United States Pélt?llt [19]
`Morita et al.
`
`[11] Patent Number:
`[45] Date Of Patent:
`
`5,767,665
`Jun. 16, 1998
`
`[54] PHASE DIFFERENCE MEASURING
`APPARATUS AND MASS FLOWMETER
`THEREOF
`
`[75] Inventors: Akita Morita. Tokyo; Hiroyuki
`Yoshimura. Kanagawa. both of Japan
`
`[73] Assignee: Fuji Electric Co. Ltd.. Kawasaki.
`Japan
`
`$069,074 12/1991 Young et a1. .................... .. 73/861356
`5.460.933 10/1995 haw er a1, 1
`5,469,758 11/1995 Kalotay ............................ .. 73/361356
`FOREIGN PATENT DOCUMENTS
`
`4205300 7/ 1993 Germany -
`4319344
`111995 Germany .
`8302105 3/1988 WIPO '
`Primary Examiner-Michael Brock
`Attorney, Agent, or F irm—Greer. Burns & Crain. Ltd.
`
`Sep' 12’ 1995
`[22] Fllcd:
`[30]
`Foreign Application Priority Data
`
`‘
`
`56p. 13, 1994
`Mar‘ 22' 1995
`Mar. 22, 1995
`
`[JP]
`[JP]
`
`Japan .................................. .. 6-217743
`Japan ' ' ' ' '
`' ' ‘ ' ' " 7'062675
`Japan .................................. .. 7-062676
`
`[51] Int. Cl.6 ............................ .. G01R 25/00; GOlF U84
`[52] us. (:1. ...................... .. 324/7652; 73/361356
`[581 Field of Search ............................ .. 324/7652. 76.53.
`324/7655 76'63; 73/861356. 861355;
`364/510‘ 484
`
`[56]
`
`References Cited
`
`U~S- PATENT DOCUMENTS
`5/1970 Pascoe ........................... .. 324/7652 x
`3,513,385
`7/1975 Vmding .......................... .. 324/7652 X
`3,895,294
`6/1990 Romano.
`4,934,196
`9/1991 Thompson ....................... .. 73/861356
`5,050,439
`5,052,231 10/1991 Christ et al. .
`
`A phase difference measuring apparatus for accurately mea~
`suring the phase difference (?ne time di?erence) of two
`signals with the same frequency with a reduced number of
`bits for
`conversion is disclosed. In addition to Output
`'
`als of an u stream side icku and a downstream side
`Sign
`P
`P
`P
`.
`p1ckup Of a mass ?owmeter. an output s1gna1 of the upstream
`side pickup or the downstream side pickup is supplied tO a
`wmparawr- a PLL circuit an 9119411356 ?lwr- a sample and
`hold circuit‘ and an A/D Convert“ These Circuits quantize
`these signals and send the quantized signals to a band pass
`?lter. The band pass filter extracts a predetermined signal
`component and outputs it to a DFT. The DPT performs
`complex Fourier transformation On the input signal. Thus.
`the phase difference between two signals with the same
`frequency (such as an upstream side pickup signal and a
`downstream Side Pickup signal) can be accurately dame‘!
`with a rcduc?d number of bits for each of the A/D Convert
`(3T5.
