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circuit.
The
inductance
i
n
the
parallel =resonant
circuit is
center-tapped
.
The
other
filter (
Filter
2)
i
ncludes two
coupled
parallel-resonant
circuits.
The out
-
pu
t
of Filter
2
is
tied
t
o
the
midpoint of the
inductance
in the Filter
1
parallel
-
resonant circuit.
Typical
configurations
for such a
combina
t
i
on of filters and
the
phase
shifts
that
occur
in
their circuits
are
indicated
in
Fig
.
3
.
S
i
nusoidal
voltages E1
an
d
E2
are in
phase at
the inputs to each
filter.
I
n Filter
1,
the
phase
of sinusoid Ei
i
s
shifted
90° by the
inductance
in the series arm
,
and
another 90° by the mutual inductance
between. the series and parallel
-
resonant
sections
.
Thus
t
he
v
oltage
across
the parallel
-
resonant circuit is shifted
180° with
re
sp
ect to
input
sinusoid
E 1
.
In Filter 2
,
the phase of sinusoid
E2
is s
hifted
90° by the
m utua
l
inductance
between the two parallel
-
resonant cir
-
cuits
,
and
t
her
efore jE2
is
applied
to
the
center
tap of the
inductor
in Filter
1
.
Sinus
o
i
ds Ei
a
nd E
2
,
after
the
phase shifts described above
,
are combined at
the
terminals
of the
Fil
ter
1
parallel
-
resonant circuit
,
and
the two resultant
voltages
(sinusoid
A
and
sinusoid
B)
are
1T-
26 out of phase
.
By means
of
this
circuit
,
a
ph
ase angle
may
be derived
which is
related
to
the
ratio of the in
-
put v oltages.
The Model 416A uses a scheme
similar
to
the foregoing to obtain
two
voltages
w
h
ich are
out
of phase by
ff-
26.
These
voltages
are used
in
the
triggering
of subsequent
circuits that
convert the two
voltages
to square
-
waves
which are app
l
ied to
the meter circuit.
The sum of these two waveforms is
another sq
u
are
wave
whic
h is proportional
to
e
,
and
the
meter scales are so
calibrated that with a cur
rent proportional
to
8 flowing in the meter circuit,
an indication wil
l
be given
w
hich is proportional to the square
root
of tan
e
,
The ratio
of
th
e reflecte
d
to
the incident voltage
in the transmission system
und
er
measurement
is eq
u
a
l to
t
he
square root
of tan 8
.
General
=-
T
he
circuit of
the Model
4 16A
is
shown
i
n block diagram form
i
n
Fig. 4
and
sc
hematically in
the
schematic diagram
at the
back of this book
.
From
external
square=
law detectors
,
the Model 416A Ratio Meter ac
=
c ept
s
two
1
=kc
voltages
,
one proportional to
the
incident
power in a trans
-
mission
system
a
nd the
other
proportional
to
the r
e
flected power
.
The
Model 416
A
input circuits
amplify
and
deliver each
voltage
to
a 1
-
kc
band
-
pass filter
.
Filter
l (incide
nt
voltage)
i
ncludes
a series resonant circuit
coupled
to
a
p
aralle
l
-
resona
nt circui
t,
and
Filter
2
(reflected
v
oltage) in
-
cludes two coupled
parallel
-
re
sonant
circuits
.
Filter
2
delivers
an
output
voltage
11
/2
out of
phase
with the outpu
t
of Filter
1.
The output
from
Filter
2 is
a
pplied
to the center
tap
of
the
inductance of
the
Fi
lte
r
1
parallel =resonant
circuit,
and the two
voltages are added
as shown in Fig
.
5
.
The
resultant
voltages
are always
f(
-
28
out
of
phase.
Under a condition of
100%
reflection
,
when the reflecte
d
and incide
nt voltages
are
of equal amplitude
,
angle
e
is
71/4,
and the resultant volta
ges be
i
n
g
Tf-28
out of phase therefore are
71
/2
out of
phase
with
respect
to ea
c
h other
.
Under
a condition
of less than
100%
reflection
,
the
phase
angle
('if
-2
6)
is
greater than
1f
/2
.
The phase
angle of
the
resulta
nt
vo
ltages
under a
condition of
50%
reflection
is
shown
in
F
ig
.
5
.
-
7-
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