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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to the art of electrical generator systems for
driving piezoelectric transducers, and more particularly concerns such a
system which generates driving signals over a wide band of frequencies and
which employs signal sampling circuitry and feedback network loops.
2. Description of the Prior Art
Resonant operation of a piezoelectric transducer device may be defined as
the frequency at which electrical to mechanical transformation takes place
and may be graphically depicted by a rapidly changing phase shift with
frequency. Since it is an energy exchange system, where the mechanical to
electrical conversion is known to be reciprocal, abrupt changes in the
load current phase presented by the piezoelectric device in motion result
as energy is absorbed and reflected. Depending on whether the transducer
is "squeezing" or "unsqueezing" in relation to its drive it may absorb or
return electrical energy.
At frequencies below resonance for all high quality mechanically unloaded
piezoelectric resonators including quartz crystals generally used for
frequency control in communications equipment, the phase relationship is
relatively fixed with the current leading the impressed voltage by
approximately 90.degree. much the same as in a capacitor and indicative of
no mechanical motion. As frequency increases and vibration begins, the
phase starts to lag going through 0.degree. phase shift and finally to
90.degree. lagging. The current magnitude reaches a peak at the 0.degree.
point which is generally referred to as series resonance, and goes to a
minimum and nearly vanishes at 90.degree. lagging, generally referred to
as parallel resonance or anti-resonance. Further increase in frequency,
results in the emergence of a current, which is again leading by
approximately 90.degree., very much like a capacitor. The rate of phase
change with frequency lessens above the 60.degree. lagging point,
culminating in a very slow change at 90.degree.. This region is sought by
many conventional generators having limited stability. Analysis of the
phase angle to energy delivery indicates almost full energy delivery at
0.degree. phase shift and almost full storage at 90.degree., with
components of each elsewhere in the vibrating region. The resonance range,
slope and smoothness of the phase curve changes with the temperature,
power level, and mechanical load impressed upon the piezoelectric
transducer. At the 0.degree. phase shift point, the most power can be
extracted with minimum voltage stress on the piezoelectric transducer.
In a mechanically loaded piezoelectric transducer with a fixed power input
such that insufficient energy is available to overcome the load and
provide for operation into the lagging phase angle storage region,
stoppage of the transducer occurs prior to achieving a 90.degree. lagging
current. With sufficient load pressure no motion at all occurs, and the
piezoelectric transducer becomes a passive capacitor throughout the entire
range. When operation is at or near parallel resonance, energy is tending
toward being fully reflected and high voltages are necessary to input
power for conversion, thus burdening the piezoelectric transducer with
dielectric breakdown and high reactive circulating current handling
problems. The 90.degree. lagging, parallel resonance point is at the end
of the region where rapid phase shift with frequency and energy conversion
occurs. After the 90.degree. lag or parallel resonance point is reached, a
discontinuity results, indicating an abrupt reversal of phase change with
frequency, which mechanical load matching systems may smooth or cover to
produce an apparent continuous phase sense reversal after the 90.degree.
lag point, where the phase leads increasingly with frequency until the
phase returns to 90.degree. leading and unchanging. This reversal of phase
sense with frequency is very troublesome, preventing prior generator
systems from achieving wide range, as all depend on a monotonic
phase-frequency characteristic for correction of the transducer frequency.
Maintaining 0.degree. phase shift, and increasing the mechanical load by
applying a force directly opposite to the motion, causes a shift upward in
the vibratory frequency that affords 0.degree. until a reversal in phase
change with frequency occurs. This signals sudden stoppage in transducer
vibration and a return to a fixed approximately 90.degree. lead.
Increasing input power with load staves off the frequency increase and
vibratory stoppage. Ultimately, however, with sufficient load, a limit is
reached and the vibration must be allowed to stall if transducer damage is
to be avoided. Heating of the vibratory transmission system generally
lowers the frequency at which the 0.degree. phase current occurs.
At the present state of the art, most generator circuits are more or less
free running power oscillators only lightly influenced by the phase
frequency relationship, due to difficulties in keeping the feedback from
changing the frequency to points outside the resonance region, since the
phase frequency relationship sense is undirectional only over a small
region and may reverse suddenly under changing conditions of load,
temperature, and drive level. When a phase lock loop is used, the delay
associated with a resonating piezoelectric device is so great that loop
stability is marginal at best and even undisturbed closed loop operation
overshoots into the phase reversal region, with the consequent driving of
the frequency above the frequency needed.
