Abstract:
A method of determining the ratio of the amplification factor before and after changing the amplification factor of a signal normalizer that amplifies the voltage amplitude of signals that are input from a signal generation means so that it stays within a predetermined range and outputs that voltage amplitude by using a signal generation means, which adds two sine-wave signals of the same frequency and voltage amplitude to form the output and controls the output voltage amplitude at any phase relationship between said two sine-wave signals by a phase control means, and an alternating-current voltage determination means, includes:  
     the step wherein when said phase relationship is reversed so that said sine-wave signals are negated, the output voltage amplitude of said signal generator stays within a predetermined range and  
     the step wherein the amplification factor of said signal normalizer and the output voltage amplitude of said signal generator are each changed so that they are inversely proportional and a difference is obtained between the output voltage amplitude of said signal normalizer before said change and that after said change.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The present invention pertains to a method and a device for determining the relative value (ratio) of the amplification factor before changing and after changing the amplification factor of a signal normalizer, and in particular, relates to a method and a device for determining the ratio of the amplification factor of a signal normalizer used in determination devices in order to improve the determination accuracy.  
           [0003]    2. Discussion of the Background Art  
           [0004]    The method whereby an analog-digital converter (A/D converter hereafter) is set up as an alternating-current voltage determination device and after the signals that are the subject of determination have been converted to discrete values, the signal components of the desired frequency are calculated by numeric operation, which is widely used as a method of determining the voltage amplitude of alternating-current signals that are the subject of determination in determination devices such as alternating-current volt-ammeters and LCR meters, etc. Determination errors in this case are attributed mainly to quantization errors, linearity errors due to bit weighting errors, and thermal noise, and there is particularly an increase in errors when the voltage amplitude of a signal that is input to the A/D converter is small. For example, errors of as much as 108 ppm are produced when signals are input where the maximum input voltage to an A/D converter with an accuracy of 18 bits is {fraction (1/10)} th  the full-scale voltage of the A/D converter. On the other hand, as a result of the increased accuracy needed for components that are the subject of determination, etc., the determination accuracy of the above-mentioned LCR meter must be 10 ppm or less when determining the alternating-current signal amplitude.  
           [0005]    The method whereby a voltage converter that raises or lowers the signal voltage by a predetermined ratio is set up in front of the A/D converter and fluctuations in the voltage amplitude of signals that are input to the A/D converter are kept within a predetermined range in order to reduce the effects of linearity errors is a method for reducing the effects of linearity errors of the A/D converter on the determination values when determining the voltage amplitude of input signals within a broad voltage range. If the voltage amplitude of the signals that are the subject of determination is large enough, it is directly determined by an A/D converter, while if this voltage amplitude is so small that it will cause linearity errors of the A/D converter, voltage conversion by a voltage converter is performed on the signals that are the subject of determination. The voltage amplitude of the signals that are the subject of determination during voltage conversion can be obtained by multiplying the voltage amplitude of the signals input from the voltage converter to the A/D converter as determined by the A/D converter by the inverse of the conversion ratio of this converter. Consequently, it is necessary to know the conversion ratio with an accuracy that is superior to the accuracy of the A/D converter and the voltage converter is generally made so that this accuracy requirement is satisfied to the utmost, or a standard signal source is generally set up and the voltage amplitude of signals obtained through the voltage converter is determined by the A/D converter and the error in the conversion ratio is corrected by calculation after the determination.  
           [0006]    When a transformer is used as an example of a voltage converter, transformers of large shape are more expensive, depending on the frequency band that is used, and except when at ½ partial pressure, there is a problem with accuracy because of coil resistance and leakage inductance.  
           [0007]    The method whereby amplifier  12  (signal normalizer hereafter) having multiple amplification factors in stages is set up in front of the input part of A/D converter  11  is another method that does not have the above-mentioned restrictions, as in the case of the alternating-current voltage determination device  10  in FIG. 1. Signal normalizer  12  has the function of amplification and output so that the voltage amplitude of signals that are input by signal generator  13  stays within a predetermined range. As a result, the maximum input voltage to A/D converter  11  is always close to the full-scale voltage of A/D converter  11 , regardless of the size of the voltage amplitude of the input signals, and the effect of linearity errors due to A/D converter  11  is reduced. However, although an amplifier is used in this method, progress has been made in terms of high integration and high performance, even with popular amplifiers on the market, and space-saving effects are marked, regardless of the frequency used.  
           [0008]    Depending on the width of the voltage range to be determined, there are cases in which multiple amplification factors of the normalizer are set up in stages in order to finely divide this voltage range. In this case, unless the ratio of the amplification factor before the amplification factor of the signal normalizer is changed and the amplification factor after it has been changed (simply amplification factor ratio hereafter) is known within a desired range of accuracy, the linearity of the determination value will be interrupted by the time when the amplification factor of the signal normalizer is changed as the dividing line, and new linearity errors will be produced. Therefore, the effect of improving errors with a normalizer will not be obtained.  
