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BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to oscillators and more
particularly to crystal oscillators having both negative and positive
feedback loops.
2. Discussion of Related Art
Many oscillator designs have been suggested in which a high Q, series
resonant circuit, such as a piezoelectric crystal is used to produce
frequency stability. Such oscillators are used as reference frequency
generators in many applications. A primary consideration in these
applications is that the oscillator output be stable against changes due
to voltage, temperature and secular changes.
U.S. Pat. No. 3,996,530 to Feistel et al shows a Butler Oscillator having
an amplitude limiting amplifier following a filter network interposed
between the voltage amplification stage and the impedance matching stage
in order to ensure that the crystal is driven by a sinusodial waveform,
free of distortion, for maximum frequency stability.
U.S. Pat. No. 3,836,873 to Healey, III et al discloses a cascode amplifier
configuration comprising first and second transistors in combination with
inductance and capacitance elements to provide an oscillator configuration
with phase shift in the vicinity of the oscillator frequency dominantly
controlled by the quartz crystal unit motional impedance parameters.
U.S. Pat. No. 3,878,481 to Healey, III discloses a VHF oscillator circuit
having first and second transistors, a first resonant circuit coupled to
each of the collectors of the first and second transistors, and a
transformer for coupling energy from the first resonant circuit in a
manner that signals substantially equal in amplitude but opposite in phase
are applied respectively to the bases of the first and second transistors.
In addition, an anti-resonant circuit comprising a crystal unit is coupled
to the emitter of the first transistor.
U.S. Pat. No. 3,569,865 to Healey III discloses a high stability voltage
controlled oscillator having a series coupled emitter follower transistor
amplifier with regenerative feedback to a tuned circuit coupled to the
base electrode of the amplifier. The tuned circuit has a narrow pass band
crystal filter in series with a variable capacitor and in parallel with a
low Q inductor with a controlled voltage adapted to be coupled to the
variable capacity device to vary the capacitive reactance of the tuned
circuit to produce oscillation over a limited frequency range with high
stability.
U.S. Pat. No. 3,571,754 to Healey III discloses a variable frequency
harmonic oscillator including a voltage tunable crystal controlled
resonator incorporating a quartz crystal unit with precisely
anti-resonated static capacitance operating substantially at the series
resonant frequency of the quartz as opposed to the anti-resonant frequency
thereof and a voltage variable reactance network coupled thereto having a
linear reactance vs. voltage characteristic.
U.S. Pat. No. 3,824,494 to Gerum discloses a crystal oscillator for use in
clocks and watches.
U.S. Pat. No. 3,911,378 to Buchanan discloses a voltage controlled
oscillator employing three series TTL inverting gates.
SUMMARY OF THE INVENTION
One object of the present invention is to provide a crystal oscillator
having a negative feedback loop to stabilize the circuit against changes
in sustaining amplifier characteristics due to voltage, temperature and
secular changes.
Another object of the present invention is to provide a balanced feedback
oscillator in which separate positive and negative feedback paths are
utilized in order to provide very high ratios of operating Q to resonator
Q; independent control of both output power and crystal dissipation; the
ability to operate with high impedance resonators; and the elimination of
separate mode traps, and overtone filters.
A still further object of the present invention is to provide a balanced
feedback oscillator which produces an increase in short-term stability and
a reduction in sideband phase noise when the product of amplifier gain and
the negative feedback exceeds unity.
An even further object of the present invention is to provide an oscillator
with superior automatic level control action.
Another object of the present invention is to provide an oscillator which
achieves a reduction in the phase noise floor by independent control of
the amplifier and crystal currents.
In accordance with the above and other objects, the present invention is an
oscillator circuit comprising an amplifier having a positive feedback
path, a negative feedback path and an output path. A series resonant
circuit is connected in the negative feedback path and at least one
impedance element is connected in the positive feedback path. The
impedance element is adjusted to produce a feedback ratio sufficient to
cause oscillation to occur at the resonant frequency of the series
resonant circuit. The negative feedback path is separate from the output
path such that the output power of the amplifier can be controlled
independently of current in the negative feedback path.
In accordance with other aspects of the invention, the amplifier comprises
a differential amplifier having an inverting input and a non-inverting
input. The positive feedback path is connected to one of the inputs and
the negative feedback path is connected to the other of the inputs.