The prior art using the so called "self sterring" phase lock loop circuit
encounters the difficulties identified and addressed herein. Circuits
incorporating clamps, special amplifiers, such as disclosed in U.S. Pat.
No. 4,056,761 and even microprocesseor control sequencing, such as
disclosed in U.S. Pat. No. 4,577,500 to solve loop stability problems,
achieve their objectives by compromising performance.
SUMMARY OF THE INVENTION
The present invention employs a phase sensing and locking circuit which
overcomes the above mentioned difficulties and permits the generator
system to use efficiently generated square waves. It also permits the
input power to be freely adjusted to provide power increase, decrease or
constancy under load characteristic while still maintaining the optimum
frequency for efficient energy conversion tenaciously and instantaneously.
It further operates various transducers with different mechanical
structures and operation frequencies within a high percentage bandwidth
without requiring any operational adjustment. Starting of transducer
vibration is smooth without abrupt threshold requirements under loaded and
unloaded conditions. According to the invention there is provided an
electrical self tuned signal generator system which converts direct
current to alternating current at optimum frequency and with such wave
shape as will efficiently drive a piezoelectric transducer, for conversion
of electrical energy to ultrasonic mechanical energy over a wider
frequency range than has heretofore been possible.
The system employs an improved form of phase lock loop. The generator
utilizes the loop to perform the energy conversion function automatically,
finding and directly maintaining the optimum drive parameters over a wide
frequency range of at least 25% of a predetermined preset frequency,
regardless of system load, temperature, transducer configuration and
manufacturing variations. Different transducers having different optimum
oscillation frequencies within this wide frequency range or bandwidth are
driven without any adjustment required to the driving electronics or to
the transducer.
The attainment of the 25% direct phase lock loop range is a major advance
in performance over that attainable with prior electrical drivers of
piezoelectric transducers, which generally can attain a working range or
bandwidth of 2% or less with respect to a specified operating frequency.
The magnitude of operating frequency range is a major measure of
performance of sonic transducer systems.
An operating range of at least 25% of set center frequency, by the present
invention, leads to other significant advantages. The 25% range or
bandwidth represents an operating range of from 19,000 to 25,000 cycles
for one class of ultrasonic transducers designed to operate at
approximately 22,000 cycles. This is more than adequate for present day
manufacturing tolerances. Transducers of known quality and performance at
22,000 cycles normally require only a few hundred cycles tolerance. Under
many applications, however, temperature, load and configuration variations
cause optimum frequency of operation to shift more than 2,000 cycles.
Accordingly, the present invention is able to accomodate this shift within
its wide operating range. As a further advantage, the reliability of the
present generator system itself is enhanced since drift in parameters of
its own components which may change with temperature and time are
compensated for by the wide range of the feedback loop.
In the present invention, loop performance is independent of the frequency
generating waveform, thus allowing switching circuitry to provide high
power levels with resulting low loss and economical circuitry. The loop
performance is also independent of power input variations and permits a
second feedback loop controlling power output to operate independently and
effectively.
The loop stabilization is achieved by two unique networks incorporated in a
transducer current sample feedback path. These networks overcome
limitations in operation of a phase lock loop. True self tuned operation
is afforded without restricting range to a particular transducer. No
calibration is required for transducer variations or for temperature
variation of the voltage controlled oscillator used by the generator
system. The previous narrow operating range of prior generator systems has
heretofore restricted and made prohibitively uneconomical or impractical
the widespread employment of the useful aspects of ultrasonic energy in
variable load, environment, and configuration applications. Instruments,
appliances, tools and new previously unfeasible configurations of
instruments and applications of ultrasonic energy may become more readily
available as a consequence of this invention. By using modern electret
piezoelectric transducers, a conversion of over 1000 micro-inches (25
microns) per watt is not unusual. Electrical to mechanical conversion
efficiency exceeds 90% by using this invention, thus reducing heating of
the piezoelectric transducer to negligible amounts even under heavy load.
