U.S. patent number 3,845,398 [Application Number 05/228,636] was granted by the patent office on 1974-10-29 for adjustable time constant operating circuit.
Invention is credited to Bernard Katz.
United States Patent |
3,845,398 |
Katz |
October 29, 1974 |
ADJUSTABLE TIME CONSTANT OPERATING CIRCUIT
Abstract
Apparatus for adjusting the time constant of an operating
circuit including an operational amplifier is disclosed in
accordance with the teachings of the present invention wherein
switch means are provided to periodically interrupt the resistive
feedback path of a differentiating circuit or the resistive input
path of an integrating circuit. The time constant of the operating
circuit is dependent upon the duration of each periodic
interruption.
Inventors: |
Katz; Bernard (Irvington,
NJ) |
Family
ID: |
22858010 |
Appl.
No.: |
05/228,636 |
Filed: |
February 23, 1972 |
Current U.S.
Class: |
327/335;
327/345 |
Current CPC
Class: |
G06G
7/186 (20130101) |
Current International
Class: |
G06G
7/00 (20060101); G06G 7/186 (20060101); G06g
007/18 () |
Field of
Search: |
;307/229,230,340
;328/127,128 ;235/197,183 ;333/19 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
korn & Korn Electronic Analog Computers 2nd Ed. McGraw Hill,
page 13. .
Electronic Analog Computers, (D.C. Analog Computers) by Korn &
Korn, McGraw Hill page 415, 1956..
|
Primary Examiner: Rolinec; Rudolph V.
Assistant Examiner: Davis; B. P.
Claims
1. In a differentiating circuit including the combination of an
operational amplifier exhibiting relatively high input impedance
and gain characteristics, an input capacitance means providing an
input channel to an input terminal of said operational amplifier
and feedback resistance means providing an electrical channel
between an output terminal of said operational amplifier and said
input terminal thereof, apparatus for adjusting the time constant
of said differentiating circuit, comprising:
switch means coupled to said feedback resistance means and adapted
to selectively interrupt said electrical channel upon the
activation of said switch means, said feedback resistance means
including first and second resistance means connected in series
relationship and said switch means including a switching device
connected to the junction formed by said first and second series
connected resistance means, said switching device being operative
to interrupt said electrical channel for a portion P of each
periodic interval of time T such that said effective time constant
of said differentiating circuit is adjusted by the factor T/T- P;
and
energizing means coupled to said switch means for providing an
activating signal to activate said switch means at periodic
intervals of time, whereby the effective time constant of said
differentiating circuit is dependent upon said periodic intervals,
said energizing means generating a
2. The combination of claim 1 wherein said switching device is
adapted to supply a reference potential to said junction during
said portion P of
3. In a differentiating circuit including the combination of an
operational amplifier exhibiting relatively high input impedance
and gain characteristics, an input capacitance means providing an
input channel to an input terminal of said operational amplifier
and feedback resistance means providing an electrical channel
between an output terminal of said operational amplifier and said
input terminal thereof, apparatus for adjusting the time constant
of said differentiating circuit, comprising:
switch means coupled to said feedback resistance means and adapted
to selectively interrupt said electrical channel upon the
activation of said switch means; and
energizing means coupled to said switch means for providing an
activating signal to activate said switch means at periodic
intervals of time, whereby the effective time constant of said
differentiating circuit is dependent upon said periodic intervals,
said energizing means including pulse generating means for
providing a periodic pulse signal characterized
4. In a differentiating circuit including the combination of an
operational amplifier exhibiting relatively high input impedance
and gain characteristics, an input capacitance means providing an
input channel to an input terminal of said operational amplifier
and feedback resistance means providing an electrical channel
between an output terminal of said operational amplifier and said
input terminal thereof, apparatus for adjusting the time constant
of said differentiating circuit, comprising:
switch means coupled to said feedback resistance means and adapted
to selectively interrupt said electrical channel upon the
activation of said switch means;
filter means coupled to said feedback resistance means; and
energizing means coupled to said switch means for providing an
activating signal to activate said switch means at periodic
intervals of time, whereby the effective time constant of said
differentiating circuit is
5. In an integrating circuit including the combination of an
operational amplifier exhibiting relatively high input impedance
and gain characteristics, input resistance means providing an input
channel from an input means to said integrating circuit to an input
terminal of said operational amplifier, and feedback capacitance
means interconnecting an output terminal of said operational
amplifier with said input terminal thereof, the improvement in
apparatus for adjusting the time constant of said integrating
circuit comprising:
switch means connected to said input resistance means for
selectively interrupting said input channel upon an activation
thereof;
capacitor means connected between said input means and said input
terminal of said operational amplifier to thereby reside in
parallel with said interconnected resistance and switch means;
and
means for applying an energizing signal to said switch means to
activate said switch means at periodic intervals of time, said
integrating circuit manifesting an effective time constant which is
a function of said
6. The combination of claim 5 wherein said switch means comprises a
switching device connected in series relationship with said input
resistance means and said means for applying an energizing signal
generating pulses having a duration of P and a period equal to T,
said switching device being operative to interrupt said input
channel for a portion T-P of each periodic interval of time T such
that said effective time constant of said integrating circuit is
adjusted by the factor T/P.
