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Timestamp: 2015-04-26 09:22:01
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Matched Legal Cases: ['art.\n6', 'art 2', 'art 31', 'art 31', 'art 31', 'art 31', 'art 31', 'art 31', 'art 1', 'art 4', 'art 5', 'art 6', 'art 7', 'art 8', 'art 9', 'art 8', 'art 6', 'art 103', 'art 9', 'art 9', 'art 100', 'art 101', 'art 100', 'art 101', 'art 103', 'art 103', 'art 101', 'art 101', 'art 101', 'art 103', 'art 8', 'art 6', 'art 9', 'art 8', 'art 101', 'art 101', 'art 101', 'art 101', 'art 101', 'art 9', 'art 101', 'art 103']

Patent US7899633 - Sensing apparatus - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inAdvanced Patent SearchPatentsAn object of the present invention is to provide a sensing instrument capable to detect a substance existing in a very small quantity, such as environmental pollutants, instantly with a high degree of precision. As a specific means for solving the problem, a frequency signal from a crystal oscillator...http://www.google.com/patents/US7899633?utm_source=gb-gplus-sharePatent US7899633 - Sensing apparatusAdvanced Patent SearchPublication numberUS7899633 B2Publication typeGrantApplication numberUS 12/154,941Publication dateMar 1, 2011Filing dateMay 28, 2008Priority dateAug 11, 2004Fee statusPaidAlso published asEP1788377A1, EP1788377A4, US7398163, US20070251322, US20090055112, WO2006016721A1Publication number12154941, 154941, US 7899633 B2, US 7899633B2, US-B2-7899633, US7899633 B2, US7899633B2InventorsNobuo Tsukamoto, Kazuo Akaike, Tsukasa KobataOriginal AssigneeNihon Dempa Kogyo Co., Ltd., Dsp Technology Associates, Inc.Export CitationBiBTeX, EndNote, RefManPatent Citations (23), Referenced by (1), Classifications (19), Legal Events (1) External Links: USPTO, USPTO Assignment, EspacenetSensing apparatus
US 7899633 B2Abstract
1. A apparatus for measuring frequency of frequency signals comprising:
a reference clock generating part to generate a clock signal for sampling frequency signals;
an analog/digital converting part for sampling the frequency signal by the clock signal from said reference clock generating part, and outputting the sampling value as a digital signal;
2. The apparatus for measuring frequency of frequency signals according to claim 1, wherein said means for obtaining the rotational vector comprises: a means for performing a quadrature detection for a frequency signal corresponding to the output signal from the analog/digital converting part; and a means for eliminating high frequency components contained in the data obtained by this means.
3. The apparatus for measuring frequency of frequency signals according to claim 1, wherein said means for calculating the velocity of the rotational vector determines an angular velocity of the rotational vector based on the calculation of {Q(n)−Q(n−1)}�I(n)−{I(n)−I(n−1)�Q(n), when the real part and the imaginary part corresponding to said sampling value at a certain timing are taken as I(n) and Q(n) respectively, and a real part and an imaginary part corresponding to said sampling value at a timing earlier than the above timing are taken as I(n−1) and Q(n−1) respectively.
4. The apparatus for measuring frequency of frequency signals according to claim 1, further comprising:
5. The apparatus for measuring frequency of frequency signals according to claim 1, further comprising:
a integrator for integrating the angular velocity determined by said means for calculating the velocity of the rotational vector
a reversely rotational vector generating part for generating a real part and an imaginary part when displaying in complex expression of a reversely rotational vector rotating in the opposite direction to the rotational vector obtained by the means for obtaining the rotational vector at the angular velocity corresponding to the output value of the integrator; and
a means provided at the pre-stage of said means for calculating the velocity of the rotational vector, and for multiplying the rotational vector obtained by the means for obtaining the rotational vector by the reversely rotational vector generated by the reversely rotational vector generating part.
