IRE TRANSACTIONS
116
ON MICROWAVE
An lV~Way
Hybrid
ERNEST
THEORY
AND
Power
TECHNIQUES
January
Divider*
J. WILKINSON~
w
5’ummary-A
circularly
symmetric
power divider is described
which splits a signal into n equiphase equismplitude
parts where n
can be odd or even. The power divider provides isolation between
output terminals and approximately
matched terminal impedances
over about a 20 per cent band. A theory of operation is given which
yields the necessary design parameters, and an experimental model
is described wtilch has a minimum isolation of -27 db between output terminals, an output VSWR of 1,6, and an input VSWR. of L2.
OUTPUTS
t-+--q
OUTPUTS
HYBRID
JUNCTIONS
I
I
I
6
—
I
INPUT
INTRODUCTION
(b)
<a)
problem
HE
a number
T
nals
It
is
often
ally
in
that
independent
of
some
1, In
junctions
the
the
1(a),
provides
signal
\
arrays.
that
between
output
band.
dividers
are
feed
Two
of
illustrated
structure
necessary
T
of
to preserve
common center conductor
of a coaxial line, and the combined load is matched
by means of a quarter-wave
inals,
junctions.
of
the
outputs
put
only
being
other
all
of
output
loads
appear
This
circular
phase
having
in
paper
no
of Fig.
outputs
independent
provides
isolated
of
and
The
power
coaxial
been
line
split
divider
in
into
which
given
which
so that
as
because
it maintains
any
but,
number
in
of
addition,
OF OPERATION
the
hollow
of length
fashion,
inner
2 consists
conductor
A shorting
of a
has
end,l
manner
between
although
they
i.e., at right
may
angles
June
Mass.
each
are
spline
at
also be connected
to the splines.
in
When
terminals,
the reflected
signal
will
split; part of it will travel directly
to the remaining
output terminals
via the resistors,
and the rest of it will
travel back to the input, splitting
again at the junction
put
and then
returning
Thus,
the reflected
terminals.
to the remaining
wave
arrives
outat the
remaining
output
terminals
in two parts, and the path
length difference between the two paths of travel will be
180° when the splines are A/4 in length. It will be shown
that when the value of the resistors and the characteristic impedance
of the spline
transmission
lines are
chosen,
also equal
the two parts
in amplitude;
of the reflected
hence,
complete
wave
are
cancellation
occurs.
plate
I A tapered
section
is shown at the input
discontinuity
caused
by the abrupt
change
* Manuscript
received by the PGMTT,
manuscript received, September 10, 1959.
~ Sylvania Electronic Systems, Waltham,
and resistors
a signal is fed into the power divider,
it divides by virtue
of symmetry
into n equiphase equiamplitude
parts. No
power is dissipated
by the resistances
when matched
loads are connected
to the outputs,
since all splines will
be at the same potential.
However,
if a reflection
occurs
properly
in Fig.
X/4.
manner,
of the splines
output
possesses
outputs.
as sketched
n splines
dis-
at the input
in a radial
at one of the output
provides
outputs,
any
between
outon the
serious
between
frequency,
THEORY
1(b),
mismatched
1(b),
nine
power
power
the
a device
matched
If
16-to-1
Fig.
across
equality
limitation
symmetry,
badly
describes
amplitude
radial
a
isolation
parallel
line”
identical,
the
the splines
the output
end and a common
junction.
Output
connectors are shown connected
to the splines in an “in
yet
+$ of the
however,
connects
connected
complex-
with
loads.
by
Fig. 2.
and
example,
has,
are
symmetry
and
has
term-
of outputs.
circular
It
terminals
terminal.
the
of the
of outputs.
advantage
the
for
in matched
because
number
be replaced
cost
number
to be used
dissipated
hand,
any
have
may
the
structure
a binary
required,
would
output
separate,
of
feed
between
1(a)
to
a number
were
divider
Fig.
addition
corporate
providing
isolation
of
In
providing
hybrids,
of
T junctions
the
hybrid
ity
To provide
ELDI
a
the equiphase
equiamplitude
condition
independent
of
frequency.
In Fig. 1(b), circular symmetry
is employed
where all the output
terminals
are connected
to the
transformer.
