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Патент USA US2411876

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Dec- 3, 1946-
w. w. HANSEN
2,411,876
PHASE ANGLE INDICATOR
'
Filed Sept. 6, 1943
2 Sheets-Sheet 1
INVENTOR
WILLIAM W. HANSEN
v
ATTORNEY
Dec. 3, 1946.
A
_VW_W_HANSEN
»
2,411,876
PHASE ANGLE INDICATO}?
Filed Sept. 6, 1943
2 Sheets-Sheet 2
BALANCE D
MODULATOR
45
AMPLIFIERS:
AMPLIFIE RS
45
59
BALANCED
MODULATOR
Q
50'
F :0. a
INVENTOR
WILLIAM W. HANSEN
BY
.
I
ATTORNEY
~ 2,411,876
Patented Dec. 3, 1346
UNITED STATE ‘S
PATENT OFFICE
2,411,876
'
PHASE ANGLE INDICATOR ’
William W. Hansen, Garden City, N. Y., assignor
to Sperry Gyroscope Company, Inc., a corpora
tion of New York
Application September 6, 1943, Serial No. 501,371
10 Claims. (Cl. 172-—245)
in symmetry about a cross-connecting network,
in which two alternating electrical quantities are
My invention relates to electrical measuring
devices in general, and more particularly to appa
ratus and methods for measuring the phase rela
tionship of two alternating or periodically vary
ing quantities.
.
Present methods employed for phase angle de- >
termination use apparatus which falls within one
of‘ three classes, or types. The more familiar bal
anced circuit and moving coil types have been fol
used to produce a like number of non-alternating
electrical forces for transmission through means
capable of producing a series of electrical ?elds
which cause an electrodynamic indicator to align
itself with respect to a reference at an angle equal
to the phase difference between the two altemat
ing quantities.
‘
>
Other objects of my invention will become ap
lowed by what may be classi?ed generally as the 10
parent and those listed more evident as the de
electronic type, within which the instant inven
tion falls.
'-
'
scription proceeds.
.
An object of my invention is to provide elec
tronic phase measuring apparatus which is not
subject to the effect of noise.
Another object of my invention is to provide a
method and apparatus for measuring the phase
difference between two periodically varying quan
periodically varying electrical quantities whose
phase angle relation is to be determined. The ‘
20 channels are identical, and each comprises a volt
tities which may or may not be of equal am
plitude.
A further object of my invention is to provide _
apparatus for measuring phase which is capable -.
of giving a linear indication through a full360°
of phase difference.
A further purpose of my invention is to provide
apparatus for determining the phase relations
between two periodically varying quantities in
which no moving parts of the apparatus carry
currents of the quantities whose phase relation
ship is to be determined.
In carrying out my invention, in a preferred
embodiment thereof, I arrange two circuit chan
nels in symmetry about a dual channel cross
connecting network, each of which has input ter
minals for receiving respectively one of the two
age divider, a phase inverter, a push-pull am
pli?er, and a balanced modulator in whose com
mon grid circuit is connected a phase shifting
network.
The dual channel cross-connecting network,
made up of two ampli?ers, and two combination
impedance matching and amplifying elements,
performs the function of supplying the phase
shifting network of each channel with a part of
.
Yet another purpose of my invention is to pro
vide a method” and apparatus for measuring the
phase angle existing between two periodically
varying electrical quantities in which two direct
currents, whose ratio is proportional to a function
of the phase angle existing between the quan
so the electrical quantity impressed upon its respec
tive opposite channel.
7
'
With the circuit arranged thus, each of the two
electrical quantities modulates a portion of the
other whose phase has been shifted through -45°
angle. ‘The vdirect current components of the re
spective modulated quantities, whose ratio is
proportional to a function of the angle of phase
right angles to each other, saidlelectrical ?elds
difference between them, are then passed through
producing a resultant ?eld the direction of which
two sets of coils disposed at right angles with each
40
is used to determine phase.
