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DESCRIPTION OF THE PRIOR ART
1. Field of the Invention
The measurement of capacitance or inductance, particularly when in the
presence of a significant amount of DC resistance, is necessary and
important in the design of components for magnetic recording. This
invention allows such measurements to be easily and accurately made.
2. Description of the Prior Art
The classical methods by which reactor values may be measured employ any of
the various kinds of bridges in which a variable impedance in one arm is
adjusted until a null appears across the bridge. (The term "reactor value"
is preferred to "reactance," since the latter term includes the effect of
frequency in determining circuit operation. "Reactor value" means
hereafter either the amount of capacitance or the amount of inductance in
a circuit element.) Three common bridges are the two Maxwell bridges for
comparing two inductances or for comparing an inductance and a
capacitance, and the Wein bridge for comparing two capacitances. The
disadvantage of using these bridges is that accurate results require a
skilled operator and up to one-half hour to complete a single measurement.
For measurement of extremely small reactor values, a Q-meter is preferred,
employing a fixed frequency oscillator output applied to a series LC
circuit, either the capacitance or the inductance being the unknown.
Current is measured by a non-reactive hot wire ammeter. When maximum
current occurs, the system is in resonance. Resonance is achieved by
adjusting one of the reactive elements among known values. Knowing one
reactor value and the resonant frequency, the unknown reactor value can
then be easily computed. However, when a significant amount of resistance
is present in the circuit, the total impedance at resonance may be only
slightly lower than the impedance far from resonance, and hence accurate
measurements are difficult, if not impossible.
The most pertinent prior art of which we are aware is disclosed in the
Hewlett-Packard Journal, March 1974, p. 2 which uses a sophisticated
bridge and a fixed frequency source with automatic adjustment of either
the value of the known reactor or the voltage across it by the use of
negative feedback techniques. U.S. Pat. No. 3,771,050 (Golahny) discloses
a comparison method for measuring reactor value and details the problems
involved in employing balanced bridge measurement. U.S. Pat. No. 3,612,993
(Tims) discloses another comparison-type instrument. U.S. Pat. No.
3,571,703 (Russell) discloses an improvement on the aforementioned
Q-meter. U.S. Pat. Nos. 3,711,770; 3,621,385; 3,713,022; 3,718,856; and
1,971,310 all disclose various circuits which have been proposed through
the years to measure reactor values.
BRIEF DESCRIPTION OF THE INVENTION
A stable servo loop is employed to control the frequency of a variable
frequency oscillator to produce resonance in a series or parallel circuit
containing the element of unknown reactor value (although its type must be
known, i.e. whether it is capacitive or inductive) and a reactor of
opposite type having a known value. The resonant frequency f.sub.r
together with the known reactor value permits the unknown reactor value to
be computed from the formula:
f.sub.r = 1/2.pi..sqroot.LC
where L and C are the respective inductive and capacitive reactor values in
the resonant circuit, one of which is known. The phase shift of the
oscillator output voltage with respect to its output current is 0.degree.
at resonance. A phase detector measures this phase shift and produces a
phase shift signal which indicates the amount of shift and whether this
shift is leading or lagging. The phase shift signal is supplied to a
controller circuit which produces the control signal for the oscillator.
The controller circuit shifts its output responsive to the phase shift
signal in such a way that the oscillator frequency changes toward and
eventually reaches and remains very close to the resonant frequency.
The preferred resonant circuit places the known and unknown impedances in
series to produce series resonance. In such a circuit, current flow is
maximum at resonance and phase shift easily measured, as explained below.
Parallel resonance may also be employed, but since current flow is
theoretically zero at resonance in a parallel circuit, measurement of
phase shift is difficult. This problem can be avoided to some extent by
measuring phase shift at other then resonance as also explained below.
Our preferred way to measure phase shift of the oscillator voltage with
respect to the oscillator current is by measuring phase shift across one
of the reactors in the series circuit. The phase of the voltage across a
purely capacitive or inductive reactor (one having negligible DC
resistance) whether at resonance or not, lags or leads, respectively, the
current through it by exactly 90.degree.. The phase detector measures the
amount and direction of the deviation from 90.degree. of the voltage
across the reactor with respect to that across the oscillator, and
supplies the required phase shift signal to the controller circuit causing
oscillator frequency to shift toward resonance. An indicator circuit
receiving the oscillator output (or input) is pre-programmed with the
known reactor value. According to known principles, the indicator circuit
solves the above equation relating f.sub.r, L and C and can easily provide
a direct visual output which specifies the value of the unknown reactor in
henrys or farads as the case may require.