6. The apparatus for measuring frequency of frequency signals according to claim 5, wherein the reversely rotational vector generating part comprises:
a data table in which a set of the real part and the imaginary part defining the position of the reversely rotational vector on the complex plane are arranged in turn along the rotational direction;
and an address controlling part for generating a reversely rotational vector by generating the address of said data table using an increment number or a decrement number corresponding to said frequency variation.
7. The apparatus for measuring frequency of frequency signals according to claim 6, wherein the reversely rotational vector generating part comprises:
a pulse width controlling part for outputting a pulse train having a duty ratio in accordance with the lower rank bit value when expressing the frequency variation obtained by said means for calculating the velocity of the rotational vector with a digital signal;
and an adding part for adding the higher rank bit value when expressing said frequency variation with the digital signal and the level of the pulse formed by said pulse width controlling part to output to said address controlling part;
This is a Divisional application Ser. No. 11/659,764 filed May 29, 2007, now U.S. Pat. No. 7,398,163 which is a National Stage of PCT/JP2005/015099 Filed Aug. 11, 2005.
Then, the present inventor pays attention to a crystal oscillator as a measuring instrument for pollutant such as dioxin or the like, from the fact that once a substance to be detected is attached to a crystal oscillator, the natural frequency of the crystal oscillator varies according to the amount of the attachment. On the other hand, there is a technology as a chemical sensing instrument using a crystal oscillator, which is described in Patent Document 1. The instrument includes a sampling circuit for outputting the absolute value of a difference frequency between the oscillation frequency of a sensor oscillator and the reference frequency generated by the reference oscillator, a frequency divider circuit dividing the difference frequency by a prescribed frequency divider ratio, a counter for counting the cycle of the frequency diver output using the cycle of the reference frequency as a clock, and a calculating device for determining the oscillation frequency of a sensor oscillator based on the counted cycle, and is for performing the identification of an adsorption gas. Since the chemical sensing instrument determines a difference frequency, it has an advantage of making the absolute value of a frequency to be measured small, and making it possible to perform measurement with a high resolution without enlarging the measurement range.
The above-described means for obtaining the rotational vector may be structured to include a means for performing a quadrature detection for a frequency signal corresponding to the output signal from the analog/digital converting part, and a means for eliminating high frequency components contained in the data obtained by this means. The above-described means for calculating the velocity of the rotational vector may be structured as a means for determining a frequency variation based on the calculation of {Q(n)−Q(n−1)}�I(n)−}I(n)−I(n−1)�Q(n), when the real part and the imaginary part corresponding to the above-described sampling value at a certain timing are taken as I(n) and Q(n) respectively, and a real part and an imaginary part corresponding to the above-described sampling value at a timing earlier than the above timing are taken as I(n−1) and Q(n−1) respectively.
In this case, the reversely rotational vector generating part can be structured to include a data table in which a set of the real part and the imaginary part defining the position of the reversely rotational vector on the complex surface are arranged in turn along the rotational direction, and an address controlling part for generating a reversely rotational vector by generating the address of the above-described data table using an increment number or a decrement number corresponding to the above-described frequency variation. As a more concrete example, it is possible to cite a structure that the reversely rotational vector generating part includes a pulse width controlling part outputting a pulse train having a duty ratio in accordance with the lower rank bit value when expressing the frequency variation obtained by the above-described means for calculating the velocity of the rotational vector with a digital signal, and an addition part adding the higher rank bit value when expressing the above-described frequency variation with the digital signal and the level of the pulse formed by said pulse width controlling part to output to the above-described address controlling part, in which, the above-described address generating part integrates the output value from the adding part, and the integrated value is used as an address in the above-described data table.
FIGS. 12A, 12B; 12C and 12D are timing charts showing one function in the above further embodiment;
2 is a reference dock generating part, outputting a clock signal which is a high frequency signal having an extremely high frequency stability for sampling the high frequency signal from the oscillator circuit 13. 21 is an A/D (analog/digital) converter, sampling the high frequency signal from the oscillator circuit 13 by a clock signal from the reference clock generating part 2 to output the sampling value in a digital value. The high frequency signal identified by the digital signal contains harmonics, in addition to a fundamental wave. In other words, when a sinusoidal wave having harmonic distortion is taken as a sample, the harmonic component is influenced by the loopback, and it is assumed that the fundamental wave frequency and the harmonic frequency are sometimes overlapped on the frequency axis in the frequency spectrum. Therefore, it is necessary to avoid such an overlapping so as to obtain a correct detection operation.