GNDI
ZO(WLINE-TO-$H,
is fundamentaddition,
frequency
the symmetry
1.
equiamplitude
in
a corporate
SHORTINGPLATE (NOT
par-
phased
which
exist
power
Fig.
sig-
engineers,
of
and,
into
output
RF
equiphase
isolation
used
Fig.
input
field
specified
commonly
Fig.
to
of frequency,
over
more
an
in a manner
degree
terminals
the
one
working
desired
high
up
equiamplitude
familiar
be obtained
fairly
in
a
those
condition
dividing
of equiphase
is
ticularly
of
3, 1959; revised
end
for
reducing
the
in line sizes when a
standard type N connector is used. A more convenient form of thk
device, which eliminates the need for a separate tapered sectio:, can
be realized by uniformly
tapering the splined coaxial section Itself.
1960
An
Wilkinson:
N-Way
Power Divider
Hybrid
b COMMON JUNCTION
[NOT GNO)
RX
y
, RX
Rx
Rx
‘t
Va+j(n
*
‘n-
‘07,)
:J
=
()
n—1
RO
&
—
() $’tS
RO
jVa~
r
= O
V.– VI:% =()
l+W+
Zo
R,
Ro
– l)~Vn+jV~~
RO
j V. —+
‘x
v’”
117
–
‘“;,Jlvn
1
1[0
v.
.
r
g,+
(3)
Zo
+,
\
11
;HIELO
(GNo}
For
perfect
V.= O, (3) may
isolation
be combined
to
yield
1
v,
—.—
v
1+:
2
1
1“
~
1 1’”’
Fig.
(4)
l;”*
&
SHORTING )LATE
(NOT GNO)
3—R,=external
loads connected between splines and shield
(GND); Ro= internal loads connected between splines and common junction poin~; Zo = characteristic
impedance of each splineto-shield transmission line; V= voltage applied to a single output
terminal;
V. =voltage
appearing at nth output
terminal;
V.
= voltage appearing at input terminal.
and
for
matched
terminal
the
must
1 by a generator
voltages
all
line
spline 1:
line
at the
because
of
equations
is a quarter
V is applied
of internal
V. appearing
be equal
transmission
sion
to Fig. 3, if a voltage
resistance
other
output
symmetry.
when
wavelength
each
long
VI = V. cos d + jll.’ZO
(0=
7r/2),
we obtain
,.
!, -
(4) and (5) yields
R = R,:
to output
Ro, then
v’; Ro.
20 =
(6)
terminals
Applying
spline
admittances,
.. —.—
Combining
Referring
output
the
transmiswe have
sin 6 = jll.’ZO
Thus,
loads R and the characteristic
if the internal
pedance
of the
spline-to-shield
adjusted
according
isolated
and
to (6), the outputs
matched.
The
these conditions
will
n output
Ro, after
loads
through
transmission
a quarter
each
wavelength
are
will be completely
input
impedance
be the parallel
im-
lines
under
combination
has been
of the
transformed
of line ZO. Hence,
20”
spline n:
V. = V. cos 6 + jIa.ZO sin O = jIa.Zo
RO
Zi.Duti = ~–
‘n
(1)
or, in other
matched
puts
It is also true that
words,
when
the input
of the power
the conditions
for isolation
In
order
and
the
?’l— 1
(~lb
+
IZU)RO
=
v
–
V1
of this
b+A) Ro=vl-vn
(2)
mately
whose
Combining
VI, v., v.:
(1)
with
(2)
equations
we
for
obtain
the
the
following
unknown
set
voltages
is also
between
out-
type
having
eight
whether
in Fig.
1(b),
a
that
was
8-to-’1
spline-to-shield
inpedance
of
impedance
lines had
of
Zo=%$=d$’o
the
tlhe isolation
realized
unsloti-ed
was
in
dividler
modified
slots
of an
characteristic
times
characteristic
eight
be
a pc)wer
Narrow
conductor
to create
or not
could
design,
procedure.
center
RESULTS
features
practical
illustrated
spline-to-shield
simultaneous
of
following
hollow
lines
output
divider
type
to the
the
to determine
matched
power
In
divider
are satisfied.