The series resonant circuit of the oscillator can be a piezoelectric
crystal. One side of the crystal can be connected to ground.
The oscillator circuit can also include a limiting circuit for varying the
feedback ratio of the positive feedback path in response to an output
level in the output path.
In accordance with other aspects, the present invention is an oscillator
circuit which comprises a differential amplifier having an inverting
input, a non-inverting input and an output. A positive feedback path
produces a positive feedback ratio to one of the inputs and a negative
feedback path produces a negative feedback ratio to the other of the
inputs. The positive and negative feedback ratios are adjusted to produce
oscillation at the resonant frequency of the resonant circuit.
BRIEF DESCRIPTION OF THE DRAWINGS
The above and other objects of the invention will become more readily
apparent as the invention is more fully explained in the detailed
description below, reference being had to the accompanying drawings in
which like reference numerals represent like parts throughout, in which:
FIG. 1 is a schematic diagram of a bridge configuration which can be used
to produce a balanced feedback oscillator according to the present
invention;
FIG. 2 shows a prior art Butler Oscillator having both positive and
negative feedback;
FIG. 3 is a schematic diagram showing one embodiment of the present
invention;
FIG. 4 is a second embodiment of the invention implemented using an
integrated circuit differential amplifier; and
FIG. 5 is a schematic diagram showing an embodiment of the present
invention using automatic level control.
FIG. 6 is a schematic diagram showing dual mode operation using the present
invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 1 shows a bridge configuration 10 including a dual feedback network
driving a differential amplifier 12 having a gain Ao. The output of the
amplifier excites two feedback paths. One feedback path provides positive
feedback through the voltage divider comprising impedances 14 and 16. One
feedback path provides negative feedback through the divider comprising
impedances 18 and 20. In order to produce oscillation at one frequency
only, a resonator can be placed at any one of the four impedances and
provide a net positive feedback at its resonant frequency. A series
resonant circuit in place of the impedances 16 or 18, or an anti-resonant
circuit in place of impedances 14 or 20 will produce the desired
oscillation. This configuration produces a very rapid transfer from
positive to negative feedback off resonance and a very high value of
d.phi./df around resonance, wherein .phi. represents phase and f
represents frequency. The result is a multiplication of the resonantor's Q
value and rapid reduction of the amplifier induced phase noise at the
close-in sideband frequencies, as will be demonstrated hereinafter.
By way of background, the basic equation for feedback amplifiers is:
##EQU1##
where: A is the closed loop gain in the presence of a feedback ratio
.beta., and an amplifier gain of Ao.
In the balanced configuration shown, .beta. is divided between the two
arms, .beta.n and .beta.p as follows:
##EQU2##
where: Z.sub.1 . . . Z.sub.4 represent the impedances of element 14, 16,
18, 20, respectively.
Substituting these for .beta. in equation (1), yields:
##EQU3##
For oscillation to occur: Ao must be real and positive, .beta.p-.beta.n
must be real and positive, and the denominator must be equal to zero. That
is:
##EQU4##
The arrangement of FIG. 1 can be used as a crystal oscillator if the
crystal is used in its series resonant mode, and substituted for impedance
18. The crystal could also be used in its anti-resonant mode in place of
impedance 14 or 20, but this requires impractically high values for
impedance 16 or 18, to avoid excessive dampening of the crystal's Q and
does not result in the same benefits that substituting the crystal for
impedance 18 provides. Using the crystal as impedance 18 also produces a
high loaded Q, plus a Q-multiplication factor.
The configuration of FIG. 1 permits the amplifier to operate with a high
power output while still maintaining the crystal current at a relatively
low value, as will be discussed. A high amplifier output is desirable in
order to limit the phase-noise sidebands. The limiting factor in reducing
phase-noise sidebands on conventional crystal oscillator signals is often
the low power level at which most oscillators operate. The sideband noise
generated within an oscillator is:
S.phi.(f)=f.sub.o.sup.2 (F.sub.o KT)/(P.sub.s Q.sup.2
f.sub.m.sup.2)+(AF.sub.o.sup.2)/(Q.sup.2 f.sub.m.sup.3) (7)
where:
f.sub.o is the resonant frequency;
F.sub.o is the noise figure;
K is Boltzmann's constant;
T is the absolute temperature;
P.sub.s is the power level;
Q is the crystal selectivity;
f.sub.m is the sideband frequency; and
A is the flicker noise constant.
where the first term is the thermal noise contribution, and the second the
flicker noise term. Both terms are reduced when high Q crystals are used,
while the first term is also helped by generating a high power level
P.sub.s in the oscillator circuit, along with a low noise figure F.sub.o.