The set point phase angle need not be exactly 90.degree., but may be any
convenient angle and the unknown reactance then computed from the
oscillator frequency achieved for the set point phase angle and the known
reactance value. Using a non-resonant phase angle is almost essential if a
parallel circuit is employed since almost no current flows through the
oscillator and hence comparing the phase angles is difficult. Attempting
to measure current instead of comparing phase angle yields imprecise
results.
Accordingly, one object of this invention, is to provide a high speed
measurement of the value of an unknown reactor.
A second object is to provide an inexpensive yet accurate instrument
measuring reactor value.
Another object is to provide an accurate reactor value measurement even
though relatively high DC resistance is present within the unknown
reactive element.
Still another object of this invention is to make available an instrument
allowing an untrained operator to achieve results in making these
measurements which are as accurate as may be achieved by a skilled
operator.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a general block diagram of the apparatus.
FIG. 2 is a detailed block diagram of a preferred embodiment.
FIG. 3 is a graph of waveforms associated with the operation of the
apparatus of FIG. 2.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 1 discloses a variable frequency oscillator 100 having a substantially
sinusoidal output applied through its output terminals 1 and 2 to one
terminal of reactive circuit element (reactor) 101 having known
capacitance or inductance and to one terminal of resistance 103. Circuit
element or reactor 102, of unknown reactor value, completes the circuit
between reactor 101 and resistance 103 to form of these three circuit
elements a series RLC circuit connected across the output terminals of
oscillator 100. Resistance 103 is preferably quite small. The frequency of
oscillator 100 is controlled by a frequency control signal received from
controller or control circuit 105.
It is of course, well known that a series RLC circuit is in resonance when
the phase shift of the voltage across the supply (oscillator 100) with
respect to the current flow through it, is 0.degree.. No way of directly
determining phase of the current is known. However, voltage across a
resistor through which the current is flowing is always exactly in phase
with the current, so the phase of this voltage may be employed as an exact
though indirect indication of the current phase. Accordingly, the phase of
the voltage across resistor 103 is compared with the phase of the output
voltage of oscillator 100, by phase detector 104 which supplies a phase
shift signal to control circuit 105 specifying the amount and direction of
phase shift between the voltage and the current of the output of
oscillator 100. Control circuit 105 uses this signal in changing the
frequency control signal to oscillator 100. Oscillator 100 is preferably
of the type which rapidly changes its output frequency in response to
changes in its control signal.
The reactor value of circuit element 101 must be chosen so it can be placed
in series resonance with unknown element 102 at some frequency within the
frequency range of oscillator 100. Thus, if the unknown value of element
102 is capacitive, then known element 101 must be inductive. If unknown
element 102 is inductive, then known element 101 must be capacitive.
Reactor value indicator 106 receives the output signal from oscillator
100, and indicates the reactor value of unknown element 102 on the basis
of the actual frequency of oscillator 100 output at resonance and the
internal programming in it of the known value of element 101.
The purpose of phase detector 104 and control circuit 105 is to change
frequency of oscillator 100 until the phase shift between its voltage and
current is 0.degree.. In operation, phase detector 104 continually
monitors the phase difference between the output voltage and current of
oscillator 100 and supplies the phase shift signal to control circuit 105
which specifies the voltage phase relationship with the current. Circuits
which perform such detection are well known in the art. One suitable is
disclosed in conjunction with FIG. 2.
If phase detector 104 indicates that oscillator 100 output voltage leads
its current then inductive reactance is greater than capacitive reactance.