`
`11 Claims, 22 Drawing Sheets
`
`[11 DSP (CPU)
`
`1A
`
`UPSTREAM
`SIDE
`SOLENOID
`PICKUP
`
`6A
`7
`A
`SAMPLE
`5A
`A/D
`ANTIALIASE _ AND __
`FILTER
`HOLD
`CONVERTER
`
`BA
`9A
`BAND
`1_ PASS _ DFT
`FILTER
`
`\
`
`2
`
`98
`BB
`78
`?yLL
`5B
`_
`*_ 222g _ DFT _ PHASE
`A/D
`ADDING F ANTIALIASE __1SA£IFI')LE_
`CIRCUIT
`FILTER
`HOLD
`CONVERTER
`FILTER
`CALCULATING
`
`,
`
`8‘:
`7c
`5c
`69 1
`BAND
`A/D
`_.‘ANT1ALIASE __SAMPLE
`FILTER
`AND '“cONvERTER *“ PASS _ DFT
`11011)
`A
`FILTER
`
`9c
`
`4
`
`3
`
`TTIMINO
`PLL
`-+OOMPARATOR— (6
`TIMES)
`
`‘
`
`18
`
`DOWNSTREAM
`SIDE
`SOLENOID
`PICKUP
`
`((1)
`PHASE
`DIFFERENCE
`
`Micro Motion 1053
`
`1
`
`

`

`US. Patent
`
`Jun. 16, 1998
`
`Sheet 1 0f 22
`
`5,767,665
`
`I03
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`

`

`US. Patent
`
`Jun. 16, 1998
`
`Sheet 2 of 22
`
`5,767,665
`
`PRIOR ART
`
`FIG. 4
`
`3
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`

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`U.S. Patent
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`US. Patent
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`Jun. 16, 1998
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`US. Patent
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`US. Patent
`
`Jun. 16, 1998
`
`Sheet 7 0f 22
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`5,767,665
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`

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`US. Patent
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`Jun. 16, 1998
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`Jun. 16, 1998
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`Jun. 16, 1998
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`Sheet 11 0f 22
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`Jun. 16, 1998
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`Jun. 16, 1998
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`US. Patent
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`Jun. 16, 1998
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`Sheet 17 of 22
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`

`US. Patent
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`Jun. 16, 1998
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`Sheet 18 of 22
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`5,767,665
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`US. Patent
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`Jun. 16, 1998
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`Jun. 16, 1998
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`Jun. 16, 1998
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`23
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`1
`PHASE DIFFERENCE MEASURING
`APPARATUS AND MASS FLOWMETER
`THEREOF
`
`BACKGROUND OF THE INVENTION
`
`1. Field of the Invention
`
`The present invention relates to a phase difierence mea—
`suring apparatus for measuring the phase difference between
`two signals with the same frequency.
`In addition.
`the present invention relates to a phase
`difference measuring apparatus for measuring the phase
`difference between two signals at a predetermined
`frequency. in particular. to a modification of an error com-
`pensating method in the measurement of the phase differ—
`ence.
`
`2. Description of the Related Art
`Such a phase difference measuring apparatus can be used
`in various fields. An example of the apparatus is an industrial
`instrument such as a Coriolis type mass flowmeter that
`detects the phase difference (time difference) of vibrations
`due to Coriolis force caused by the mass and speed of a fluid
`that flows in an upstream side pipe and a downstream side
`pipe. so as to obtain a flow rate thereof.
`FIG. 1 is a schematic diagram showing a primal construc-
`tion of a Coriolis type mass flowmeter.
`In FIG. 1. reference numeral 101 is a U shaped pipe in
`which a fluid flows. At a center portion of the U shaped pipe
`101. a permanent magnet 102 is securely disposed. Both
`edges of the U shaped pipe 101 are secured to a base 103.
`Reference numeral 104 is a solenoid coil that surrounds the
`U shaped pipe 101. Reference numeral 105 is a support
`frame that supports the solenoid coil 104. The frame 105 is
`securely disposed on the base 103. A base side portion of the
`U shaped pipe 101 functions as a nodal point of vibration
`such as a turning fork. thereby preventing vibration energy
`from being easily lost. Reference numerals 1A and 1B are
`solenoid pickups that detect velocity of both legs of the U
`shaped pipe 101. When the U shaped pipe 101 is vibrated at
`its natural frequency (sin cut) by the electromagnetic force
`that works between the solenoid coil 104 and the permanent
`magnet 102 secured to the U shaped pipe 101. Coriolis force
`works on the fluid that flows in the U pipe 101.
`FIG. 2 is a isometric View showing a vibration of the U
`shaped pipe.
`The magnitude of the Coriolis force is proportional to the
`mass and speed of the fluid that flows in the U shaped pipe.
`The direction of the Coriolis force accords with the product
`of the vectors of the moving direction of the fluid and the
`angular velocity of the U shaped pipe 101. In addition. since
`the flow direction of the fluid on the input side of the U
`shaped pipe 101 is the reverse of that on the output side.
`Coriolis force that works at both legs of the U shaped pipe
`101 produces a twisting torque. This torque varies with the
`excitation frequency. The amplitude of the torque is propor—
`tional to the mass and flow rate of the fluid that flows in the
`U shaped pipe 101. FIG. 3 is an isometric view showing a
`vibration mode caused by the twisting torque.