The first term produces a l/f.sub.m.sup.2 spectral slope while the second
accounts for a l/f.sub.m.sup.3 spectral slope.
A following buffer amplifier can contribute:
S.phi.(f)=(4F.sub.A KT)/P.sub.s +A/f.sub.m (8)
where F.sub.A is the buffer amplifier noise figure and where the first term
is a flat thermal noise contribution, while the second adds a l/f.sub.m
flicker noise spectrum. Here again the first (thermal) term is reduced if
the signal level is high.
This analysis indicates the advantages of generating a high output level
directly from the oscillator rather than depending on a buffer amplifier
to provide power. There can also be a reduction in the number of stages
required. A good isolation amplifier may still be required to reduce load
reaction on the oscillator.
A review of the classic Pierce/Colpitts oscillators will show a conflict
between the requirements for low crystal current, and optimum transistor
current.
It is generally considered desirable to hold the crystal current at a low
value, typically 1 mA or less, in order to reduce short- and long-term
variations in frequency. However, the classic oscillators generate an a.c.
collector current that is less than the crystal current by a factor
proportional to circuit Q, which is usually between 2 and 10.
If the oscillator is self-limiting, the d.c. collector current is typically
between 0.5 and 1 times the a.c. current. One thus ends up with a d.c.
collector current in the order of 50 to 500 microamperes. If an automatic
level control (ALC) circuit is used that operates on the transconductance
of the sustaining amplifier (and this is the usual case) then the d.c.
current is usually at, or below, the lower end of that range. An
examination of noise figures, and gain-bandwidth products (f.sub.T) for
low noise rf transistors indicate that the best units have minimum noise
figures and maximum f.sub.T in the range of 0.5 to 3 mAdc (with higher
power units to 15 mA). Thus the two goals indicated above are not
compatible in the classic oscillators unless ALC is achieved through a
variable attenuator in the feedback path so that an optimum d.c. current
can be maintained.
Negative feedback may be used to increase the effective Q of a crystal by
providing a multiplier effect as demonstrated by the following discussion.
The rate at which phase changes in an oscillator circuit is dependent on
the loaded Q of the crystal. In most oscillator circuits this is less than
the Q of the resonator alone, varying from 50% to 90%. By considering the
impedance of the crystal in the vicinity of series resonance, we can
derive the d.phi./df of the crystal alone, since:
##EQU5##
where: R is the crystal resistance;
L is the crystal inductance;
C is the crystal capacitance;
.omega. is the angular frequency.
##EQU6##
Since Q is defined as:
##EQU7##
At the resonant frequency:
.omega.o.sup.2 LC=1 (14)
where: .omega.o is the resonant angular frequency
##EQU8##
Thus the Q of the resonator determines the rate of change of phase and in
turn, the sideband phase noise decay rate.
In calculating the d.phi./d.omega. rate for a dual feedback oscillator in
which the crystal is in the negative feedback path, assume that .beta.p is
a constant, while .beta.n is proportional to the crystal impedance, so
that:
##EQU9##
where: K is the negative feedback factor.
##EQU10##
where: M.sub.Q is the Q multiplication factor. Thus the Q is multiplied by
the factor .beta.nAo. Even though we cannot change the crystal's Q, we can
theoretically multiply its effect on d.phi./d.omega. with combined
positive and negative feedback in which the negative loop includes the
crystal.
The common Butler Oscillator, uses both positive and negative feedback. As
shown in FIG. 2, this oscillator comprises a transistor 22 having an
inductor 24 connected between its collector and base. A crystal 26 is
connected between the transistor emitter and ground. A capacitor 28 is
connected between the transistor base and ground. A second capacitor 30
and the load 31 are connected from the transistor collector to ground.
This class of oscillators can be considered as a dual feedback design
since the crystal 26 is in series with the emitter of the sustaining
amplifier 22, providing negative feedback, while the capacitive voltage
divider 28, 30 across the output tank, provides positive feedback.