Control circuit 105 changes its frequency control output to oscillator 100
to cause oscillator frequency to decrease, thereby steering the frequency
closer to resonance with circuit elements 101, 102 and 103. If phase
detector 104 produces an output indicating that oscillator 100 voltage
lags its current, control circuit 105 changes its output signal in such a
way that the frequency of the output of oscillator 100 increases,
decreasing reactance of the capacitive and increasing reactance of the
inductive element. In both the voltage leading current and voltage lagging
current case, the change in oscillator 100 frequency tends to decrease the
phase angle between its output voltage and its current. The decrease in
phase angle is detected by phase detector 104 whose output is
correspondingly modified thereby to cause control circuit 105 to change
its own output, and therefore also oscillator 100 frequency, more slowly.
Proper limits on the rate of change of frequency in this feedback loop
makes it stable, and change in oscillator frequency to eventually cease,
when the phase angle between its output voltage and current reaches the
0.degree. set point. This achieves resonance in the series RLC circuit.
Design of feedback systems is well known in the art, so proper selection
of parameters for stability of the system is considered to be a trivial
task.
Reactor value indicator 106 contains a preprogrammed constant indicating
the value of known element 101. The final frequency attained by oscillator
100 then allows reactor value indicator 106 to solve the equation set out
earlier, for the capacitance or inductance of unknown element 102.
Applicants have determined that this general scheme yields accuracy
significantly higher than that available with the prior art because the
effect of resistor 103 is largely eliminated in achieving resonance. Phase
angle can be measured much more accurately than changes in total power
absorption by the RLC circuit, which is the conventional method.
Without compensation, the reactor value computed for element 102 will
include effects of stray reactance throughout the system. By shorting
across element 102, the actual value of this stray reactance may be
measured and computed, in the same fashion the previous measurement was
made. It is possible that this stray reactance will be of such a small
value relative to that of element 102 that oscillator 100 frequency range
will not be great enough to establish resonance for it and reactor 101
alone in the circuit. If such is the case, a reactor having a value which
will increase inductance or capacitance to cause resonance within the
oscillator 100 frequency range when element 102 is shorted can be added in
series to the circuit. The decrease in resonant frequency thereby achieved
when element 102 is shorted permits calibration of indicator 106.
FIG. 2 discloses a preferred embodiment of the apparatus of FIG. 1, adapted
to measure the inductance of unknown inductive circuit element 201,
corresponding to element 102, in FIG. 1. The function of known element 101
is performed by capacitor 200, whose value is accurately known. Unknown
inductance 201 is displayed as broken down into its two component
elements, reactive component 201a and resistive component 201b. Variable
inductor 209 may be changed to any one of several known values, and forms
a portion of the inductance in the series RLC circuit. Inputs to phase
detector 104 are from the terminals of capacitor 200 and the terminals of
oscillator 100. Phase detector 104 comprises first and second identical
crossover detectors 203 and 204 receiving these inputs, whose outputs are
supplied to exclusive OR gate 205, the third distinct element of phase
detector 104. Control circuit 105 comprises a high gain amplifier 207
receiving the output of exclusive OR gate 205 at its "-" input terminal
through resistor 211 and a set point voltage from resistor 210 at its "+"
input terminal. The output of amplifier 207 is connected to its own -
input terminal by capacitor 206, thereby causing its output to form the
time integral of the difference between the voltages at the + and -
terminals. Absent capacitor 206, the output voltage of amplifier 207 is
equal to the + terminal voltage less the - terminal voltage times a large
positive constant, and may shift from a negative to a positive value, as -
terminal voltage is respectively greater or less than + terminal voltage.
For this particular use, it is preferred that output of amplifier 207 be
clamped in some convenient way to restrict its output voltage excursions
to the range of oscillator 100 input voltage necessary to achieve the
desired oscillator output frequency range. For convenience amplifier 206,
resistor 211, and capacitor 206 will be hereafter referred to as the
integrator, since that is, in fact, the function they perform in concert
on the input voltage difference. The output of the integrator is filtered
by low pass filter 208 to remove high frequency components and applied to
the control terminal of oscillator 100 to control the frequency of its
output. Oscillator 100 is of the type whose frequency varies
monotonically, increasing with increasing control signal voltage over a
preselected range, which, for an inductance range of 0 to 1.0 uhy., may
conveniently be from 1.5 to 2.2 mhz. Reactor value indicator 106 may
either receive oscillator 100 output directly and use its frequency in
determining the value of inductor 102 or employ the input frequency
control voltage to oscillator 100. Which signal is used is immaterial to
the invention.