Since an n-th harmonic wave frequency is expressed as n�(fundamental frequency) in terms of the fundamental frequency in the result of capturing, when it is put to be f2 and substituted into the above-described equation (1); it is possible to calculate with what frequency the harmonics can be captured. By using this calculation, it is possible to establish the frequency of the high frequency signal from the oscillator circuit 13 as fc and the sampling frequency (frequency of the clock signal) as fs so as not to overlap the frequency of the fundamental wave and the frequency of the harmonics. For instance, the fc is established to be 11 MHz, and the fs to be 12 MHz. Then, the fundamental wave of a frequency signal identified by an output signal being a digital signal from the A/D converter 21 is a sinusoidal wave of 1 MHz in this case. It should be noted that if fc/fs is taken to be 11/12, the fundamental frequency and the harmonic frequency are not overlapped with one another, but the fc/fs is not limited to this value.
In order to understandably explain the operation to capture the rotational vector, the sinusoidal wave signal identified by the digital signal from the A/D converter 21 is assumed to be A cos(ω0t+θ). Whereas the carrier removal 31 is provided with a multiplication part 31 a which multiplies the above-described sinusoidal wave signal by cos(ω0t) and a multiplication part 31 b which multiplies the above-described sinusoidal wave signal by −sin(ω0t), as shown in FIG. 2. Thus, the quadrature detection is performed by such a calculation. The outputs from the multiplication part 31 a and multiplication part 31 b are expressed by equation (2) and equation (3), respectively.
●cos
Accordingly, since the frequency signal at 2ω0 is eliminated by allowing the output of the multiplication part 31 a and the output of the multiplication part 31 b to pass through lowpass filters 32 a and 32 b respectively, the frequency signal at 2 ω0 is eliminated, ��A cos θ and ��A sin θ are finally captured from the lowpass filter 32. Note that the lowpass filter 32 is described as to be structured from the lowpass filters 32 a and 32 b. The actual digital processing in the lowpass filter 32 calculates the moving average of a plurality of consecutive data, for instance, 6 data, for the time series data outputted from the carrier removal 31.
When the frequency of a sinusoidal wave signal expressed by A cos(ω0t+θ) varies, A cos(ω0t+θ) becomes A cos(ω0t+θ+ω1t), where ω1 is assumed to be sufficiently smaller than ω0. Accordingly, ��A cos θ becomes ��A cos(θ+ω1t), and ��A sin θ becomes ��A sin(θ+ω1t). In other words, the output obtained by the lowpass filter 32 is a signal corresponding to ω�π, that is, the frequency variation ω12π of the sinusoidal wave signal [A cos(ω0t+θ)]. These values are a real part (I) and an imaginary part (Q), when the rotational vector rotating at a frequency difference between the sinusoidal wave signal frequency identified by the digital signal from the A/D converter 21 and frequency ω0/2π of the sinusoidal wave signal frequency used for the quadrature detection.