These and other objects and many of the attendant advantages of this
invention will be readily appreciated as the same becomes better
understood by reference to the following detailed description when
considered in connection with the accompanying drawings in which:
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of an ultrasonic generator system embodying the
present invention;
FIG. 2 is a block diagram of an ultrasonic generator system embodying
modifications of the system of FIG. 1;
FIG. 3 is a schematic diagram of a switching power amplifier employed in
the system of FIGS. 1 and 2;
FIG. 4 is a schematic diagram of another power amplifier which may be
employed in the system of FIG. 2;
FIG. 5 is a schematic diagram of an alternate current sampling system which
may be used in the system of FIG. 1;
FIG. 6 is a schematic diagram of a phase detector and oscillator I.C.
useful in the systems of FIGS. 1 and 2; and
FIG. 7 is a schematic diagram of direct current power supply and power
control circuitry, along with fault current sensing and current
interruptor circuitry, which may be used in the systems of FIG. 1
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring now to the drawings wherein like reference characters designate
like or corresponding parts throughout, there is illustrated in FIG. 1 a
self tuned ultrasonic generator system, generally designated as reference
numeral 10, which converts direct current to alternating current having
optimum frequency and shape necessary to drive, a piezoelectric transducer
12, for converting the applied electrical energy to mechanical energy over
a wide frequency range.
A voltage controlled oscillator 18 applies a square wave from an output 19
to an input 20 of the amplifier 16. The amplifier 16 essentially operates
as a highly efficient switch which alternately connects the positive
direct current input 15 and a ground input 22 to an amplifier output 24.
The alternating current output from the amplifier 24 is in turn impressed
across a filter and a matching LC network 26, which has an inductor 28
connected between the amplifier output 24 and both a primary winding 30 of
a transformer 32 and a capacitor 34. The capacitor 34 is connected to
ground. The sine wave current appearing across the capacitor 34 is applied
to the piezoelectric transducer 12 via the primary winding 30 to drive the
transducer 12 for generating mechanical sonic vibrations.
The current appearing at a transformer secondary winding 36 is applied to a
load resistor 38. A sample of the transformer output current is applied
via a line 40 to an input 42 of the DC power supply and control circuit
14. The sample of the transformer output current is also applied via a
line 44 to a filter network 46 which has a series connected resistor 48
and an inductor 50, and a parallel capacitor 52 connected to ground. The
output from the filter 46 is applied as a feedback to an input 54 of a
digital phase detector 56 through a capacitor 58. A reference input 60 of
the digital phase detector 56 is connected to the output 19 of the voltage
controlled oscillator 18 via a reference feed line 66.
A damper network 68 which is comprised of a capacitor 70 (or an equivalent
circuit) is connected between the input 60 and the input 54 of the phase
detector 56. An output 72 from the phase detector 56 is applied to a
resistor 74 and then to a parallel connected capacitor 76 which integrate
the output of the phase detector 56 with a time constant under one
millisecond. The integrated output across the capacitor 76 is applied to
an input frequency tuning terminal 78 of the oscillator 18 to complete the
loop.
The digital phase detector 56, described in further detail below in
connection with FIG. 6, is a complex digital circuit with three-state
output and leading edge sense logic. The output 72 disconnects to an open
circuit if the two inputs 54, 60 are and remain identical in phase.
Normally, when the feedback signal (FB) at the input 54 leads the signal
from the oscillator output 19, applied to the reference input 60 (FR) via
the feed line 66, the output 72 of the phase detector 56 produces positive
pulses which raise the input voltage and frequency of the oscillator 18.
The phase detector 56 produces ground pulses which lower the oscillator
input voltage and output frequency if the feedback input 54 lags the
oscillator output sample 66 applied at the reference input 60.
The phase detector circuit 56 operates on a cycle of a pair of positive
transitions alternately on the two inputs 54, 60. A transition on one
input locks out that input and either a "1" or "0" is the output depending
on which input was first, until a second transition appears at the other
input. The second transition then opens both inputs for the next detection
of positive edge transitions and simultaneously opens the detector output
72 to the floating state. During this period, when the detector 56 is
waiting for the next edge pair, the detector 56 is vulnerable to a noise
or stray spike pulse. In normal steady state operation, both of the inputs
54 and 60 are in phase only briefly due to the input impedance of the
tuning port 78 of the oscillator 18. This impedance makes the voltage
across the capacitor 76 droop, and this causes the oscillator frequency to
decrease, but the oscillator frequency is restored by the appearance of a
slight lead in the phase of the feedback input signal at the detector
input 54. The detector 56 in turn sends a positive pulse of this lead
duration from the output 72 which returns the voltage across the capacitor
76 to that needed to maintain the oscillator 18 at the frequency which
provides 0.degree. phase shift.