,
other. The ?ow of current through these coils;
A still further object of my invention is to pro
establishes two electrical ?elds, which are also
vide a phase meter of the electronic type in which
at right angles with each other. The direction
two cross-connected channels are employed to
of the resultant electrical ?eld is equal to the
modulate each of two alternating electrical quan
phase difference between the two electrical quan
tities with the inputs of the respective opposite
titles, and as determined by an electrodynamic
channels vwhose phases have been shifted
indicator gives measurement thereof.
through a ?xed and predetermined angle, and in
A more comprehensiveunderstanding of my
which the direct current components of the re
invention will be afforded from the following de
spective’ modulated currents so produced are used
to establish a vector force whose angle, with re 50 tailed description, when taken together with the
accompanying drawings of which
spect to a reference line ?xed in space, is equal to
'Fig. l is a circuit diagram of an embodiment ,
the phase difference between the two alternating
of
my invention;
electrical quantities.
Fig. 2 a detail of the 45° network appearing in
It is also a purpose of my invention to provide
.
a circuit having two separate channels, arranged 55, the circuit shown in Fig. l ;
titles, are used to establish two electrical ?elds at
2,411,876
Fig. 3 a modi?ed block diagram of the circui
shown in Fig. 1;
‘
Fig. 4 a modi?ed showing of the balanced modu
lators in Fig. 1; and
Fig. 5 a vector diagram of the forces which re
sult from the coil arrangement shown in Fig. 3.
Like reference numerals have been used
4
source 92 through plate resistors 38 and 39 and
deliver the output of amplifying stage 40 to a
balanced modulator 50, through capacitors 4| and
Balanced modulator 50 comprises two electronic
discharge elements 41 and 52 which are connected
in the usual manner, with the exception of a phase
throughout in the drawings to designate like
shifting, network 45 in the common grid circuit.
parts.
This network, shown in detail in Figure 2, is
In the circuit diagramed in Fig. 1, illustrat 10 made up of lattice sections I0| the arms of which
ing an embodiment of my invention, two channels
comprise the pure resistances, I02 and capaci
II and I3, interconnected by a cross-connecting
tances, I03. It receives the‘ output of the lower
network I2, are employed in a manner which will
half of cross-connecting network I2, as will be
be explained with reference to Fig. 3. Two pe
explained later, and shifts ,the phase thereof
riodically varying electric quantities E2 and E1, 15 through —45°.
the phase relationship between which is to be de
Control grid 48 of element 41 and 53 of element
termined, are impressed respectively upon input
52 receive the output of ampli?er 40 as explained
terminals I4 and I4’ of the channels II and I3.
above. Cathodes 5| and 55 of these tubes, shown
Upon the input terminals l4 of channel II is
as tetrodes and connected as triodes, are tied to
impressed one of the two periodically varying elec 20 gether and directly connected to ground, while
trical quantities E2 where it is divided for de
grid leak resistors 43 and 44 are connected in the
livery to the balanced modulator 50, and to the
grid circuits of the respective tubes.
upper half of the dual channel cross-connecting
Negative bias is supplied to grids 48 and 53 and
network |2. Here it is ampli?ed and then trans
to the corresponding grids of the tubes in balanced
mitted through the phase shifting network 45' to 25 modulator 50’ of channel I3 from energy source
balanced modulator 50'. In like manner the
46, in order that the tubes may be made to op
quantity E1 is taken from input terminals I4’ for
erate on the curved portion of their plate char
delivery to the balanced modulator 50', and a
acteristic curve where the plate current is ap
portion thereof to the lower half of cross-connect
proximately equal to the square of the voltage.
ing network I 2, which delivers it to the phase 30 Plates 49 and 54 are connected in series through
shifting network 45 associated with balanced mod
coils 59, 60, 6| and 10 and the winding of poten
ulator 50. Within the balanced modulator 50.
tiometer 58, whose movable arm is connected to
quantity E2 is used to modulate the quantity E1
the winding of potentiometer 99. By-pass con
whose phase has been shifted through —-45° and,
densers 56 and 51, in series with each other, are
similarly, in balanced modulator 50' the quantity 35 coupled in parallel with the coils 59, 60, 6| and
E1 modulates that part of E2 whose phase has
10.
been shifted through 45°.