FIG. 3 shows a graph showing the rotational vector, which is A in length and ω1 in angular velocity. In FIGS. 2 and 3, ω1t is expressed as φ. Accordingly, if the frequency of a frequency signal from the A/D converter 21 is ω0/2π when a substance to be detected is not adsorbed by the crystal oscillator 11 for instance, ω1 is zero, and the angular velocity of the rotational vector is zero. However, when the frequency of the crystal oscillator 11 is varied by adsorption of a substance to be detected on the crystal oscillator 11, which varies the sinusoidal wave signal frequency, the rotational vector rotates at the angular velocity corresponding to the variation. When the frequency of a frequency signal from the A/D converter 21 at the time when the substance to be detected is not adsorbed on the crystal oscillator 11, is shifted from ω0/2π, the rotational vector rotates at the angular velocity corresponding to the shifted frequency. In any case, since the angular velocity of the rotational vector is the value corresponding to the oscillation frequency of the crystal oscillator 11, it is possible to determine the variation of the oscillation frequency caused by adsorption of a substance to be detected on the crystal oscillator 11 by seeking for respective rotational vectors when, for instance, the crystal oscillator 11 is immersed in a solvent and when the substance to be detected is added to the solvent to let the substance to be detected be adsorbed on the crystal oscillator, and by determining the difference between the angular velocities for the respective times.
Thus, the carrier removal 31 serves to perform a quadrature detection to the above-described sinusoidal wave signal, and the lowpass filter 32 serves to eliminate the high frequency component from the quadrature detection result. Accordingly, the carrier removal 31 and the lowpass filter 32 perform a quadrature detection for a frequency signal from the A/D converter 21 using a digital signal, so that they serve as a means for obtaining the real part and the imaginary part when the rotational vector rotating at an angular velocity corresponding to the frequency difference between the frequency of the frequency signal and the frequency ω0/2π of the sinusoidal wave signal used to the quadrature detection is displayed in complex expression.
Δφ=K�img[ΔV�conj{V(n))] (4)
Where Δφ is the difference between the phase Δφ (n) of V(n) and the phase φ (n−1) of V(n−1), imag is an imaginary part, and conj {V(n)} is a conjugate vector of V(n).
conj{V(n)}=I(n)−jQ(n) (6)
Δφ=ΔQ�I(n)−ΔI�Q(n) (7)
Here, once the rotational vectors V(n−1) and V(n) are determined, it is possible to use various mathematical methods for determining or evaluating the angle Δφ between them. The approximate equation (4) is only an example for the method. As a mathematical expression for it, {V(n)+V(n−1)}/2, which is a vector V0 which connects the middle point and the original point of a line connecting the respective terminals of V(n) and V(n−1), is used, and this vector V0 may be substituted into equation (4) in place of V(n). The reason why such an equation (4) can approximate is because V0 and ΔV can be regarded as being orthogonal, and therefore, the length of ΔV can be handled as being corresponding to the imaginary value of ΔV when V0 is regarded as an actual axis. An intuitively understandable method for determining Δφ is to find argV(n) and argV(n−1) and to subtract them. However, since a table associating a set of imaginary value and actual value for each vector with the phase φ for the vector is necessary in this case, it is advisable to perform calculation based on the previously described equation (4) in terms of load of computer. Note that argV(n) is tan−1 (imaginary value/actual value).
The operation of the above-described embodiment will be explained next. For instance, 11 MHz frequency signal, oscillated from a crystal oscillator (oscillator circuit 13) of the sensor part 1, and including a sinusoidal wave as a fundamental wave is converted in the A/D converter 21, by, for instance, 12 MHz frequency signal, and signals including sinusoidal wave signals which are about 1 MHz fundamental waves are outputted from the A/D converter 21. Assuming that the sinusoidal wave signal is A cos(ω0t+ω1t+θ) (where ω1 is sufficiently smaller than ω1) for convenience of the explanation here, a rotational vector rotating at an angular velocity corresponding to the variation of the frequency of the sinusoidal wave signal is captured by quadrature detection of the sinusoidal wave signal and further elimination of the lower frequency components. In other words, the real part and the imaginary part of the rotational vector are captured as I value and Q value. These I value and Q value are subtrahend processed at the subtrahend processing part 4, further divided by the scalar |V| of the rotational vector V in the correction processing part 5 so that the effect of tedious extension of the rotational vector is eliminated, and the result is inputted to a frequency difference calculating part 6. It should be noted that the explanation is made by attaching the same symbol �V� to the rotational vectors before and after the correction processing to avoid complexity of the explanation.