The factors, Ao, .beta.p and .beta.n for the Butler Oscillator can be
determined as follows:
##EQU11##
where: RL is the resistance of load 31; and
re is the emitter resistance of transistor 22 and is equal to
0.026/I.sub.E,
##EQU12##
where: C.sub.2 is the capacitance of capacitor 30; and
C.sub.1 is the capacitance of capacitor 28,
##EQU13##
where: R.sub.X is the resistance of crystal 26.
The Q multiplication factor is, as before,
##EQU14##
The Q-factor is not realized in practice unless Ao is maintained at a high
value. This does not occur when .beta.p is made much larger than .beta.n,
as is the usual practice, since limiting, or ALC, will reduce Ao until:
##EQU15##
If .beta.p>>.beta.n, than Ao drops to a low value, greatly reducing the
Q-factor.
The benefits of Q multiplication cannot be realized then, unless
.beta.p-.beta.n is maintained at a low value commensurate with the
available value of 1/Ao. Applied to FIG. 2:
##EQU16##
This is the factor through which the gain is reduced by the presence of
the crystal's resistance in the emitter circuit.
As an example of the magnitude of M.sub.Q, assume re=15, R.sub.X =50,
R.sub.L =1500 then Ao=100, .beta.n=0.033 and .beta.p=(1/100)+0.033,
resulting in M.sub.Q =.beta.nAo=0.033.times.100=3.3. This represents an
effective increase in (d.phi./df) over that produced in a conventional
single-feedback oscillator, such as the Pierce, or Colpitts types, even
though the full benefits of Q multiplication are not produced.
Referring to FIG. 3, the basic oscillator 100 of the present invention is
shown. This oscillator is referred to as a differential crystal oscillator
(DXO). The DXO uses a differentially connected transistor pair 102 and 104
providing separate inputs for positive and negative feedback networks. The
oscillator is tuned by an L-C circuit comprising inductor 106, capacitor
110 connected from the collector of transistor 102 to ground, and the
series connection of capacitors 108, 126 and 128 between the collector of
transistor 104 and ground. The value of capacitor 110 equals the sum of
capacitors 108, 126 and 128 so that the tuned circuit is balanced relative
to transistors 102 and 104. The oscillator 100 is biased as a linear
amplifier by a resistive voltage divider comprising the resistors 112 and
114 connected to the bases of the transistors, and by separate emitter
resistors 118 and 120. The emitter resistors provide for small differences
between the transistors and prevent either transistor from being cut off.
The transistor emitters are connected by a resistor 122 and a capacitor
124, which effectively tie the emitters together for a.c. operation. An
inductor 124 is connected between the transistor bases to equalize the
current between the bases. Capacitor 126 is connected between the base of
transistor 102 and the junction of capacitor 108 with resistor 116.
Capacitor 128 is connected between the base of transistor 102 and ground.
A capacitor 130 is connected between the base of transistor 104 and one
side of a crystal 132. The other side of crystal 132 is connected to
ground. An inductor 134 is connected in parallel with crystal 132. The
purpose of capacitor 130 is to aid in the tuning of crystal 132 and to
block d.c. signals. Inductor 134 provides a d.c. to ground shunt around
crystal 132 to eliminate any d.c. voltage across the crystal.
The operation of DXO 100 can be understood more easily by considering the
circuit with the crystal 132 not present and an a.c. short to ground
placed on the base of transistor 104. The circuit will oscillate at the
resonant frequency of the L-C collector circuit or "tank" circuit. This
occurs because of the positive feedback from the collector of transistor
104 to the base of transistor 102 through the voltage divider formed by
capacitors 108, 126 and 128. The voltage across capacitor 128 is a
fraction of the collector voltage of transistor 104 but is large enough to
sustain oscillation.
If we assume that the short to ground is now removed from the base of
transistor 104, the circuit will stop oscillation because of strong
negative feedback produced by the connection between the tuned circuit and
the base of transistor 104 by resistor 116. With the crystal disconnected,
the voltage at the junction of capacitors 108 and 126 exceeds that at the
junction of capacitors 126 and 128, and therefore, feedback equation (4)
above has a large positive denominator and the circuit provides little
overall gain.
