the signs are preferably so chosen that the
real part of Z1 is positive in the frequency range of in
An example in which the terminal impedances Z1 and
Z2 are both complex will not be presented. The broken-`
line curves of FIG. 2 show the resistance R1 and the
reactance X1 of the impedance Z1. The solid-line curves
show the resistance R2 and the reactance X2 of the other
impedance Z2. These characteristics are plotted over a
frequency range of 100 to 10,000 cycles per second, on
a logarithmic scale.
The impedance Z1 is typical of
that encountered at the oiiice end of a telephone cable.
The resistance R1 is constant at 900 ohms and the re~
actance X1 is that of a capacitor having >a value of two
microfarads. The impedance Z2 represents that of a long,
loaded, 22-gauge cable with a building-out network at
the near end and an image-impedance termination at the
other end. It is seen that there is some irregularity in R2
and X2 in the neighborhood of 3,500 cycles, the cut-olf fre
quency of the cable.
FIG. 8 presents a graphic comparison of the im
It will be assumed that the repeater 1 has a uniform
pedance of the terminated repeater and the terminating
gain of 0.7_ nepers (about six decibels) and negligible
impedance to be matched;
phase shift over the band of interest. Therefore, the
FIG. 9 shows the resistance RIB and the reactance XIB
of another image impedance ZIB suitable for the repeater; 60 transfer constant is
FIGS. 10 and l1 show impedances suitable, respec
One possible image impedance ZIA is now found from
tively, for the impedances --Z„7 and -Zb of FIG. 4 to
Equation 3 by substituting _0.7 for 0 and choosing both
realize ZIB.
i signs as -|-. The curves of FIG. 3 show the required
FIG. l shows a two-way, negative-impedance repeater
R111, which is positive, and reactance X111, which
1 with an impedance Z1 connected to the terminals 2_3
is negative.
and an impedance Z2 connected to the terminals 4_5.
The next step is to synthesize the repeater network.
The impedances Z1 and Z2 are unequal and either or both
FIG. 4 shows one suitable configuration in the form of a
may be complex.
symmetrical lattice structure with two equal series
It will be assumed that reñection is to be minimized 70 branches each of impedance Za and two equal diagonal
at the terminals 2_3. Therefore, the same impedance
branches each of impedance Zh. To simplify the draw
ing, only one series and one diagonal branch are shown
in detail. The other branches are indicated by broken
in series, as shown in FIG. l1. Of course, the approxi
mation may be made more exact by adding elements to
lines connecting the appropriate terminals. These imped
ances are found from the image impedance and the trans
_Zag Or _2112.
In the two embodiments described, the required values
fer constant by using the relationships:
of the resistors in ohms and capacitors in microfarads are
Z..=ZIA caring
as follows:
R2 ____
z_b;Z,rA 09th '2"
10 R.,
Since 0 is negative, both Z,L and Z1, will have negative
real parts. Impedances with negative real parts are
easily obtained by means of four negative-impedance con
verters, each having an impedance conversion ratio ap
proximately equal to _1. Each series branch of the lat
tice includes such a converter 8 terminated in an imped
ance _2a. Each diagonal branch comprises a converter
9 terminated in an impedance _2b.
FIVG. 5 shows a balanced bridgedfi" network, equivalent 20
to the lattice of FIG. 4,- which may be used for the re
peater 1. The bridging branch comprises a winding 11
closely coupled to each of the two series windings 12 and
13 in the two sides of the line, and a negative-impedance
R, ______________________________________ __
___ 0.416
C3 _________ __
C4 ___
ments are only illustrative of the application of the prin
ciples of the invention. Numerous other arrangements
may be devised by those skilled in the art without depart
ing from the spirit and scope of the invention.
What is claimed is:
1. An active transducer adapted to operate between a
converter 14 terminatedy in an impedance _2a. The. 25 terminal impedance Z1 at one end and a terminal imped
shunt branch, connected between- the midpoints of the
ance Z2 of different Value at the other end> substantially
series windings 12 and 13, comprises a second negative
without reflection at the one end, the image impedance
impedance converter 15 terminated in an impedance
of the transducer being approximately equal to
-Za z
Gc/aod simulation of the impedance _Z,v over the band 30
of interest may be provided by the impedance branch
_2,11 shown in FIG. 6, comprising a resistor R1 in series
with the parallel combination of a second resistor R2
and a capacitor C1. The impedance _Zb or _Zh/2 may
be simulated satisíactorily by the branch _21,1 shown in 35
FIG. 7, which comprises the series combination of a re
sistor R3 and a capacitor C2 in series with the parallel
where 0 is the transfer constant of the transducer.
2. A transducer in accordance with claim 1 in which
one of the terminal impedances is complex.
3. A transducer in accordance with claim 1 in which
0 has a negative real part.
4. An active transducer adapted to operate between a
combination o_f a resistor R4 and a capacitor C3. One or
terminal impedance Z1 at one end and a terminal imped
more of the component elements may be made adjustable,
ance Z2 ojf different value at the other end substantially
as indicated by the arrows, to permit an adjustment of 40 without reflection at the one end, the image impedance
the repeater gain or to allow for changes in the imped
of the transducer being approximately equal to
ancesZ1 and Z2.
The curves of FIG. 8 show how well the driving-point
impedance Z of the terminated repeater 1 matches the
terminal impedance Z1. The solid-line curves R and X
ì/íZ tanh 0] +Z1Z2ïi
where 0 is the transfer constant of- the transducer.
are the resistance and the reactance, respectively. The
5 ._A transducer in accordance withclairn 4 in which one
resistance R1 and reactance X1 of the impedance Z1 are
of the terminal impedances is complex.
plotted in broken-line curves for comparison. It is seen
6. A transducer in accordance with claim 4 in which
that the resistive match and the reactive match are both
á' has a negativereal part.
excellent over the voice band, and are close enough out 50
side ofthe band- to prevent singing. Of course, the match
References Cited in the iile of this patent
can> be made closer by adding elements to the impedances
»Z311 and _2131.
FIG. 9 shows another possible image impedance Z113,
Merrill ____________,_____,___ 1an. l5, 1952
foundv from Equation 3 by choosing both i signs as _. ,
Here, also, the resistance R113 is positive and the reactance
X113 is negative. This image impedance may be closely
approximated in the lattice network of FIG. 1 if the
impedance _Z1l is simulated by the impedance branch
Barney ___.,_____ ______ __ July 27, 1954
Rounds _______________ __ Nov. 9, 1954
Merrill ____ _____,____,_,___ Apr. 17, 19,56
Linvill _____ ____ __~______ Apr. 9, 1957
Arndt ________________ __ July 22, 1958
_Z112 shown in FIG. 10, which is simply a resistor R5, 60
Merrill _ ________ -______ Mar. 17, 1959
Radcliíïe _ ____ ____ ____ __ Sept. 15, 1959
and the impedance _Zrb is simulated by the impedance
branch _Zbz comprising a resistor R6 and a capacitor C1
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