As stated before, the voltage which is to be
The outputs of balanced modulators 50 and 50'
modulated is supplied to the balanced modulator
are passed through coils 59, 60, 6| and 10 and 59',
of each channel from ‘the input of the channel op
60’, 6|’ and 10' respectively. As shown in Fig. 3, 40 posite to it. Thus a part of E2 is taken from po
the coils 59, 60, 6| and 10 are disposed at right
tentiometer I5 and impressed upon the control
angles to the coils 59', 60', 6|’ and 10'. Within
grid 64 of element 63 in cross-connecting net
these coils are generated two electrical ?elds
work I2.
which cause the electrodynamic indicator | 05,
Here the upper halves of elements 63 and 8|
shown in Fig. 3, to align itself with respect to a
acts as ampli?ers for supplying the voltage E2
reference in such manner that the angle 0 (Fig. 5)
to phase shifting network 45' in channel I3, each
representing the phase difference between E1 and
stage of ampli?cation producing 180° of phase
E2 is measured.
shift. The lower halves perform like functions for
Since both channels of the circuit are identi
supplying the voltage E1 to network 45 in channel
cally connected, only one will be explained and 50 II. For one frequency, element 8| may act as
only such elements of the other as are necessary
an impedance matching device, this being neces
to the description will be referred to.
sary only if the impedance level of the phase
As shown in Fig. 1, the voltage E2 is taken from
shifting networks 45 or 45' is low. In any case,
the terminals M to potentiometer |5, from which
however, its primary‘ function is that of ampli?
point it is conducted to cross-connection network .55 cation.
l2 and also through channel I I. That portion of
The phase shifting networks 45 and 45', con
E2 which passes through the channel is delivered
nected in the common grid circuit of the balanced
to a phase inverter l6, illustrated as a triode,
modulator of each channel, form a part of the
where it is received by its control grid I1. Anode
load impedance of the twin triode 8|.
I8, and cathode |9 of this element are connected 60
Grids 64 and 12 of element 63 are connected
to positive energy source 92 and ground respec
to receive the voltages E2 and E1, respectively, and
tively through plate resistor 23 and cathode re
anodes 65 and 13 to receive positive energy from
sistor 22. The output of stage I6 is taken from
source 92 through plate resistors 14 and 15.
its anode and cathode for delivery to a push-pull
cathodes-66 and 1| are tied together and ground
ampli?er 40, comprising in part the electronic dis
ed through resistor 61, which has a by-pass con
charge element 3 I.
denser 68 coupled in parallel therewith. The out
This device, which may take the form of a twin
put of plate 65 is delivered to grid 82 of element
triode, is coupled in the conventional manner for
8| through coupling condenser 16 and similarly
push-pull amplication. Its control grids 32 and
plate 13 is coupled to grid 85 through capacitor
29 are coupled to the anode and cathode of tube 70 11. A common cathode circuit comprising cath
II; respectively through capacitors 24 and 28.
ode resistor 18 and by-passing condenser 19 con
Cathodes 34 and 31 are connected to ground ’
nects the cathodes 83 and 81 to ground and re
through resistor 26. Grid leak resistors 25 and
sistors 94 and 93 provide a direct current return
21 are provided for grids 32 and 29 respectively.
path for grids 82 and 85 respectively.
Plates 33 and 36 receive positive energy from 75
Plates 84 and 86 receive positive energy from
2,411,876
6
Assuming the tubes 41 and 52 to have similar
source aiithrough'plate resistors 88 and 89 ‘and
deliver the voltages E2 and E1 through coupling V,’ characteristics and equal external load resist
an'ces, all components higher than the second
condensers 95-and; 95 ‘to the phase shifting net
works 45' and 45 respectively.
order maybe neglected, and
‘
A circuit balancing branch for the two balanced
modulators 50 and 50’ comprising resistor 91,
' (9)
voltage regulator 98 and potentiometer 99,~bal- '
ances the operation of these elements by con
‘Equations 5 and. 6 in Equation 9 we have
trolling the plate voltage delivered to their re
spective tubes, from source 92.