Finally, by connecting a crystal resonator 132 to ground as shown in FIG.
3, the circuit will oscillate if the series resonance of the crystal is
within the bandpass of the tuned circuit, and is low enough in resonant
resistance to reduce the .beta.n to the point where equation (5) is
satisfied.
The DXO 100 is capable of generating a very high ratio of output power to
crystal power dissipation, typically ratios of more than 100 (40 db) are
achievable, because the current through crystal 132 is dependent neither
on the output level of the oscillator nor on the current level in the
positive feedback path. Thus the requirement for a low crystal current can
be met while maintaining a high value for Ao so that the thermal noise
component is reduced and a high Q multiplication factor is achieved.
Experiments with the DXO 100 indicate that if it is designed for a high
power output to crystal dissipation ratio, it can present a signal
sufficiently above the noise level of the following stages to greatly
reduce the added noise.
Thus, the DXO 100 is capable of achieving a high Q multiplier effect as
defined by equation 23 so that the circuit Q is above the crystal Q and is
also capable of achieving a high power output so that the noise of the
final signal is significantly reduced. This is due to the fact that the
negative feedback path is separate both from the positive feedback path
and the output circuit. Thus, the current in the crystal 132 can be
precisely controlled independently of the power output of the amplifier
and the current in the positive feedback path. This not only results in a
high Q multiplier and low thermal noise, but also permits a high impedance
crystal to be used.
It will be understood that maintaining positive and negative feedback paths
separate permits the sustaining differential amplifier to operate with a
high gain Ao to achieve a high Q multiplication factor. Keeping the
negative feedback path containing the crystal separate from the output
path permits the output signal to be large thus eliminating the need for
additional signal amplification and the addition of noise. DXO 100 can be
modified for other purposes whereby only one of these advantages may be
achieved. For example, rather than connecting the lower lead of crystal
132 directly to ground, the oscillator output might be taken from this
lead to provide a signal with less noise since the current only flows
through the crystal within its narrow pass band. This signal would be
provided to a common base amplifier having a low input impedance. This
configuration would have a high Q multiplier but would require a following
amplifier.
The basic principles of the DXO can be implemented by using a differential
integrated circuit R.F. amplifier such as CA3001, CA3040, or the MC1733.
These amplifiers exhibit voltage gain values from 10 to 400 and a
bandwidth of up to 50 .mu.Hz without L-C circuits, so that an essentially
aperiodic oscillator can be built with them. The basic circuit for this
configuration is shown in FIG. 4.
The circuit of FIG. 4 comprises a differential amplifier 200 having a gain
Ao and inverting and non-inverting inputs 202 and 204. A crystal 206 has
one terminal connected to ground and the other terminal connected to the
inverting input 202 through a capacitor 208. Negative feedback is
generated by a resistor 210 having a value of 5 times of the crystal
resistance RX. Positive feedback is generated by a voltage divider
consisting of resistors 212 and 214 connected from the amplifier output to
the non-inverting input of the amplifier. A resonant circuit comprising
inductor 216 and capacitor 218 is connected between the inverting and
non-inverting inputs 204 and 208. The output of amplifier 200 is d.c.
blocked by capacitors 220 and 222. MOS I.C. differential amplifiers such
as amplifier 200 have a very low output impedance and can drive low
resistances as low as 500 ohms. This allows the use of resistors 210, 212
and 214 in the feedback networks, as shown, and, when combined with a dual
voltage supply, the circuit is very simple. The only adjustment, once the
positive feedback ratio and the amplifier gain are selected, is to pick a
resistor for feeding the crystal so that the proper value for the negative
feedback ratio can be obtained. It is a simple matter to adjust this value
to compensate for the variation in the crystal's series resistance so that
a large amount of excess gain is not produced.
A design incorporating amplitude limiting is shown in FIG. 5. This circuit
is essentially the same as shown in FIG. 3 and comprises transistors 300
and 302 interconnected by an inductor 304 for providing equal DC bias to
the bases of the transistors. The transistor emitters are connected by a
resistor 306 and a resonant circuit 308 is connected between the
transistor collectors. Positive feedback is provided through a divider
comprising capacitor 310, capacitor 312, and variable capacitor 314.