In explaining the operation of FIG. 2, it is important to realize that in a
RLC series circuit receiving sinusoidal current from a supply, the phase
shift of the voltage across any capacitor is 90.degree. lagging at all
times with respect to current through it. Thus, sensing voltage phase
shift across capacitor 200 provides an indirect measure of current phase,
as does resistor 103 for the circuit of FIG. 1. This is true whether other
capacitance is present in the RLC circuit or not, although all capacitance
in the circuit affects its frequency. Because inherent resistance in
either a capacitor or inductor will affect voltage phase shift across the
circuit element, it is necessary to eliminate its effect as much as
possible. This is the consideration leading to the selection of voltage
across capacitor 200 as the reference voltage, rather than using the
90.degree. leading shift across an inductor. The inherent resistance 201b
in an inductor is orders of magnitude higher than stray parallel
resistance in a capacitor, assuming good quality components in each case.
FIG. 3 displays typical waveforms associated with the operation of the
apparatus in FIG. 2 as it pulls oscillator 100 frequency into resonance.
The operation is displayed on a greatly shortened time scale and with a
relatively few number of cycles of oscillator 100 output so as to simplify
explanation. In actual operation, several hundred or more cycles of
oscillator 100 output might be necessary to shift its frequency from a
distant non-resonant condition, to resonance. Waveform 304 displays the
output of first crossover detector 203. When voltage across terminal 1 of
oscillator 100 (waveform 302) becomes positive with respect to terminal 2,
crossover detector 203 output becomes high as shown, and when terminal 1
voltage crosses terminal 2 voltage in the negative direction, goes to its
low condition. Second crossover detector 204 similarly changes its output
(waveform 305) to indicate the times and directions capacitor 200 terminal
2 voltage crosses that at its terminal 1, as displayed by waveform 303 in
FIG. 3. Capacitor voltage waveform 303 is shown lagging oscillator 100
voltage (waveform 302) by less than 90.degree., since oscillator 100
frequency is shown as being below resonance. Exclusive OR circuit 205 is
of conventional design, and provides its high output as shown in waveform
306 when a single one of its two inputs from crossover detectors 203 and
204 is high, and its low output when neither or both inputs from crossover
detectors 203 and 204 are high. When voltage waveforms 302 and 303 are
exactly 90.degree. out of phase, the output of exclusive OR circuit 205
will be exactly balanced, i.e. each interval of high output is equal to
each interval of low output. This is illustrated in FIG. 3 by the later
parts of waveforms 304, 305, and 306, where voltage waveform 302 is
exactly in phase with current waveform 301 and 90.degree. out of phase
with capacitor voltage waveform 303. The frequency of the output of
exclusive OR gate 205 is twice that of the fundamental current waveform
301. Integrator output will be assumed to have an unshifted voltage level
with respect to its inputs as shown by waveform 308, although such a
change may be likely or desirable, if for example a level change is
required to place the output within the required range of oscillator 100
input. When the high portions of waveform 306 are very narrow compared to
the intervals between them, the integral will be correspondingly low, as
waveform 308 illustrates. As the pulses of waveform 306 become more
balanced, waveform 308 approaches the balance of set point voltage 307
more closely. The set point voltage input to amplifier 207 is preselected
during a standard calibration operation to be a slight amount above the
average of the high and low voltage levels from crossover detectors 203
and 204, as is indicated by line 307. The output of the integrator can
vary from its maximum allowable voltage V.sub.max (waveform 306) to its
minimum voltage V.sub.min accordingly as the output of exclusive OR gate
205 swings respectively further from or closer to the set point voltages.
These limits can be imposed by suitable diode clamps on the output of
amplifier 207.