`When the amplitude of the twisting torque is detected by
`the pickups 1A and 1B. the mass and flow rate of the fluid
`can be obtained. However. the real vibration of the U shaped
`pipe is the sum of the vibration caused by the solenoid coil
`104 and the vibration caused by the twisting torque due to
`the Coriolis force. The vibration on the upstream side of the
`U shaped pipe 101 is expressed by sin((nt-ot). whereas the
`vibration on the downstream side thereof is expressed by
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`5.767.665
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`2
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`sin((ot+0t). Thus. there is a phase difference (2(1). or time
`difierence (At) between signals el and e2 detected by the
`pickups 1A and 13. as shown in FIG. 4. The phase difference
`varies depending on the type of the pipe and the excitation
`frequency. In the case of the U shaped pipe 101. when the
`resonance frequency thereof is 80 Hz.
`there is a time
`difference of approximately 120 us at the maximum flow
`rate. Aresolution of 0.01% of the maximum phase difference
`should be compensated. Thus. a time measuring resolution
`of 12 ns is required.
`The time difference can be measured by various methods.
`One of the simplest methods is a method for counting time
`difference gate pulses using a reference clock. An example
`of this method is shown in FIG. 5. In FIG. 5. an upstream
`side pickup signal Pu and a downstream side pickup signal
`Pd are amplified by respective amplifiers 111 (with an
`amplification factor of B). The amplified signals are supplied
`to respective comparators 112. The comparators 112 digitize
`respective input signals and output digitized signals to an
`exclusive—OR circuit 113. The exclusive-OR circuit 113
`performs an exclusive-OR operation for the digitized signal
`and outputs a gate pulse Pg with a pulse width that is
`equivalent to the time difference between the upstream side
`pickup signal Pu and the downstream side pickup signal Pd.
`The gate pulse Pg is supplied to a counter 114. The counter
`114 measures gate pulse time by counting a reference clock
`115 within gate pulse. The frequency of the reference clock
`should be 85 MHZ or higher.
`When this U shaped pipe is used in a real plant. since it
`is bent. it has problems of pressure loss and difliculty of
`cleaning. To solve such problems. a straight-pipe type Corio-
`lis flowmeter has been proposed. FIG. 6 shows an example
`of the straight-pipe type Coriolis flowmeter.
`In FIG. 6. reference numeral 121 is a straight pipe in
`which a fluid to be measured flows. At a center portion of the
`straight pipe 121. a permanent magnet 123 is securely
`disposed Both edges of the straight pipe 121 are secured to
`a base 120. Reference numeral 122 is a solenoid coil that
`surrounds the straight pipe 121. Reference numeral 124 is a
`support frame that supports the solenoid coil 122. The frame
`124 is secured to the base 120. Since the straight pipe has a
`higher rigidity and a higher twisting resistance than the U
`shaped pipe. the time difference between the upstream side
`pickup signal and the downstream side pickup signal
`becomes smaller.
`
`For example. the resonance frequency of the straight pipe
`is approximately 1 kHz and the time diflerence at
`the
`maximum flow rate is approximately 2 us. The measurement
`should be performed with a resolution of 0.01% of the
`maximum time difference. Thus. a time measuring resolu-
`tion of 0.2 us is required. To count pulses. a reference clock
`with a frequency of 5 GHz is required. It is impossible to
`produce such a clock oscillator. Even if such a clock
`oscillator can be produced. when comparators that obtain
`time difference signals from pickup signals are used. and
`since jitter due to intermediate zone of input signals takes
`place (the intermediate zone is an instable level between “1”
`and “0). it is doubtful of being able to obtain an accuracy of
`0.2 ns.
`
`Thus. the measurement is performed as shown in FIG. 7.
`The following subtraction between the upstream side pickup
`signal Pu and the downstream side pickup signal Pd is
`performed by a difierential device (subtracting device) 131.
`sirn’wr-kuysinmr—OIFZ cos 0min u
`
`Thus. a weak phase signal with an amplitude of sin a (where
`or is 0.1 ns against a period of 1 ms) is obtained. The phase
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`signal is supplied to an amplifier 132 (with an amplification
`factor of B). The amplified signal is supplied to a narrow
`band filter 133. The narrow band filter 133 extracts only a
`predetermined frequency component. The resultant signal is
`supplied to a full-wave rectifying and detecting device 134.
`The full-wave rectifying and detecting device 134 outputs a
`DC level of B sin on. The resultant signal is supplied to an
`A/D converter 135. The A/D converter 135 outputs a digital
`value of sin (1. Thus. the phase diflerence or is obtained. Due
`to the offset current of the amplifier and voltage drift caused
`temperature. if the temperature environment of the plant is
`not stable.