10
\ .
io=2la1eb+2aaeaebl
By substituting the values of-ee and es given by
In operation the phase inverter and push-pull
v
(10) io=2E1 sin (wt-45°) Ea1+2azE1 sin (0)”) ]
which maybe expanded and put in the form'
ampli?er of each- channel function normally.
Likewise the ampli?ers of the cross~connecting
networkv l2 operate in the'usual manner, making
Since the alternating current components of
unnecessary a detailed explanation of the op 15 i0 are by-passed by condensers 56 and 51 (Fig. 1),
eration of the circuit up to the point where each
the direct current i1dc ?owing in‘ coils 59, 60, GI and
of the impressed voltages E2 and E1 is modulated.
‘I0, as de?ned by the second term of ‘Equation
Considering the modi?ed circuit , diagram
11, is
shown in Fig. 3, the voltage E2 is received by bal
anced modulator 50 where it modulates a part of 20
E1 whose phase has been shifted through —-45°
(12)
=2azE1E2 sin (0+45°)
A similar analysis of the operation of balanced?
by phase shifting network 45. Similarly voltage
E1 modulates a part of E2 whose phase has been
modulator 50' in channel l3 willrgive a value for
shifted through a like angle by network 45'. ,
the direct current izae ?owing in coils 59’, 60',
Networks 45 and 45' are made up of cascaded
lattice sections, as :shown in Figure 2, and sim
ulate ideal in?nite ‘cables. The characteristic im
GI’ and 10’, which may be expressed as
pedance of each network varies inversely as'the
if the instantaneous value of voltages es and 8b
square root of the frequency of the impressed
expressed as .
voltage at an angle of —45°, which is independent 30
of frequency.
(14) '
1
(15)
Assuming the balanced modulator circuits of
each channel to be symmetrical and the tubes
thereof to be operating in accordance with the
éa=E1 sin wt, and
€b=E2 sin (wt-0-45")
be substituted in Equation 10.
Thus it is seen that two currents, whose ratio
is proportional to a'function of the angle 0 ex
square law, their operation will be described'ac
cordingly and by speci?c reference to only one
pressing the phase diiference between the voltage
E1 and E1, are passed respectively through the
of them.
coils of each channel.v Now, if these coils be ar
Balanced modulator 50 of channel II, will be
considered for purposes of explanation as shown
ranged at right ‘angles with each other as shown
in Fig. 4. Assuming the two voltages E1 and E2 40 in Fig. 3, two electrical ?elds will be produced
to be varying sinusoidally and to differ in phase
by the ?ow of currents ‘ildc and i2dc which are
also at right angles.
by 0 degrees, then the instantaneous value of E1
These electrical ?elds will in turn produce de
and E2 may be expressed as:
'
'
?ecting
forces F1 and F2, at 90° with each other,
(1)
e1=Er sin wt ‘
as shown in Fig. 5(a), due respectively to ildc
(2)
e2=E2 sin (wt-0)
and 'i2dc, and the resultant F of forces F1 and F2,
Usingthe series expansion for electrode cur-.
at an angle 7, may be expressed as
rents, the plate current i1 ?owing. in coils 58 an
60 may be expressed as
_
~
50
and the plate current 1': ?owing in coil GI and
10 as‘
'
_
=kE1Eg|0+45°
'
55
where they (a)s are constants, the valueof each
depending upon tube characteristics and external
' circuits, and es and éb the instantaneous voltages
tively 'on the input terminals of the balanced 60
modulator 50.
‘
.
Therefore if the angular de?ection is measured
from the 45° position 0' as, shown in Fig. 5(b)
then
(17)
appearing as'signal and carrier voltages respec
7
FLQ=kEIE2LQI
which may be termed the phase meter equation.
