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Dec. 10, 1946.
‘H. G. ocH ETAL
2,412,227
ELECTRICAL DIFFERENTIATOR
Filed May 1, 1941
FIG. I
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H. 6.0CH
WVENTORS' KOSWARTZEL JR.
BY
Mm
A TIORNEV
Patented Dec. 10, 1946
UNITED STATES PATENT OFFICE
2,412,227
ELECTRICAL DIFFERENTIATOR
Henry G.‘ Och, West Englewood, and Karl D.
Swartzel, Jr., Teaneck, N. J., assig-nors to Bell
Telephone Laboratories, Incorporated, New
York, N. Y., a corporation of New York
Application May 1, 1941, Serial No. 391,332
3 Claims.
(Cl. 178‘—44)
1
2
This invention relates to electrical measuring
circuit of the vacuum tube 4 assist in maintain
circuits and particularly to an electrical network
ing the proper phase relationships in the ampli
for deriving a function of the input voltage.
?er so that the output voltage of the ampli?er
The object of the invention is an electrical netwill accurately represent the desired value.
work for continuously deriving the differential or 5
In the following equations let
time derivative of the input voltage.
eo=the voltage to be analyzed,
A feature of the invention is the use of a re
e=the output voltage,
verse feedback circuit associated with a linear
RIZthe resistance of resistor I‘,
ampli?er in such manner as to produce in the
Rzzthe resistance of resistor n,
output of the ampli?er a‘ voltage varying as the in Rzthe resistance of’ resistor '3 or '4;
differential of the input voltage.
czthe capacitance 0f capacitor |5’
In many measuring devices’ such 3'5 artillery
S=the change of the plate current of vacuum
predictors, airplane bomb sights, vibration meastube a due to a unit voltage applied to the grid
uring devices and many others, it is necessary to
of vacuum tube 2, that is’ the over-mu trans_
obtain the rate of change of some measurable i5
conductance of the complete ampu?en
quantity.
In accordance with the present inven-
_
tion this measurable quantity is expressed as a
variable electrical voltage which is applied to the
input of an electrical network.
The network
_
_
Using the Prmclples Set forth m U- 5- Efatent
2,102,571, December 21, 1937, H- s- Black’ It can
‘r be shown that
modi?es the applied voltage to produce in the 20
output circuit a voltage varying in accordance
23
RC
#5
1
e=e0('R—)(1+'§ P)<1+,1B 1—‘—*_R“(f“
with the rate of change or differential of the in-
23120 +3 1’)
put voltage, and, in some cases, a voltage vary-
mindégeecgzawii’lhg Phe Input voltage‘
(1)
25 Where no is the gain around the feedback loop
Fig. 1 diagrammatically shows an electrical
network embodying one aspect of the invention;
and is equal to
-
Fig. 2 shows the network of Fig. 1 modi?ed to
produce a pure dlfrerentlal voltage-
_
S
"
"
<2)
l( i) i( t) ( 5X 1i)
R1 1+R2 +122 1+R| +Y’C H122
1+R1
30 When the gain around the feedback loop is large,
The voltage to be analyzed is cmwmwnally
designated by the voltage source 60, and is applied
to the input of the network through a resistor I.
say 1000, the last two members of the gain equa
“on are Very nearly unity and the gain can be
expressed as
‘This voltage is applied directly to thecontrol clea
trode, or grid of the ?rst vacuum tube 2, which 35
=-__
,
J
may have a conventional grid biasing resistor 3
in the cathode circuit. The vacuum tube 2 is
e e“ R\
1+ 2 p
R1 80 {E R1 pm
(3)
But 10 is the common mathematical operator 111.
coupled to the vacuum tube ‘by the known neli-
dioatlng differentiation with respect to time and,
Work Comprising the resistors 5, 6 and 7- The
therefore, the output voltage e includes a com
vacuum tube 4 is similarly coupled to the vacuum 40 [30119111] proportional to err and a component pro
tube 3 by means of the known network COmportional to the time derivative or differential
prising the resistors 9, l0 and H. The output of
of en,
-‘
the vacuum tube 8 is supplied to the load resistor
By a Suitable choice of the circuit elements
l2 and is available as a voltage appearing across
R1, R and c, and providing the gain around the
this resistor. Power is fed back from the anode 45 feedback loop is large, it; is evident from Equation
of the Vacuum tube 3 t0 the Control electrode, 01‘
3 that the absolute, as well as the relative, values
grid of the vacuum tube 2 through the serially
of the signal compgnent,
connected resistors l3 and I4. A capacitor [5 is
connected from the junction of the resistors I3
<§>60
and I4 to ground, that is, eifectively to the cath- 50
R1
ode circuits of the vacuum tubes.
and the differential component
The capacitors l6 and I9, respectively in serial
R20
relationship with the resistors l1 and 20 in shunt
(R—l)peo
to the input circuits of the vacuum tubes 4 and
8, and the capacitor It! in shunt to the output 55 may be controlled within a certain range, but,
2,412,221’:
3
as a practical matter, the signal component can
not be made equal to zero, so as to give a pure
differential component. However, this result may
be obtained, as shown in Fig. 2, by canceling out
the signal component.