If a stray pulse from a noise spike or a sudden reflected transducer output
from a mechanical load step or sound pressure occurs, before the next
reference input transition to the input 60, a large false positive output
could result at the output 72 and drive the output frequency of the
oscillator 18 above the normal operating region into the region of phase
sense reversal. The circuit 10 would hang up, constantly trying to raise
the detector output frequency to get rid of the phase lead, which due to
phase sense reversal only produces more phase lead. The filter 46 and the
damper 68 are incorporated to prevent this loop failure.
The filter 46 serves several functions. It attenuates high frequency spikes
and noise that may try to enter into the sine wave applied to the input
54. The filter 46 can be used to make up for any circuit phase shift
between point A at the input 20 of the amplifier 16, and point B at an
input to the piezoelectric transducer 12. The filter 46 works in
conjunction with the damper 68 to provide an appropriate delay
compensation. The rate of phase shift change with frequency caused by the
components in the matching network 26 and in the filter 46 is small
compared to that produced by the piezoelectric transducer 12 and is
generally set to provide a transducer voltage-current phase relationship
of from 15.degree. lead to 0.degree. . It will be noted that the filter 46
is a low pass filter broadened out with the series resistance 48. The
filter 46 is totally passive. This is important to avoid introducing gain
which would reduce noise immunity.
The phase detector 56 is quite capable of accurately operating with
variations in input levels from its power supply level of fifteen volts
down to 700 millivolts without any wave shaping or modification. The
detector 56 has a selfbiased inverting buffer (not shown) at the feedback
input 54. The capacitor 58 blocks the DC output from the filter 46 in
order for this buffer to provide the only gain in the feedback path. At
loop startup when the current sample input level on the line 44 is below
the operating threshold of the phase detector 56, the initial frequency
will automatically be at the lower band edge and sweep upwards in
frequency which is desirable since any spurious responses of the
transducer 12 will be above the operating frequency.
The damper 68 performs a significant damping function to prevent the loop
response overshoots from building and driving the loop to the phase sense
reversal region of the transducer 12. The damper 68 by means of the
capacitor 70 adds the fast edge transition of the square wave going to the
input 60, to the input 54 of the phase detector 56. When the phase at the
feedback input 54 leads the phase at the reference input 60, the signal
added by the damper 68 causes no effect. But when the phase at the
feedback input 54 begins to lag the phase at the reference input 60, the
effect is to shut out the action which would normally cause the detector
output 72 to go low and reduce the frequency generated by the oscillator
18. Instead, having received a synchronous second edge, the output 72 of
the phase detector 56 goes to the open state, and the frequency of the
oscillator 18 is reduced gradually by the normal droop at the capacitor
76, due to the input impedence at the input 78 of oscillator 18, providing
a very necessary digital integration. Without the damper 68, the sudden
downward correction would soon produce overshoots into the reverse sense
region, and consequent jump toward the high band edge. The overshoots are
unavoidable due to the time delay associated with the transient response
of the piezoelectric transducer 12 which is a tuned narrow band
mechanically vibrating body with inherent inertia. The capacitor 70 of the
damper 68 requires a capacitance value chosen such that a sufficient
amount of the fast edge of the square wave signal, at the reference feed
line 66, to the detector input 60, adds to the sine wave coming from the
capacitor 58 without loading the input 54 unduly.
If desired, the circuit 10 may be operated by shorting or removing the
inductor 50 if the inconvience of precision adjustment of the high power
components in the filter matching network 26 is tolerable.