_ With the two sets of coils 59, 60, BI and ‘Ill and
Here the voltage ea equals ea, or
59', 50’, 6|’ and 10' arranged as shown in Fig. 3,
a magnetic needle I05, pivoted to align itself in
(5)
ea=Ee sin (wt—0), and
the direction of the resultant force F, is used to
(6)
€b=E1 sin (wt-45°)
65 give an indication of the phase angle 0. Or, if
which is e1 shifted in phase by a —,45°, due to
the effect of the earth's ?eld- is to be eliminated,
the action of network 45.
~
the direct currents into and izdc may be passed
The resultant current in ?owing through coils _ through two movable coils arranged at right
59, 80, 6| and ‘I0 is equal to the algebraic sum of
angles with each other in a permanent magnetic
i1 and 12, or
‘
70 ?eld.
The‘coil arrangement illustrated as comprising
two'sets of coils each of which is made up of two’
which in terms of Equations 3 and 4 may be vex
pairs with one coil of each pair located on oppo
site sides of the electrodynamlc indicator "I5, is
75 necessary to establish continuous ?elds. Since
2,411,876
7
8
the elements of modulator 50 act as class B ampli
?ers, current ?ows in the plate circuit ofeach
tube for only one-half cycle and the coil which‘
is connected in the plate circuit of the respective
tubes must be divided for full cycle operation.
network associated with said second balanced
modulator, means for applying the other 01' said
electrical quantities directly to said second bal
anced modulator and to the phase shifting net
Examination of Equation 17 shows that it is
possible for needle I05 to pass through a full 360°
as 0 varies a corresponding amount, thus giving a
linear indication throughout the entire range of
lator, means for creating a ?rst electrical ?eld
from the output" of said ?rst balanced modulator,
work associated with said ?rst balanced modu
means for creating a second electrical ?eld trans—
verse to the ?rst from the output of said second
360°, and making calibration of the instrument 10 balanced modulator, and means for measuring
extremely simple.
the resultant electrical ?eld produced with re
Since phase reversals of the periodically vary
spect to a reference.
ing quantities are not used in any manner, the
5. An electronic circuit comprising a ?rst bal
apparatus is free from the effects of noise and is
anced modulator having input terminals for re
accordingly highly accurate.
15 ceiving a ?rst of two periodically varying elec
Modi?cations of my invention are of course
trical quantities differing in phase from each
other by an angle 0, phase shifting means within
said ?rst balanced modulator for receiving a por
tion of the second of said periodically varying
electrical quantities, a second balanced modulator
possible and may suggest themselves in view of
the foregoing disclosure. It is therefore intended
that all matter contained in the above description
or shown in the accompanying drawings shall be
considered as being illustrative, and that the
spirit and scope of my invention be regarded as of
such breadth as is de?ned by the appended claims.
- What is claimed is:
'
1. Apparatus for determining the phase rela
tionship between two periodically varying elec
trical quantities comprising separate means for
modulating a portion of each of said electrical
quantities whose phase has been shifted through
a predetermined angle with a portion of the other
periodically varying electrical quantity whose
phase is unshifted, and means responsive to the
direct current components of the two modulated
electrical quantities thus produced for giving an
indication of the phase difference between the
two quantities.
'
2. In an electronic phase meter, a ?rst bal
anced modulator including phase shifting means
for modulating a ?rst of two periodically varying
electrical quantities with the second of said quan
tities after the latter has been shifted in phase
through a predetermined angle, a second bal
anced modulator including phase shifting means
for modulating the second periodically varying
electrical quantity with the ?rst quantity after
its phase has been shifted through a predeter
mined angle, and indicating means responsive to
. the outputs of said ?rst and second balanced
modulators.
3. In an electronic phase meter, a circuit hav
having input terminals for receiving the second
of said periodically varying electrical quantities,
phase shifting means within said second bal
anced modulator for receiving a portion of the
?rst of said periodically varying electrical quan
tities, and indicating means for receiving the out
put of said ?rst and second balancedlmodulators
to give an indication of the angle 0.