Negtive feedback is provided through a resistor 316 and a DC blocking
capacitor 318. An automatic level control circuit 320 is connected between
the output of the oscillator and the junction between capacitors 312 and
314 through a resistor 322. A crystal 324 is connected between the base of
transistor 302 and ground.
The circuit of FIG. 5 provides positive feedback through the capacitive
divider 310, 312, 314 to one base and negative feedback through a divider
comprising resistor 316 and crystal 324 to the other base. The result is
an L-C oscillator constrained by the crystal circuit to oscillate only at
the series resonant frequency of the crystal. The L/C ratio can be
selected to provide a wide range of bandwidths. A low L/C ratio will
produce a narrow bandwidth suitable for use with SC-cut and/or overtone
mode crystal operation. Higher L/C ratios can be used for the less
critical fundamental modes. It is worth noting that the tuned circuit is
loaded by the .beta.n resistance at .omega..sub.o and is loaded only by
R.sub.n plus the input impedance of the transistor at frequencies
immediately off resonance.
An alternate method of obtaining an output signal is to connect the input
of a common base amplifier in series with the lower terminal of the
crystal. Since current only flows through the crystal within its narrow
pass bands, the output will contain less noise than the collector resistor
connector, and will be sinusoidal in shape. As discussed above, however,
signal level at the output will be lower so that more noise may be added
by the series connected amplifier.
The ALC circuit 320 feeds back a level control signal indicative of the
output signal amplitude. This level control signal is a d.c. signal and is
provided through resistor 322 to alter the positive feedback ratio at the
base of transistor 300. Level control circuits themselves are known and
circuit 320 will not be described in detail. Such a circuit can comprise a
rectifier or any similar circuit for providing a d.c. output which is
indicative of the amplitude of an a.c. input signal. Capacitor 314 is an
electronically variable capacitor whose capacitance is a function of the
d.c. current applied thereto. Capacitor 310 blocks all d.c. signals except
those from ALC circuit 320 so that the capacitor 314 responds directly to
the level control signal. As the amplitude of the oscillator output signal
increases, the capacitance of capacitor 314 increases due to an increase
in the gain control signal. This causes a reduction in the positive
feedback ratio .beta.p and stabilizes the output signal level. The
significant feature of the invention in this regard is that the current
through the crystal is not affected as would be the case if ALC is used in
the circuit of FIG. 2 where the transconductance of the amplifier would be
changed.
As will be understood from the foregoing discussion, the present invention
provides an oscillator wherein the current through the crystal contained
in the negative feedback loop can be set independently of the output power
of the oscillator. This permits low crystal current and high crystal
resistance to be used without affecting the output level. The balanced
circuit also produces soft limiting with even order harmonic cancellation.
Limiting occurs first in the positively driven transistor and since
amplifier gain is inversely proportional to the difference between
positive and negative feedback, only a slight reduction of positive
feedback is necessary to stabilize the amplitude.
No additional overtone or mode traps are required. A single tuned circuit
confines the oscillation to the selected frequency band.
Dual mode operation is also very convenient with the invention. In dual
mode operation, one resonator can be run on two of its modes or overtones
simultaneously. Since the crystal is grounded at one terminal and operates
in the series mode, two oscillators can be tied to one resonator with
crossover filters on either side to separate the mode currents. Such a
configuration is shown schematically in FIG. 6 wherein two crossover
networks 400 and 402 are connected between the resonator 404 and two DXO
circuits 406 and 408. Each network 400, 402 presents a series-resonant
pole between the resonator and its DXO, and also an anti-resonant pole to
the frequency of the other DXO. In addition, loading capacitors can be
used to trim each mode independently.
The most important concern is the need for high Q inductors in these
networks, since the equivalent series resistance of the series inductance
adds to the resistance of the crystal and reduces its operating Q. The
shunt "anti-resonant" reactances must also exhibit high Q to provide a
rapid transition from low impedance (pass) to high impedance (reject).
Grounded, series mode crystal operation is also usable when several
crystals are being switched into one oscillator, or when the crystal is on
long leads, e.g., one being used as a transducer.
The foregoing description is set forth for purposes of illustrating the
invention but is not deemed to limit its scope. Clearly, numerous
additions, substitutions and other modifications could be made without
departing from the scope thereof as set forth in the appended claims.
* * * * *
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