If isolation and power feedback is not required for any particular
application, the system 10 can be simplified as shown by a system 10A in
FIG. 2. System 10A employs the same numbered components as shown and
described for the system 10 in FIG. 1, except that the transformer 32 and
the DC power supply and control 14 in a feedback network are omitted. A
variable DC is applied at the input 15 of the amplifier 16 from an
independent power source 14'. A diode limiter 71 consisting of two diode
rectifiers 73 and 75 connected in parallel, is placed in series with the
return current from the transducer 12. A limited current sample 79 across
the diodes 73, 75 is applied to an input 77 of a filter 46' which employs
a series resistor 48' and a parallel capacitor 52' (the inductor 50 of the
filter 46, being omitted, or shorted out). The filter 46' acts as an
effective filter without the inductor 50. However no phase setting
adjustment is available to make up for the phase shift between circuit
points A and B. In this arrangement, the phase shift may be set to
0.degree. by proper selection or adjustment of the inductor 28 and/or the
capacitor 34 in the filter matching network 26. Except for the
simplification provided by system 10A the arrangement and operation of
system 10A is the same as described above for system 10.
FIG. 3 is a circuit diagram of a push pull switching square wave power
amplifier, suitable for the amplifier 16 shown in FIGS. 1 & 2. A square
wave at input 80 from the voltage controlled oscillator 18 is applied to a
buffer stage BS1 of the amplifier 16 which is an inverting buffer assembly
having six stages BS1 through BS6. Fifteen volts DC at an input line 82
supplies the operating power for the stages BS1 through BS6 which is a
conventional hex inverting buffer IC such as CMOS RCA 4069 UBE. An output
86 of the buffer stage BS1 is split into two paths 88, 90. These two paths
respectively terminate at field effect switching transistors 100 and 102.
The two transistors 100, 102 respectively drive primary windings 104, 106
of a power transformer 108 which has a secondary winding 110, grounded at
one end 112. The other end 114 of the secondary winding 110 is connected
to the filter matching network 26.
The two paths 88, 90 serve to generate push-pull input signals to the field
effect switching transistors 100, 102. To insure that only one field
effect switching transistor is on at any one time, the positive leading
edge of the signal appearing at each input 118 and 120 is delayed until
the signal appearing on the opposite field effect transistor is well below
its turnon voltage. This is accomplished by a diode 122, a capacitor 124,
and a resistor 126 in the path 88, and by a diode 128, a capacitor 130 and
a resistor 132 in the path 90. To insure low loss and minimum heating in
the field effect transistors 100 and 102, the signals at inputs 118 and
120 have fast rise times since they are passed through respective buffer
stages BS4, BS5, and BS6 in the path 118, and buffer stages BS2, and BS3,
in the path 120. The transistors 100 and 102 alternately draw DC+ current
through a respective primary winding 104, 106 of the transformer 108. The
transformer 108 is a voltage step-up component producing an efficiently
generated high power AC output at the secondary winding 110.
The switching square wave power amplifier 16 shown in FIG. 3 and used in
systems 10 and 10A of FIGS. 1 and 2, can be replaced in system 10A by a
transformerless switching square wave power amplifier 16A shown in FIG. 4
which employs four amplifying transistors 141 through 144. The output from
the square wave oscillator 18 is applied to the base of the transistor 141
which drives the transistor 142. The high voltage square wave output at a
collector 146 of the transistor 142 is applied to both of the transistors
143 and 144. The PNP transistor 143 and NPN transistor 144 constitute a
complementary pair which provide push-pull power gain. Since this
transformerless amplifier 16A has no phase inversion, it can operate with
the transformerless current sample 79 shown in FIG. 2. This simplified
circuit arrangement is adaptable for use in low cost ultrasonic soldering,
bonding, and other portable applications requiring low to moderate power.
The filter matching network 26 shown in FIGS. 1 and 2 receives the output
from the switching amplifier 16. The output across the capacitor 34 can be
connected to the piezoelectric transducer 12 in any one of three possible
ways. One economical way is by using a diode limiter 71 having a pair of
diodes 73, 75 as shown in FIG. 2. The diodes 73, 75 are arranged in series
with a ground return 121 of the transducer 12 as shown in FIG. 2. A second
method is by use of the current transformer 32 shown in FIG. 1. The
primary winding 30 is connected in series with high side supply line 29 to
the transducer 12. This permits grounding the ground return line 12' at a
ground point 12" without affecting the current sample taken across the
secondary resistor 38. The transformer 32 provides a sample of current
amplitude and phase information on the line 44. The amplitude information
is used to provide the feedback power control to be described below in
connection with FIG. 7.