Description
This invention relates to operating circuits employing operational
amplifying means and, more particularly, to apparatus for adjusting
the time constant of an operational amplifier differentiating
circuit and an operational amplifier integrating circuit.
A conventional resistance-capacitance circuit exhibits, in one
configuration, differentiating properties which may be
advantageously utilized to provide an output signal proportional to
the derivative of an input signal applied thereto. In a second
configuration, the resistance-capacitance circuit provides
integrating properties whereby an output signal is proportional to
the integral of the input signal. As is understood, the respective
time constants of these circuits is equal to the product of the
resistance and the capacitance thereof. The time constant is
determinative of the proportional relationship between the input
and output signals. Unfortunately, the simple
resistance-capacitance circuits exhibit desirable differentiating
or integrating properties only under certain limiting
conditions.
The operational amplifier, however, with its attendant high gain
and high input impedance admits of a practical differentiating or
integrating circuit. Accordingly, the output signal produced by a
differentiating circuit comprised of an operational amplifier
including an input capacitance means and a feedback resistance
means is proportional to the derivative of the input signal applied
thereto. The proportionality constant or gain of this
differentiating circuit is equal to the time constant thereof,
i.e., the produce of the feedback resistance and the input
capacitance. The foregoing is equally applicable to an integrating
circuit comprised of an operational amplifier having an input
resistance means and a feedback capacitance means. It is desirable
in some applications of the operational amplifier differentiating
or integrating circuit to vary the time constant and,
correspondingly, the gain of the circuit. The techniques heretofore
utilized by the prior art to vary the time constant of the
differentiating circuit employ a single variable feedback resistor
or alternatively, a plurality of fixed resistors each operable to
be selectively connected into the feedback circuit. Similarly, the
time constant of an integrating circuit has previously been varied
by utilizing a single variable input resistor or a plurality of
switchable input resistors. These techniques, however, are
extremely susceptible to extraneous noise which has a deleterious
affect on the operation of the differentiating or integrating
circuit. In addition, the aforedescribed techniques usually require
a plurality of electrical contacts and their accompanying leakage
capacitance characteristics.
Therefore, it is an object of the present invention to provide an
operating circuit admitting of an adjustable time constant.
It is another object of the present invention to provide improved
apparatus for adjusting the time constant of a differentiating
circuit and an integrating circuit.
It is a further object of the present invention to provide
apparatus for adjusting the time constant of a differentiating or
integrating circuit without introducing undesirable noise
signals.
Various other objectives and advantages of the invention will
become clear from the following detailed description of exemplary
embodiments thereof and the novel features will be particularly
pointed out in connection with the appended claims.
In accordance with one embodiment of this invention, a
differentiating circuit including an operational amplifier is
provided wherein the time constant of said differentiating circuit
is adjusted by periodically interrupting the resistive feedback
channel of said circuit, such that the effective time constant of
the differentiating circuit is dependent upon the duration of
interruption. In another embodiment hereof, the time constant of an
integrating circuit is varied by periodically interrupting the
resistive input channel therefor.