`the measurement error becomes large.
`Consequently. in practice.
`the accuracy of 0.01% of the
`maximum flow rate cannot be obtained.
`
`To prevent the influence of voltage drift in the amplifier.
`a method for obtaining the phase difierence by Fourier
`transformation of digital signals has been proposed. FIG. 8
`is a block diagram showing the construction of an apparatus
`corresponding to such a method.
`Referring to FIG. 8. an upstream side pickup signal Pu
`and a downstream side pickup signal Pd are obtained by an
`upsneam side pickup 1A and a downstream side pickup 1B.
`respectively. The upstream side pickup signal Pu and the
`downstream side pickup signal Pd are supplied to respective
`amplifiers 141. The amplifiers 141 amplify the upstream side
`pickup signal Pu and the downstream side pickup signal Pd.
`The amplified signals are supplied to respective sample and
`hold circuits 142. The sample and hold circuits 142 sample
`and hold the amplified signals. The sampled levels are
`supplied to respective AID converters 143. The A/D con-
`verter 143 digitizes the sampled levels. The resultant digital
`signals are stored in a data memory 144. The data memory
`144 stores the digital signal as a discrete data sequence. A
`digital signal processor (DSP) 145 performs a digital filter-
`ing operation on the discrete data sequence so as to remove
`a noise component.
`In addition.
`the DSP 145 analyzes
`frequencies of the input signal. and performs a complex
`Fourier transformation for obtaining a real part and an
`imaginary part of the signal at exiting frequency. so as to
`obtain the phases of the real part and imaginary part of the
`excitation frequency of the solenoid coil.
`Next. the theory of phase measurement corresponding to
`the complex Fourier transformation will be described
`Assuming that the Fourier transformation of a time func-
`tion f(t) is denoted by F(U). F(U) can be expressed by the
`following equation (1).
`
`F(U) =J
`
`+°¢
`
`f(t) e-ivrdr
`
`(1)
`
`Next. assuming that the Fourier transformation of a time
`function f(t+a) is F(U'). F(U‘) can be expressed by the
`following equation (2).
`
`w
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`F(U') =J-
`
`10+ a) e-iwdr
`
`when t+a=T
`
`+00
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`= J-
`
`flm—juTd‘uadT: Dina I
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`+00
`
`fine-fun”
`F(U)
`
`= F(U)?“
`
`FIGS. 9A and 9B are schematic diagrams showing the
`relationship between F(U) and F(U'). Thus. it is clear that the
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`5.767.665
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`advance of a phase on the time axis is the advance of a phase
`in the frequency range. Consequently. assuming
`
`F(U}=A+jB,
`
`thus.
`
`F(U')=F(U) flames) (cos Ua+j sin Ua)
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`From these vector components. the phase can be obtained.
`In the above-described phase calculation. since the reso-
`lution of the vector components affects the resolution of the
`phase. each of the AID converters for the pickup signals
`requires a large number of bits. In addition.
`the phase
`detection sensitivity depends on the number of bits of the
`A/D converters. For example. assuming that the excitation
`frequency of a straight pipe is 1 kHz and the minimum
`detectable time is 0.1 us. the number of bits required for both
`A/D converters is 24.
`Although 24-bit type A/D converters are available. the
`conversion speed is 16 ms. which is too slow to sample a
`pickup signal with a frequency of 1 kHz. Moreover. in the
`case that the full scale of the A/D converter is 10 V. LSB
`(Least significant bit) is 0.6 pV. In a plant with a bad noise
`environment since the error indication becomes large. such
`the conversion level cannot be smaller. Actually. in practice.
`the time difference cannot be measured with a resolution of
`0.1 us.
`In the case of the straight-pipe type Coriolis flowmeter
`that has a low pressure loss and easy-cleaning construction.
`when the method for obtaining the time difference corre—
`sponding to the complex Fourier transformation of the
`digital signal process is used. since the practical detecting
`resolution is low (approximately. 5 as). an accuracy of 1%
`cannot be accomplished.
`As a method for compensating an error in measuring a
`time difference. one of two signals to be measured is
`manually input to two input terminals of a phase diiference
`measuring portion so as to be used as a compensation signal.