A third arrangement illustrated in FIG. 5 for connecting the filter
matching network 26 to the transducer 12 is by a sampling circuit 150 to
replace the transformer arrangement shown in the system 10, FIG. 1. Here
the transformer 32 is arranged as shown in FIG. 1 with the primary 30
connected from the output 29 of the network 26 to the high side of the
transducer 12. An additional transformer 160 has a primary 162 connected
between a grounded output 29' of the matching network 26 and the low side
of the transducer 12. A secondary 166 of the transformer 160 is shunted by
a resistor 167 and is connected to a terminal 169. This arrangement
provides on a line 170 a ground fault detection signal by the amplitude
comparison of the current sample provided by the secondary 36 of the
transformer 32 on a line 44' and the secondary 166 of the transformer 160.
The difference in the level of the two samples on the line 170 is used to
provide quick shut off of the power input to the generator system 10 in
the event of a ground fault at the transducer 12. A suitable fault current
interrupter circuit is described below in connection with FIG. 7.
A sample of the current derived from the limiter 71 of FIG. 2, or from the
transformer 32 of FIG. 1, or from both transformers 32 and 160 of FIG. 5,
is passed to the digital phase detector 56 employed in both systems 10 and
10A of FIGS. 1 and 2 respectively. FIG. 6 shows circuit details of an
integrated circuit 180 which is commercially available as an RCA CD 4046
CMOS IC which incorporates the voltage controlled oscillator 18 and the
digital phase detector 56.
The current sample passes through the filter 46 or 46' (shown in FIG. 2).
The filter 46 is comprised of the resistor 48 connected in series with the
inductor 50 and in parallel with the capacitor 52 connected to ground. If
the inductor 50 is omitted then the filter 46 has the configuration of the
filter 46' of FIG. 2. The passive filter 46 or 46' is connected to the
capacitor 58 which connects the ungrounded terminal of the capacitor 52 to
a pin P14 of the integrated circuit 180 which is the feedback input 54, to
the digital phase detector 56. The output of the phase detector 56 at a
pin P13 is connected to the input of the oscillator 18 at a pin P9 through
the resistor 74 which together with the capacitor 76 connected from a pin
P9 to ground, integrates the phase detector output pulses with a time
constant of less than one millisecond. The output from the oscillator 18
at a pin P4 supplies the reference input to the phase detector 56 by
direct connection to a pin P3. As shown in FIGS. 1 and 2, this signal is
also connected to the feedback input 54 at the pin P14, through the damper
capacitor 70 which is connected between the pins P3 and P14. A pair of
pins P5 and P8 are grounded. The square wave output of the oscillator 18
at pin P4 is also applied to the input of the power amplifier 16 as
described above. A pin P16 is supplied with +15 volt DC to operate the
integrated circuit 180.
The voltage controlled oscillator 18 is adjusted to operate with a 25%
range about center frequency by a capacitor 182 connected across a pair of
pins P6, P7, a variable resistor 184 in series with a resistor 188,
connected to a pin P11, and a variable resistor 186 in series with a
resistor 190 connected to a pin P12. The voltage controlled oscillator 18
in the RCA 4046 I.C. 180 has a published temperature stability of
approximately 150 PPM per degree Celsius at its best operating voltage
which is 15 volts DC. Without a wide band loop, this variability of output
frequency on heating and cooling would require constant adjustment of the
oscillator to maintain operation under temperature changes. In the present
invention, the phase detector output is not restricted by clamping or
other means to obtain loop stability. When the oscillator 18 is set for an
operating range such that the center of operation occurs at a tuning
voltage at pin 9 of 7.5 volts at 25.degree. C., the circuit still gives
successful operation even at extreme temperature of from +70.degree. C.
to -20.degree. C. with a change in the 7.5 volt point from 13 volts to 2
volts. Commercially produced voltage controlled oscillators having greater
stability such as the INTERSIL TYPE ICL8038 are available with 50 PPM
stability, enabling even wider temperature operations.
FIG. 7 is a schematic diagram of a power supply and power control circuit
14 forming part of the system 10 shown in FIG. 1. The current sample from
the transformer 32 is applied at an input 200 to a diode 202 where the
current is peak detected and then filtered by a grounded capacitor 206 in
parallel with a resistor 204 which provides a DC voltage at an inverting
input 208 of an operational amplifier 210, such as found in a Moto | | |