The invention will be more clearly understood by reference to the
following detailed description of exemplary embodiments thereof in
conjunction with the accompanying drawings in which:
FIG. 1 is a schematic drawing of a first embodiment of the
differentiating circuit of the present invention;
FIG. 2 is a schematic drawing of another embodiment of the
differentiating circuit of the present invention; and
FIG. 3 is a schematic drawing of the integrating circuit of the
present invention.
Referring now to the drawings wherein like reference numerals are
used throughout, and in particular to FIG. 1, there is illustrated
a differentiating circuit comprised of operational amplifying means
101, capacitance means 106 and resistance means 107. Operational
amplifying means 101 may comprise a conventional operational
amplifier well known to those skilled in the art including an
inverting input terminal 102, a non-inverting input terminal 103
and an output terminal 105. The operational amplifying means 101
admits of a conventional differentiating circuit configuration
wherein capacitance means 106 is coupled to inverting input
terminal 102 and feedback resistance means 107 provides an
electrical channel from output terminal 105 to inverting input
terminal 102. The non-inverting input terminal 103 of operational
amplifying means 101 is preferably coupled to a reference potential
such as ground potential.
It is understood by those skilled in the art that the capacitive
input of the operational amplifier differentiating circuit provides
undesirable susceptibility to random noise. Accordingly, the noise
responsive characteristics of the circuit illustrated in FIG. 1 may
be greatly improved by providing a further resistance means in
series with input capacitance means 106. Alternatively, filter
capacitance means 108 may be connected in parallel relationship
with feedback resistance means 107. Those skilled in the art will
recognize filter capacitance means 108 as a conventional high
frequency "stop."
The conventional differentiating circuit of FIG. 1 is modified by
the addition of switch means 109 connected in series relationship
with feedback resistance means 107 nd adapted to assume a first or
second state. Hence, switch means 109 may comprise the armature of
a conventional relay circuit. If desired, the switch means 109 may
comprise a conventional field effect transistor or a silicon
controlled switching device or other switching transistor.
Accordingly, the switch means 109 is adapted to assume a first
state whereby feedback resistance means 107 is interconnected
between output terminal 105 and input terminal 102. Conversely, the
switch means 109 is adapted to assume a second state whereby the
electrical channel including the feedback resistance means 107 is
interrupted. Pulse generating means 110 is coupled to switch means
109 and is adapted to provide a periodic pulse signal thereto for
controlling the state assumed by switch means 109. If switch means
109 comprises a relay circuit, pulse generating means 110 may be
connected to the energizing coil thereof; and if switch means 109
comprises a switching transistor pulse generating means 110 may be
connected to the control electrode thereof. The frequency of the
applied pulses should be high with respect to the frequency of an
input signal applied to input terminal 104. In addition, pulse
generator means 110 may include means to vary the time duration of
each periodically generated pulse for a purpose soon to become
apparent.
The operation of the apparatus illustrated in FIG. 1 will now be
described. For purposes of explanation, it will initially be
assumed that switch means 109 admits of its first state and
activating pulses are not supplied thereto by pulse generating
means 110. Thus, if the reactive impedance of filter capacitance
means 108 exceeds both the reactive impedance of capacitance means
106 and the resistance of feedback resistance means 107 then the
output signal produced at terminal 105 in response to an input
signal provided at terminal 104 may be represented as E.sub.out = -
R.sub.1 C.sub.1 (dE.sub.in /dt) where R.sub.1 is equal to the
resistance of feedback resistance means 107, C.sub.1 is equal to
the capacitance of input capacitance means 106 and E.sub.in
represents the voltage of the signal supplied to terminal 104. This
equation is manifested for all frequencies below the "stop"
frequency, i.e., until the reactive impedance X.sub.C2 of filter
capacitance means 108 is equal to the resistance R.sub.1 of
feedback resistance means 107.
At frequencies above the "stop" frequency, the reactive impedance
X.sub.C2 of filter capacitance means 108 becomes less than the
resistance R.sub.1 of feedback resistance means 107. A relation
between any frequency above the "stop" frequency and the "stop"
frequency itself may be shown to be:
f/f.sub.stop = (1/X.sub.C2)/(1/X.sub.C2stop) = X.sub.C2stop
/X.sub.C2 = R.sub.1 /X.sub.C2
It may thus be observed that at very high frequencies, the effect,
of feedback resistance means 107 is negligible in comparison to the
effect of the filter capacitance means 108.