EXPERIMENTAL
Im=:-–—
= R.
a
of
according
were
power
millled
in
divider
transmission
of
approxi-
coaxial
Ro/w%. Hence,
line
the
IT8
fRE TRANSACTIONS
ON
MICROWAVE
THEORY
2
3
OUTPUT TERMINAL
Fig.
in accordance
with
to RO (50 ohms)
splines,
(see Fig.
were
obtained
150-ohm
~-watt
internal
very
loads.
resistors
soldered
manner
Isolation
using
and
equal
in value
to a short
resistors
combination
for
the
was found
ratio
is 27 db, although
inals—a
of Fig.
it is not constant
3. The output
S—Isolation
N-way
to the theory
VSWR
for
between
output
terminals
hybrid
power divider.
1.6
three
500 MC
/
50-ohm
to yield
be noted,
of 500 mc the minimum
fact contrary
i
a
L4 -
at the operating
450 to 5.50 mc. It will
frequency
I
8
OUTPUT TERMINAL
vSWR VS. TERMINAL
values
of
VSWR and isolation
characteristics.
The measured isolation between outputs
is plotted
in Fig. 5 over the frerange
[
7
1.8
frequencies.
Standard
General Radio 50-ohm loads were
used to terminate
the unused terminals
when measuring
quency
[
6
circuiting
VSWR
combination
low reactance-to-resistance
the center
I
5
to the ends of the
output
a parallel
composition
This
I
4
NUMBERlI$0LAT16N WITH RESPECTTO TERMINAL I 1
1
I
INPUT TERMINAL VSWR
vs. FREQUENCY
Eight
in a radial
4).
January
4.
were then
joining
ring
(6).
TECHNIQUES
I
I
I
Fig.
AND
that
at
isolation
for all output
=
%
1.2
,.o~
2
term-
1
440
I
460
Fig.
6-VSWR
based on the model
is plotted
in Fig.
6 and is
3
480
4
5
OUTPUT TERMINAL
NUMBER
,
I
500
520
FREQUENCY IN MC
characteristics
for N-way
6
7
8
1
540
I
560
1
580
hybrid
power
divider.
about 1.6 at 500 mc, where the input VSWR
is about
1.2. The output-to-input
ratio was measured and found
to be – 9 db at all frequencies,
indicating
that the device
was behaving
as an 8-to-1 lossless power divider
with
negligible
insertion
loss.
The experimental
model described
above differs in
further
several
wire
respects
from
the theoretical
theoretical
model assumes a diameter
in wavelengths.
In the experimental
The
principle
effect
of this
appears
model.
which
model
First,
the
is negligible
it was 0.1A.
to be that
it shifts
development
work,
the
inequality
of isolation
between output terminals
is believed to be due to a more
fundamental
reason, It will be noted that, shunting
any
pair of output
terminals,
there is a short circuited
twoline formed
by the pair
terminals.
When
finite impedance
but
the length
is shunted
at frequencies
of splines
leading
to these
of the splines is A/4, an inbetween output
terminals;
off the center
frequency,
a finite
re-
the center frequency
for best performance
to a lower
value than the design frequency,
and, perhaps, changes
the effective
resistance
of the internal
loads, since the
current
throughout
the length of the resistors may no
longer be uniform.
Second, measurement
of the phase
between
outputs
showed several degrees of phase in-
actance
appears
between
output
terminals
which
is
directly
proportional
to the characteristic
impedance
of
the two-wire
line formed by the splines. Because of the
circular
arrangement
of output
terminals,
diametrically
opposite
splines (terminals
1–5 in Fig. 5), for example,
would form a transmission
line of higher characteristic
equality,
indicating
that the perfect symmetry
assumed
in the theory had not been achieved in the splined struc-
impedance
than
adjacent
Fig. 5). Since, the shunting
ture
and internal
loads.
Finally,
the exact
value
of the
pair
of output
isolation
will
terminals,
the center
the
for any terminal.
mentioned
above
can
be
overcome
with
frequency
1–2 in
for each
it is to be expected
not be uniform
characteristic
impedance
of the spline-to-shield
transnot exactly
~~Ro. Although
mission lines was probably
effects
splines
(terminals
effect is difference
where
for all terminals,
there
that
the
except
is no shunting
at
effect