The rotational vector V rotates at the angular velocity of the difference between a frequency of the sinusoidal signal A cos(ω0t+ω1t+θ) and the frequency ω0/2π of the sinusoidal signal used for the quadrature detection, namely, at the velocity of ω1 (refer to FIG. 3). In order to make the explanation understandable, assuming that the angular velocity corresponding to the natural frequency of the crystal oscillator 11 when the sensor 1 is, for instance, immersed in a solution for detecting the existence of a substance to be detected, and yet in the absence of the substance to be detected (at the time below the detection limit of the crystal oscillator 11) is ω0, since ω1 is zero, the rotational vector V stands still. Accordingly, Δφ, the output of the time averaging processing part 7, is zero.
On the contrary, when a substance to be detected, for instance, dioxin exists in the above-described solution, the oscillation frequency (natural frequency) varies according to the amount of dioxin adsorbed to the crystal oscillator 11. In this case, the above-described rotational vector V starts rotation at an angular velocity corresponding to the variation of the frequency. In order to simplify the explanation, when the variation of the frequency is assumed to be 1 Hz, the rotational vector V rotates one turn in a second. Here, the present embodiment intends to detect an angular velocity of a rotational vector by finding the difference Δφ between the phase φ(n) of V. (n) and the phase φ(n−1) of V(n−1) which are sampled consecutively. When the sampling interval is assumed to be 1/100 second, Δφ is 3.6 degrees. In other words, the angular velocity of the rotational vector V is determined only within the lapse of time of the sampling interval, so that the variation of the oscillation frequency of the crystal oscillator can be determined.
Now, as to the rotational vector, a sampling value at a certain timing, for instance, at n-th time, is assumed to be I(n)+jQ(n) as shown in FIG. 9. When this vector is put back to a position along an actual axis, it is advisable to prepare a reversely rotational vector V′ rotating in the opposite direction to the above-described rotational vector V and to multiply the vector by the reversely rotational vector V′. A vector I+jQ formed by putting back of the rotational vector V by the reversely rotational vector V′ becomes {I(n)+jQ(n)}�{I(n)+jQ(n)}. Equation (8) is obtained by rearranging this equation, and the frequency range correcting part 8 conducts calculation of this equation.
I+jQ={I(n)�I′(n)−Q(n)�Q′(n)}+j(I(n)�Q′(n)+I′(n)�Q(n)} (8)
To generate the reversely rotational vector V′ is, practically, to make values of cos φ and sin φ come into existence assuming that values of the real part and the imaginary part of the vector, namely, the phase of the reversely rotational vector V′ is φ, so that a vector on the complex plane reversely rotates. FIG. 10 shows an I/Q table 90 in which sets of cos φ and sin φ of the vector are arranged in sequence along the rotational direction of the vector. The reversely rotational vector generating part 9 includes the above-described I/Q table 90 in this example, reads the addresses in the I/Q table 90 using an increment number or a decrement number according to the output of the integrator 70, and outputs them to the frequency range correcting part 8. For instance, the address is read one by one from �0� to �11� at the clock readout timing. On returning to �0� again, the vector makes one rotation clockwise on the complex plane in 12 clocks, and when the addresses are read at every other address by setting the increment number to 2, the angular velocity of the vector is doubled. Accordingly, it is possible to generate the reversely rotational vector reversely rotating at an angular velocity according to the frequency difference Δφ (angular velocity according to the angular velocity of the rotational vector V) calculated at the previously described frequency difference calculating part 6 (refer to FIG. 8) by determining an increment number according to the output value of the integrator 70.
The direction of the reversely rotational vector V′ is determined according to the direction of the rotational vector V, and the output of the integrator 70 becomes a positive value or a negative value according to the direction. As for readout of the address in the I/Q table 90, when the output of the integrator 70 is a positive value, the readout is conducted with an increment number according to the positive value, and when the output of the integrator 70 is a negative value, the readout value is conducted with a decrement number according to the negative value. In other words, the I/C table 90 is in the relation of cos and sin, and the correction direction of the rotational vector V is controlled by incrementing or decrementing the address of the I/Q table 90 in an address controlling part 103. Note that the I/Q table in FIG. 10 is diagrammatically prepared to make the understanding of the present invention easy, and is not a preferable example of preparation for an actual table.