If, now, pulse generating means 110 provides high frequency pulses
admitting of a frequency that greatly exceeds the "stop" frequency
(in practice, the "stop" frequency may be, say, 10 Hz and the pulse
frequency may be 5,000 Hz) and having a period equal to T and a
pulse duration equal to P, then feedback resistance means 107 is
provided in the feedback circuit for a time P during each period T.
Since the resistance R.sub.1 of feedback resistance means 107 is
much greater than the reactive impedance X.sub.C2 of filter
capacitance means 108 at the pulse frequency of 5,000 Hz, it is
apparent that the output signal produced at terminal 105 will
exhibit an insignificant high frequency ripple component. In fact,
the ripple component is a function of the ratio between the "stop"
frequency and the pulse frequency, or 10/5,000 = 0.2 percent.
However, it should be intuitively appreciated that the alternate
insertion and removal of feedback resistance means 107 by the
operation of switch means 109 results in a time averaged
multiplying effect on the resistance R.sub.1 of the feedback
resistance means. Consequently, if the signal provided at terminal
104 admits of a frequency below the "stop" frequency, the effective
value of R.sub.1 may be expressed as (T/P) R.sub.1. The output
signal produced at terminal 105 in response to an input signal
provided at terminal 104 may be represented as E.sub.out = T/P
R.sub.1 C.sub.1 dE.sub.in /dt. Thus, it is seen that switch means
109 is operable to adjust the time constant of the differentiating
circuit illustrated in FIG. 1 by the factor T/P.
Another embodiment of the present invention is illustrated in FIG.
2 which comprises operational amplifier 101, input capacitance
means 106, feedback resistance means 201 and 202, and switch means
109. Feedback resistance means 201 and 202 are connected in series
relationship forming a common junction 203 therebetween. Hence, a
feedback resistance circuit comprised of feedback resistance means
201 connected in series with feedback resistance means 202 is
provided. The common junction 203 is selectively coupled to a
reference potential such as, for example, ground potential, by
switch means 109. The switch means 109 is operably coupled to pulse
generating means 110 and, therefore, is identical to the switch
means aforedescribed with respect to FIG. 1. It is observed that
the configuration illustrated in FIG. 2 is similar to the
configuration in FIG. 1 wherein the feedback resistance means 107
of the latter has been replaced by series connected feedback
resistance means 201 and 202.
The operation of the embodiment illustrated in FIG. 2 will now be
described. When switch means 109 assumes its first state the common
junction 203 is provided with reference potential such as ground.
Whereas pulse generating means 110 provides activating pulses 111
for switch means 109 resistance means 201 is effectively coupled
between input terminal 102 and input terminal 103 which is also
provided with ground, and resistance means 202 is effectively
coupled between output terminal 105 and input terminal 103 during
each activating pulse interval P. Conversely, resistance means 201
and 202 provide a feedback resistance circuit during each interval
T-P. Accordingly, when switch means 109 assumes its second state,
the current from terminal 104 to input terminal 102 is
substantially equal to the current from output terminal 105 to
input terminal 102 because input terminal 102 will not conduct
current to the operational amplifier 101, and
C.sub.1 dE.sub.in /dt = 1/(R.sub.2 + R.sub.3) .sup.. E.sub.out (T-P
)/T.
Solving this equation for the output voltage E.sub.out,
E.sub.out = - T/(T-P) (R.sub.2 + R.sub.3) C.sub.1 dE.sub.in /dt
where R.sub.2 and R.sub.3 represent the resistance of resistance
means 201 and 202 respectively. Since the switch means 109 assumes
its first and second states at the frequency of the pulses 111, it
is apparent that the feedback resistance means comprised of series
connected feedback resistance means 201 and 202 is alternatively
inserted and removed from the feedback circuit in a manner
analogous to that previously described with respect to FIG. 1.
Accordingly, the operation of switch means 109 results in a time
averaged multiplying effect on the resistance R.sub.2 + R.sub.3 of
the series connected feedback resistance means. It is apparent that
in the previously described embodiment, the multiplying factor was
a function of the pulse duration P. However, in the presently
described embodiment the multiplying factor is a function of the
"guard" time T-P. Consequently, the output voltage E.sub.out may be
represented by the aforenoted equation:
E.sub.out = - T/(T-P) (R.sub.2 + R.sub.3) C.sub.1 dE.sub.in
/dt.