6. A phase angle meter comprising two cross
connected channels arranged in a symmetrical
circuit, each channel having a pair of input ter
minals for receiving one of two periodically vary
ing electrical quantities whose phase relation
ship is to be determined, a voltage divider for
passing a part of each of said electrical quan
tities into the opposite channel, means for shift
ing the phase of each part so passed through
a ?xed and predetermined angle, means within
each channel to modulate the quantity from the
opposite channel whose phase has been shifted
with said electrical quantity appearing on its in
put terminals, means within each channel for
separating out the direct current component of
said modulated quantity, means for receiving di
rect current components of the output of each
channel to produce two electrical ?elds at right
angles with each other, and means for indicat
ing the direction of the resultant ?eld produced
by said electrical ?elds to give an indication of
phase angle.
_
ing two pairs of input terminals each of which
7. In an electronic phase meter, a symmetrical
receive one of two periodically varying electrical
circuit comprising two channels, arranged in
quantities, a ?rst balanced modulator including
symmetry about a cross-connecting network,
phase shifting means for modulating the ?rst of
having a pair of input terminals for each chan
said quantities with the second after the latter’s
nel, means within each channel for modulating
phase has been shifted through a predetermined
a periodically varying electrical quantity appear
angle, a second balanced modulator including
ing on the input terminals of the opposite chan
phase shifting means for modulating the second
nel which has been shifted in phase through a
of said periodically varying electrical quantities
?xed and predetermined angle, with the period
with the ?rst, after the latter has been shifted 60 ically varying quantity received on its input ter
in phase through a predetermined angle, coil
minals, means for utilizing the direct current
means for receiving the output of said ?rst bal
components of the modulated output of the re
anced modulator, coil means disposed at an angle
spective channels to produce two electrical ?elds
to said ?rst coil means for receiving the output
at right angles with each other, and means for
of said second balanced modulator, and electro
dynamic indicating means responsive to electri 6) indicating the direction of the resultant ?eld with
respect to a reference to indicate the phase angle
cal ?elds established in said coil means.
relationship
between the two periodically varying
4. In apparatus for measuring the phase rela
electrical quantities.
tionship between two periodically varying elec
8. In an electronic phase meter, two symmet
trical quantities, the combination comprising a
rical channels arranged about a cross-connect
?rst and second balanced modulator having
ing network interconnecting said symmetrical
phase shifting networks connected in the respec
channels, each of said channels having input
tive grid circuits thereof, means for applying one
means for receiving one of two periodically vary
. of said electrical quantities directly to said ?rst
ing electrical quantities, means for diverting a
balanced modulator and to the phase shifting
part of each 01' said electrical quantities into the
2,411,876
9
opposite channel through said cross-connecting
network, separate amplifying and impedance
matching means within said cross-connecting
network for operating upon each of said di
verted electrical quantities, phase inverting
means within each channel for inverting the
phase of the electrical quantity received by said
is
determined angle, modulating each electrical
quantity Whose phase is shifted with the other
quantity, separating the direct current compo
nents out of the modulated quantities produced
by the previous step, producing two electrical
?elds at right angles with eachother from the
said direct current components, and measuring
channel, a push-pull amplifying means for re
the resultant ?eld so produced to. give a phase
ceiving the output of each of said phase invert
angle measurement.
ing means, a balanced modulator within each 10
10. In an electronic phase meter, a ?rst bal
anced modulator including phase shifting means
for modulating a ?rst of two periodically vary
channel having signal input terminals for receiv
ing the respective outputs of each of said push
pull amplifying means, and input terminals for
_
ing electrical quantities with the second of said
quantities after the latter has been shifted in»
receiving a carrier quantity from said cross-con
necting network, means within each of said bal 15 phase through a predetermined angle, a second
balanced modulator including phase shifting
anced modulators for shifting the phase of said
means for modulating the second periodically
carrier quantity, and means for receiving the
varying quantity with the ?rst quantity after its
output of each of said balanced modulators to
phase has been shifted through the same pre
give an indication of phase angle.
determined angle, and indicating means respon
9. A method for determining the phase rela
sive to the outputs of said first and second bal
tion between two periodically varying electrical
anced modulators.
quantities, comprising the steps of shifting the
WILLIAM W. HANSEN.
phase of each quantity through a ?xed and pre
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