A preferable example of the reversely rotational vector generating part 9 is shown in FIG. 11. The reversely rotational vector generating part 9 is provided with a bit dividing part 100 which divides an output value from the integrator 70 into a higher rank bit value and a lower rank bit value in this example. For instance, when an output value of the integrator has 16 bits, it is outputted by dividing it into a higher 8-bit value and a lower 8-bit value. In this example, the higher 8-bit value (decimal converted value) is prepared by multiplying a higher 8-bit BCD code (binary-coded decimal) value among the output values from the integrator 70 expressed in 16 bits by 1/M (where M is minus 8th power of 10), and thus-obtained value is multiplied by M to get the value restored to the original higher 8-bit BCD code value. Then, the lower 8-bit value (decimal converted value) is prepared by subtracting the above value from the 16-bit BCD code value which is previously described output value. It should be noted that the method for dividing an output value from the integrator 70 into a higher rank bit value and a lower rank bit value is not limited to this method, and may simply take out a higher rank bit value and a lower rank bit value.
A pulse width controlling part 101 is provided on the output side of the lower rank bit (on the output terminal side outputting a lower 8-bit value in this example) of the bit dividing part 100, and an adder 102 is provided at the post-stage of the pulse width controlling part 101, so that a pulse train outputted after pulse width controlling according to a lower rank bit value, and a higher rank bit value are added by the adder 102. An address controlling part 103 is provided on the post-stage side of the adder 102, and the address controlling part 103 is structured to integrate a value obtained by the adder 102, and control readout of the address in the IQ table 90 according to the integrated value, in other words, to control the increment number or the decrement number of the address.
The operation of this embodiment will be explained next. When the frequency of the crystal oscillator 11 is deviated from the state that a substance to be detected is not adsorbed by adsorption of the substance to be detected on the crystal oscillator 11 first, the rotational vector V rotates at the angular velocity corresponding to the frequency difference which is the variation of the frequency. However as described above, the frequency of the crystal oscillator in the case of a substance to be detected is not adsorbed is rarely equal to ω0. Then, a signal at a level of a higher rank bit level, for instance, a higher 8-bit value, in the output value of the integrator 70 corresponding to the angular velocity of the rotational vector V is inputted to the adder 102. Whereas, a lower rank bit value, for instance, a lower 8-bit value, in the output value of the integrator 70 is inputted to the pulse width controlling part 101. A pulse width calculation is conducted by sampling signals generated at every pulse numbers previously established for the clock pulse of computer in the pulse width controlling part 101, and the pulse train at the duty ratio corresponding to an input value is outputted.
The pulse train is a combination of a +1 level pulse generated in one clock and a−1 level pulse generated in one clock. Assuming that pulse width calculation is conducted every 20 clocks, and the duty ratio corresponding to the input value of the pulse width controlling part 101 is 50%, the +1 level pulse and the −1 level pulse are outputted 10 pulses each alternately as shown in FIGS. 12A, 12B, 12C and 12D. When a level corresponding to, for instance, a higher 8-bit value is assumed to be �5�, �6� and �4� are outputted alternately from the adder 102 during a period from generation of a sampling signal to generation of the next sampling signal, the address controlling part 103 integrates these output values, and the integrated values thereof become addresses of the I/Q table 90. That is, since the increased portion of the integrated value is alternate repeat of �6� and �4� in this case, the increment number of the address is alternate repeat of �6� and �4�, and as a result, the address is accessed with the increment number of average �5�, which is the level corresponding to the higher 8-bit value, so that a real part and an imaginary part of the reversely rotational vector V′, which are described in the address, are read out. In short, the reversely rotational vector V′ rotating at an angular velocity corresponding to this �5� is generated. Note that the I/Q table 90 in FIG. 10 is prepared to make the understanding easy, and is not matched with the movement in this case. Thus, calculation according to previously-described equation (8) is conducted for the respective values of the real part and the imaginary part read out from the I/Q table 90 in the� frequency range correcting part 8, so that the rotational vector V is multiplied by the reversely rotational vector V′. Note that 81 is a bit processing part which conducts a rounding-off processing of a lower rank bit to reduce the number of calculation bits after the frequency difference calculating part 6.