It is now readily apparent that the effective time constant of the
differentiating circuit illustrated in FIG. 2 is adjusted by the
factor T/(T-P).
It should be understood by those skilled in the art that the pulses
111 supplied to switch means 109 are adapted to selectively
activate the switch means whereby said switch means assumes its
first or second state in accordance with the sense of pulses 111.
Consequently, pulse generating means 110 may be specifically
designed to produce positive or negative activating pulses. It will
be recognized, therefore, that switch means 109 may respond to an
applied activating pulse to assume its second state. In addition,
pulse generating means 110 may include further means to vary the
duty cycle P of the pulses 111 generated thereby such that the
effective time constant of the differentiating circuit may be
correspondingly varied.
Referring now to FIG. 3, there is illustrated an integrating
circuit having a variable time constant comprised of operational
amplifying means 101, input resistance means 301 and feedback
capacitance means 303. The operational amplifying means 101 has
been described hereinabove. Accordingly, further description
thereof is not deemed necessary. Input resistance means 301 is
coupled via series connected switch means 109 to inverting input
terminal 102 of operational amplifying means 101. Feedback
capacitance means 303 interconnects the output terminal 105 and
inverting input terminal 102. An additional capacitance means 302
is optionally connected in parallel relationship with the series
connection of input resistance means 301 and switch means 109 and
may be omitted if desired. Switch means 109 is identical to the
aforedescribed switch means of FIG. 1. Accordingly, the switch
means is coupled to pulse generating means 110, the latter being
adapted to supply a periodic pulse signal having a period T and a
pulse duration P.
It is recognized that the integrating circuit of FIG. 3 may be
analyzed in accordance with principles of superposition. Thus, when
switch means 109 assumes its second state, the input resistance
channel to inverting input terminal 102 is interrupted.
Consequently, the illustrated circuit functions as an inverting
amplifier having a gain equal to - C.sub.3 /C.sub.4, where C.sub.3
is the capacitance of feedback capacitance means 303 and C.sub.4 is
the capacitance of additional capacitance means 302. It should be
appreciated that, if C.sub.3 = C.sub.4, the resulting inverting
amplifier comprises a unity gain amplifier. However, when switch
means 109 assumes its first state, input resistance means 301 is
connected to inverting input terminal 102. If the reactive
impedance X.sub.C4 of additional capacitance means 302 exceeds the
resistance R.sub.4 of input resistance means 301, then the output
signal produced at terminal 105 in response to an input signal
E.sub.in provided at terminal 104 may be represented as E.sub.out =
- 1/R.sub.4 C.sub.3 .intg. E.sub.in dt. This equation obtains for
all frequencies until the reactive impedance X.sub.C4 of additional
capacitance means 302 is equal to the resistance R.sub.4 of input
resistance means 301. It may now be appreciated that the alternate
insertion and removal of input resistance means 301 by the
operation of switch means 109 results in a time averaged
multiplying effect on the resistance R.sub.4 of the input
resistance means. The output signal produced at terminal 105 in
response to an input signal provided at terminal 104 may thus be
represented as E.sub.out = - T 1/P R.sub.4 C.sub.3 .intg. E.sub.in
dt. Hence, switch means 109 is operable to adjust the time constant
of the illustrated integrating circuit by the factor T/P.
Although not illustrated herein, it should be readily appreciated
that the input resistance means coupled to operational amplifying
means 101 may assume a configuration analogous to that displayed by
the feedback resistance means of the differentiating circuit of
FIG. 2. Analysis of the integrating circuit modified in this manner
is similar to the analysis set forth hereinabove with respect to
FIG. 2 and need not here be provided.
While this invention has been particularly shown and described with
reference to exemplary embodiments thereof, it will be obvious to
those skilled in the art that the foregoing and various other
changes and modifications in form and details may be made without
departing from the spirit and scope of the invention. It is
therefore intended that the appended claims be interpreted as
including all such changes and modifications.
* * * * *