`The measurement value of the phase difference measuring
`portion is used as an offset value. During the measurement.
`the oflset value is subtracted from the measurement value so
`
`as to compensate the measurement value.
`However. when measuring a phase diflerence with high
`accuracy. variations of the frequency. amplitude. and DC
`level of a measured signal make errors. Thus. the reference
`phase difference used for the compensation should be mea—
`sured with the frequency. amplitude. and DC level that do
`not vary. Conventionally. a reference phase difference
`(compensation signal) with no phase difference is generated
`with one signal. Thus. when the phase difference of signals
`whose fiequencies and amplitudes vary from time to time is
`measured. the reference phase difference should be manu-
`ally designated to 0. Since the reference phase dilference is
`generated with the same signal. the same amplitude and the
`same DC level cannot be used for the two measurement
`
`signals. resulting in an error. In addition. when the phase
`difference deviates significantly from 0°. a satisfactory accu-
`racy cannot be accomplished with the referenoe of phase
`difierence=0.
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`2
`( )
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`SUMMARY OF THE INVENTION
`
`65
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`An object of the present invention is to provide a phase
`difference measuring apparatus with a high detecting reso-
`lution so as to obtain a phase difference with high accuracy.
`Another object of the present invention is to provide a
`phase diflerence measuring apparatus for compensating a
`phase difference measurement error so as to obtain a high
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`measurement accuracy regardless of variations in frequency.
`amplitude. and DC level of a measurement signal.
`A further object of the present invention is to provide a
`mass flowmeter with high detecting resolution so as to
`obtain a phase difference with high accuracy and also to
`accurately measure a flow rate.
`A first aspect of the present invention is a phase difference
`measuring apparatus for measuring the phase difference of
`two signals with the same frequency. comprising a calcu-
`lating means for calculating the sum or the difference of the
`two signals. a quantizing means for quantizing the output
`signal of the calculating means and the two signals. a band
`pass filter means for extracting only a predetermined fre-
`quency component from the quantized signals. and a phase
`difference calculating means for performing a Fourier trans-
`formation and a predetermined operation for the output
`signal of the band pass filter means so as to calculate the
`phase difference of the signals at a measuring frequency.
`As a second aspect of the present invention. the quantiz-
`ing means of the first aspect includes a comparator for
`digitizing the amplitude of one of the two signals. a PLL
`circuit for generating a signal with a frequency 11 times
`(n—Z—Z) higher than the frequency of the output signal of the
`comparator. and an MD converting means for quantizing the
`output signal of the calculating means and the two signals at
`a timing of the output signal of the PLL circuit.
`As a third aspect of the present invention. the calculating
`means of the first aspect has a gain selecting function for
`selecting a detection range and a resolution at a timing of the
`phase difference to be detected.
`As a fourth aspect of the present invention. the quantizing
`means of the first or second aspect includes a sample and
`hold means for sampling and holding the two signals and the
`output signal of the calculating means.
`A fifth aspect of the present
`invention is the phase
`difference measuring apparatus of the first or second aspect.
`further comprising an amplitude varying means for varying
`the amplitude of at least one of the two signals. and a
`compensating means for obtaining compensation data cor-
`responding to the variation of the amplitudes of the two
`signals and for compensating the phase difference corre-
`sponding to the compensation data.
`A sixth aspect of the present
`invention is the phase
`difference measuring apparatus of the first or second aspect
`further comprising a signal amplitude difference detecting
`means for detecting the amplitude difference of the two
`signals. and a gain control amplifier for matching the ampli-
`tude of one of the two signals with the amplitude of the other
`signal corresponding to the amplitude difierence.
`According to the present invention. in addition to two
`signals with the same frequency. a third signal that is
`generated by adding the former two signals or by subtracting
`one of the two signals from the other signal is used. The
`amplitudes and phases of the three signals are used. Thus.
`the number of bits required for each A/D converter can be
`smaller than for the conventional method that uses the two
`signals. In addition. the phase difference of the two signals
`can be accurately detected. Consequently.
`to obtain an
`accuracy of 0.01%. the number of bits required for each of
`the A/D converters is as small as 14 to 16 bits.
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`In addition. since the comparator that digitizes the ampli-
`tudes of one of the two signals with the same frequency and
`the PLL circuit that generates a signal with a frequency that
`is n times higher than the frequency of the output signal of
`the comparator (n22). the cut-off frequency of each digital
`filter can be varied corresponding to the variation of the
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`signal frequencies without need to change constants of the
`program used for the digital filter calculations.