Since the reversely rotating vector generating part 9 shown in FIG. 11 forms a phase lock loop (PLL), when a signal value inputted to the frequency range correcting part 8 from the lowpass filter 32 side is stabilized, the angular velocity of the rotational vector V and the angular velocity of the reversely rotational vector V′ are immediately locked to be in a stable state, and the respective signals are as shown in FIG. 12. Accordingly the output value of the integrator 70 when the angular velocity of the reversely rotational vector V′ are locked, correspond to the angular velocity of the rotational vector V and the frequency of the crystal oscillator is measured on the basis of the output value of the integrator 70, and the measurement range is widened as a result.
When the duty ratio corresponding to an input value of the pulse width controlling part 101 is more than 50%, pulses at a +1 level last by the numbers corresponding to a portion exceeding 50% as shown in FIG. 13, and the pulse at +1 level and the pulse at −1 level are generated alternately thereafter. Accordingly, since �6� lasts at first in the increment of the integrated value of this pulse train, the increment number of the address is continuously �6�, then �6� and �4� are alternately repeated. Accordingly, the average value of the angular velocity of the reversely rotational vector V′ during the interval from the sampling of an input value of the pulse width controlling part 101 to the next sampling is between an angular velocity corresponding to �5� and an angular velocity corresponding to �6�, and is a magnitude according to the above-described duty ratio. In other words, this angular velocity corresponds to a value of �5� plus the fractional portion of �5�, which means the interval between �5� and �6� is interpolated according to the inputted value of the pulse width controlling part 101 (the lower rank bit value in the output of the integrator 70). It should be noted that in this example, the timing of pulse width calculation is 20 clocks each, but the clock number may be, for instance, the bit number of the lower rank bit, that is 8 in this example, and the pulse width calculation may be conducted for every 8 clocks.
The case that the frequency difference of a crystal oscillator is 500 Hz is taken as an example of the case that the output value of the integrator 70 does not appear in a higher rank bit, and the variation of the input level and the output level of the pulse width controlling part 101 through simulation is studied. The results of the study are shown in FIG. 14 and FIG. 15 respectively. As shown in FIG. 14, the input level of the pulse width controlling part 101 is stable at nearly 1 msec, which shows that the angular velocity of the rotational vector V is locked instantaneously by the PPL including the reversely rotational vector generating part 9. The outputs of the pulse width controlling part 101 are actually level signals between +1 and −1, and these values are inputted to the address controlling part 103, but the outputs are drawn in a straight line at +1 and −1 because of the resolution of drawing. As for the case that the output value of the integrator 70 appears in a higher rank bit, taking the case of the frequency difference of a crystal oscillator being 10000 Hz as the example, the output levels of the adder 102 are shown in FIG. 16. In this example, the outputs of the adder 102 are almost stable at �81�.
As an experiment to verify the instrument of the present invention, the frequency fc of the frequency signal from the oscillator circuit 13 is assumed to be 1 MHz, the frequency fs of the reference clock signal is assumed to be 12 MHz, and actual data processing is conducted by a computer. The frequency of a high frequency signal (sinusoidal wave signal) for the test used as the frequency signal from the oscillator circuit 13 is slightly deviated from 1 MHz. FIG. 17 is a view showing the manner of sampling a high frequency signal for the test with a reference clock signal to determine the digital value. When the frequency spectrum is studied for the signal identified by thus obtained digital value, it is as shown in FIG. 18. Accordingly, the high frequency signal which is a 1 MHz sinusoidal wave signal as the fundamental is taken out from the AID converter 21 here.
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