In FIG. 3, the voltage between terminals 1 and 2 of oscillator 100,
waveform 302, is shown as lagging current waveform 301, and therefore less
than 90.degree. out of phase with capacitor voltage waveform 303. This
means that reactance of capacitor 200 is too great and reactance of
inductor 201 is too small respectively, and frequency must therefore be
increased. The output of first crossover detector 203 (waveform 304) leads
the output of second crossover detector 204 (waveform 305) by less than
90.degree. and the output of exclusive OR gate 205 is therefore low, and
less than the set point voltage much greater than half the time. The
output of the integrator thus shifts toward V.sub.max at a rate which
decreases as set point voltage 307 is approached. When waveform 308
reaches the point just below the set point voltage which produces an
output voltage from the integrator which exactly averages the input
voltage V.sub.r to oscillator 100 necessary to produce resonance,
oscillator 100 frequency stops changing, since this condition will
stabilize both integrator and filter 208 outputs. Filter 208 receives the
output of amplifier 207 and capacitor 206 and integrates (averages) it,
producing an output having waveform 310. Filter 208 output voltage
reaching V.sub.r results in resonance and stabilization of oscillator 100
frequency. Whenever oscillator 100 frequency is too high, the output of
exclusive OR gate 205 becomes high greater than 50% of the time, the
output of the integrator slowly decreases and causes oscillator 100
frequency to slowly shift downwardly. In this manner, oscillator 100
output is maintained at or very near the resonant frequency of the series
circuit.
Reactor value indicator 106 is shown by dotted lines as having as an input
from both the output of filter 208 and the output of oscillator 100. This
is intended to denote alternative methods of providing the desired reactor
value indication. The frequency can be used as explained for FIG. 1, to
directly determine total inductance present. It is also possible to use
the output of filter 208 since a direct functional relationship exists
between the frequency of oscillator 100 and the output of filter 208.
Converting the analog value to a visual indication of the reactor value of
circuit element 102 is a trivial task, and may be done, e.g. as simply as
by a properly calibrated voltmeter. The known value of inductor 209, as
well as any stray reactance must be of course used to adjust the value of
the total computed inductance in the RLC circuit.
Known inductor 209 has been provided for two reasons. The value of inductor
201 may be too small to permit resonance within oscillator 100 frequency
range, so inductor 201 will reduce the resonant frequency to within this
range. The problem of calibration previously discussed also makes
insertion of inductor 209 desirable. By varying its value, the range of
measurable values of inductor 201 may also be conveniently extended.
It is also possible to provide switching apparatus allowing the
substitution of several known capacitances for capacitor 200 to provide a
similar range switching function for the apparatus. Insert of each
different capacitor or the changing of the value of inductor 201 can be
accompanied by an operation which automatically programs reactor value
indicator 106 to provide the correct unknown inductor 201 value indication
for each selected capacitor or inductor value. It is also possible to make
known capacitor or inductor selection automatic by allowing oscillator 100
to sweep through its frequency range for each capacitor or inductor,
stepping from one known reactor value to another until resonance is
detected. Many other variations are also possible to increase the accuracy
and convenience of the device.
In implementing measurement of reactor values, it is not necessary to
achieve resonance in a series circuit as described above. A set point
phase shift other than 0.degree. may be selected and the feedback control
elements adjust frequency to achieve this phase shift. Such a phase shift
is more difficult and expensive to measure, which is why it is not a
preferred embodiment. However, given the known values of oscillator 100
phase shift and frequency and reactor 101, the value of unknown reactor
102 can be easily calculated according to elementary A.C. circuit theory.
It should be understood that known reactor 101 and unknown reactor 102
must have reactances of opposite type, i.e. one must be capacitive, the
other inductive, even in such an embodiment where resonance is not
achieved.
Neither is it necessary to employ a series circuit. A parallel, or tank
circuit may also be employed. However, analysis is complicated by the
inherent resistance in the inductive branch of the tank circuit. And as
previously mentioned, at resonance, the impedance of a purely reactive
tank circuit is infinite, making detection of current phase angle
difficult. It is possible to use a non-resonant set point phase angle, but
this has all the disadvantages mentioned in connection with the series
circuit, and has the additional disadvantage mentioned of more difficult
analysis.
It is also theoretically possible to use a non-sinusoidal oscillator
output. However, analysis of such waveforms is extremely complex and
unnecessary since the sinusoidal waveforms are completely adequate for the
purpose. Many other such embodiments may be used to employ the principles
of this invention, but are not preferred because of difficulties in
implementation, such as those briefly described above.
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