`When the calculating means that obtains the sum or the
`difierence of the two signals has the gain selecting function.
`the detecting range and resolution of the phase difference to
`be detected can be varied. When the quantizing means has
`the sample hold means that samples and holds the two
`signals and the output signal of the calculating means. these
`signals can be accurately measured.
`When the amplitude varying means that varies the ampli—
`tudes of the two signals and the compensating means that
`compensates the phase difference thereof are additionally
`used. the phase difference can be accurately obtained regard-
`less of the difference in the amplitudes of the two signals.
`Alternatively. when the signal amplitude difference detect—
`ing means that detects the difference in the amplitudes of the
`two signals and the gain control amplifier that matches the
`amplitudes of the two signals corresponding to the detected
`amplitude difference are used.
`the same effect can be
`obtained.
`
`A seventh aspect of the present invention is a phase
`difference measuring apparatus for measuring the phase
`difference of two signals at a predetermined frequency.
`comprising a compensation signal generating means for
`generating a compensation signal for designating at least one
`kind of a phase difference with the same frequency as the
`frequency of one of two measurement signals. a selecting
`means for selecting the measurement signals and the com-
`pensation signal. a phase difference measuring means for
`measuring the phase difference of each of the measurement
`signals and the compensation signal. and a compensation
`control means for controlling the selecting means so as to
`compensate the measurement value supplied from the phase
`difference measuring means.
`As an eighth aspect of the present invention. the com—
`pensation signal generating means of the seventh aspect
`includes a digitizing means for digitizing one of the two
`measurement signals. a frequency multiplying means for
`multiplying the frequency of the digitized signal by a
`predetermined value. an address generating means for gen-
`erating addresses which cycle is accord with one cycle of the
`measurement signal corresponding to the output signal of
`the frequency multiplying means. at least one storage means
`for prestoring data that represents one cycle of a sine wave
`with the addresses that are output from the address gener-
`ating means. and two D/A converters for converting the sine
`wave data that is output from the storage means into an
`analog signal.
`A ninth aspect of the present invention is the phase
`difference measuring apparatus of the seventh or eighth
`aspect. further comprising first and second amplitude detect-
`ing means for detecting the amplitudes of the two measure-
`ment signals. third and fourth amplitude detecting means for
`detecting the amplitudes of the two compensation signals. a
`first comparing means for comparing the output signal of the
`first amplitude detecting means with the output signal of the
`third amplitude detecting means. a second comparing means
`for comparing the output signal of the second amplitude
`detecting means with the output signal of the fourth ampli-
`tude detecting means. and a pair of amplitude control means
`for matching the amplitude of each of the measurement
`signals with the amplitude of each of the compensation
`signals corresponding to the compared results.
`A tenth aspect of the present invention is the phase
`difference measuring apparatus of the seventh or eighth
`aspect. further comprising first and second DC level detect-
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`5.767.665
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`ing means for detecting the DC levels of the two measure-
`ment signals. third and fourth DC level detecting means for
`detecting the DC levels of the two compensation signals. a
`first comparing means for comparing the output signal of the
`first DC level detecting means with the output signal of the
`third DC level detecting means. a second comparing means
`for comparing the output signal of the second DC level
`detecting means with the output signal of the fourth DC level
`detecting means. and a pair of DC level control means for
`matching the DC level of each of the measurement signals
`with the DC level of each of the compensation signals.
`An eleventh aspect of the present invention is the phase
`difference measuring apparatus of the eighth aspect. further
`comprising a shifting means for shifting the addresses
`generated by the address generating means. and a designat—
`ing means for controlling a shift amount and generating at
`least one type of a phase difference signal.
`A twelfth aspect of the present invention is the phase
`difference measuring apparatus of the seventh. further com-
`prising a notifying means for notifying the compensation
`control means of the input of a reference signal to the phase
`difference measuring means. a storage means for storing the
`measurement value of the phase difference measuring means
`corresponding to the input from the notifying means. and an
`adjusting means for obtaining the difference between the
`stored value and the measurement value of the phase dif-
`ference measuring means and for canceling the phase dif-
`ference of the reference signal corresponding to the differ-
`ence.
`
`A thirteenth aspect of the present invention is a phase
`difference measuring apparatus for measuring the phase
`difference of two signals at