In Fig. 2, the ampli?er 2| represents the linear
ampli?er of Fig. 1, and circuit elements having
reference characters similar to those in Fig. l
have similar functions. The output of the net
4
In a typical embodiment of the invention, the
resistor l was 4 megohms, the resistor 3 was
1500 ohms, the resistors 5, 6, ‘I, 9, II), II were
respectively 1/2, 9A, 2, 1/4, 1% and 1 megohms, the
resistor l2 was 6000 ohms, the resistors l3 and M
were each 2 megohms, and the resistors i1 and 20
were each 100,000 ohms. The capacitors I5, IE,
I8, l9 were respectively 1, .001, .0001, .03 micro
farads. The vacuum tubes 2, 4, 8 were commer~
cial vacuum tubes respectively designated by the
trade-names 6SC7, 6SJ7 and 6Y6G. A ‘TOO-volt
battery, grounded at the mid-point, was used,
U. S. application Serial No. 391,331, to K. D.
+350 volts being applied to the anodes of tubes
Swartzel, Jr., ?led of even date herewith. The
2 and 4, +250 volts to the anode of tube 8, +75
summing ampli?er 22 has a feedback path
through the impedance 25, and will produce in its 15 volts to the screen grid of tube 5, ground or zero
volts to the cathode of tube 4 and the screen grid
output circuit a voltage proportional to the alge
of tube 8, -135 volts to the cathode of tube 8
braic sum of the voltages supplied to the input
and —350 volts to the grid of tube 4.
circuit. Signal voltage from the source 60 is
What is claimed is:
supplied directly through the resistor 24 to the
1. In combination, a source of voltage to be
input of the summing ampli?er 22. As the net 20
analyzed, a linear ampli?er having an input and
work 2| includes an odd number of vacuum tubes
work 2| is supplied through a resistor 23, to a
summing ampli?er 22, of the type disclosed in
in cascade, the signal voltage supplied by the
network 2| to the summing ampli?er 22 is re
an output circuit, a ?rst resistor in serial rela
tionship with said source connected to the input
circuit of said ampli?er, and a feedback path from
versed in phase with respect to the signal voltage
25 said output circuit to said input circuit includ—
supplied through the resistor 24.
ing two resistors connected in serial relationship
Let
in said path, and a capacitor connected from the
Ri=resistance of resistor l,
junction of said resistors in shunt to said path,
R1a=resistance of resistor 13,
whereby the output of said ampli?er contains
Ru=resistance of resistor 14.
30 components corresponding to the voltage from
R23=resistance of resistor 23,
said source. and to the differential or time deriva
Rz4=resistance of resistor 24.
tive of said voltage, a second linear amplifier
having an input and an output circuit, a fourth
Then if
resistor in serial relationship with the output cir
Rlz-l'R14=I?i
35 cult of said ?rst ampli?er and the input circuit
R1
R24
of said second ampli?er, a feedback path from
the output circuit to the input circuit of said
second ampli?er, and a ?fth resistor in serial
summing ampli?er 22 will just cancel each other,
relationship with said source connected to the
and the output of the summing ampli?er 22 will
contain only the diiferential component.
40 input circuit of said second amplifier.
2. The combination in claim 1 in which the
It will generally be found that the capacitor l5
ratio of the sum of said two resistors to said ?rst
has a certain amount of leakage resistance, which
resistor equals the ratio of said fourth resistor
may be considered as a resistor of suitable value
to said ?fth resistor.
in shunt with the capacitor l5, which will tend
3. The method of producing a voltage varyin;r
to produce a component of signal voltage in the
with the rate of change of a signal voltage, which
output of the ampli?er 2|, and thus change the
comprises amplifying said signal voltage, feeding
relative values of signal voltage and differential
back a portion of said ampli?ed voltage of such
voltage in the output, compared to the values
magnitude and phase as to produce a component
given by a perfect capacitor. By suitable choice
of the values of the resistors R1, R13, R14. R23. 50 of voltage varying with the rate of change of said
the signal voltages supplied to the input of the
R24, R25, and the capacitor C15, the relative values
signal voltage, supplying said ampli?ed signal
of signal voltage and differential voltage may be
voltage and said component to a utilization cir»
cuit, and supplying to said utilization circuit signal
made to approximate the values obtained with a
perfect capacitor.
voltages of reversed phase to neutralize the ampli
By connecting a number of the circuits shown 65 ?ed signal voltage in said utilization circuit.
in Fig, 2 in tandem, it is obvious that the second.
HENRY G. OCH.
or higher, differentials of the signal voltage may
KARL D. SWARTZEL, JR.
be obtained.
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