           [0009]    For instance, when the amplification factor of signal normalizer  12  is set using a popular type of network resistance for the part comprising signal normalizer  12 , an accuracy of only 100 ppm at the most can be realized. Therefore, by setting up normalizer  12 , the effect of linearity errors of A/D converter  11  on the determination values is reduced, but a new linearity error is produced due to the insufficient accuracy of the amplification factor ratio in signal normalizer  12 . Consequently, in order to obtain appropriate results when using a signal normalizer for the purpose of reducing the effect of linearity errors of the A/D converter on determinations, it is necessary to precisely determine the amplification factor ratio of the signal normalizer so that linearity of the determinations is maintained.  
           [0010]    The method in which only the amplification factor of signal normalizer  12  is changed while keeping constant the amplitude of signals input to input normalizer  12 , the output amplitude of signal normalizer  12  is determined by A/D converter  11  before and after this change is determined, and determinations are performed based on this determination ratio is a method for determining the amplification factor ratio of the signal normalizer  12 . For instance, when determinations of the signal normalizer are performed with an amplification factor of 1× and 10×, first, the amplification factor of signal normalizer  12  is set at 1× and signals are input from signal generator  13  to signal normalizer  12  so that the maximum input voltage to A/D converter  11  is {fraction (1/10)} th  the full-scale voltage of A/D converter  11 . The voltage of the determination frequency component is calculated from the determination results with A/D converter  11  at this time and serves as V 1 . Then the amplification factor of signal normalizer  12  is set at 10×. The voltage amplitude of the signals input to signal amplifier  12  is not changed and therefore, the maximum input voltage to A/D converter  11  is the full-scale voltage of A/D converter  11 . The voltage of the determination frequency component is calculated from the determination results with A/D converter  11  at this time and serves as V 2 . As a result, the amplification factor ratio obtained from the determination results is found as V 2 /V 1 .  
           [0011]    By means of the above-mentioned method, the maximum input voltage to A/D converter  11  during V 1  determination is {fraction (1/10)} th  the full-scale voltage of the A/D converter. Consequently, the determination of V 1  contains the linearity error of A/D converter  11  and therefore, the amplification factor ratio lacks accuracy and the result of reducing the determination error by normalizer  12  is not adequately obtained, even if the voltage amplitude of the input signals is determined by concomitantly using signal normalizer  12 .  
         SUMMARY OF THE INVENTION  
         [0012]    The present invention includes a method and a device for determining the amplification factor before the amplification factor of a signal normalizer is changed and the amplification factor after it is changed at a predetermined accuracy, its purpose being to obtain the appropriate error-reducing results with this signal normalizer based on the amplification factor ratio as determined using this method or device when the determination device has a signal normalizer for the purpose of reducing linearity errors.  
           [0013]    Moreover, the invention prevents the scale of the circuit from becoming very large with an increase in the determination frequency by using a signal normalizer.  
           [0014]    The invention also allows for reduced cost by constructing the present invention so that inexpensive parts can be used.  
           [0015]    In a first aspect, the invention includes a method for determining the amplification factor ratio before and after changing the amplification factor of a signal normalizer that amplifies the voltage amplitude of signals that are input from a signal generation means so that it is within a predetermined range and outputs that voltage amplitude by using a signal generation means, which adds two sine-wave signals of the same frequency and voltage amplitude to form the output and controls the output voltage amplitude at any phase relationship between said two sine-wave signals by a phase control means, and an alternating-current voltage determination means, comprising an adjustment step wherein when the above-mentioned phase relationship is reversed so that the above-mentioned sine-wave signals are negated, the output voltage amplitude of the above-mentioned signal generator stays within a predetermined range and  
           [0016]    the step wherein the amplification factor of the above-mentioned signal normalizer and the output voltage amplitude of the above-mentioned signal generator are each changed so that they are inversely proportional and a difference is obtained between the output voltage amplitude of the above-mentioned signal normalizer before the above-mentioned change and that after the above-mentioned change.  
           [0017]    Moreover, a second aspect of the invention includes a step wherein the output voltage amplitude of the above-mentioned signal generation means is amplified.  
           [0018]    Furthermore, in a third aspect of the invention, the above-mentioned adjustment step includes a step wherein the voltage amplitude of at least one of the above-mentioned two sine-wave signals is controlled and in that it further comprises:  
           [0019]    the step wherein the amplification factor in the above-mentioned amplification step is determined and  
           [0020]    the step wherein the output voltage amplitude of the above-mentioned signal generation means that has been adjusted by the above-mentioned adjustment step is determined.  
           [0021]    A fourth aspect of the invention includes  
           [0022]    the step wherein one of the above-mentioned two sine-wave signals is produced by the synthesis of two or more sine-wave signals with the same frequency and  
           [0023]    the step wherein the voltage amplitude of the above-mentioned two or more sine-wave signals is controlled in the above-mentioned adjustment step.  
           [0024]    Moreover, a fifth aspect of the invention includes a device for determining the amplification factor ratio before and after changing the amplification factor of a signal normalizer that amplifies the voltage amplitude of signals that are input from a signal generation means so that it is within a predetermined range and outputs that voltage amplitude and that consists of a signal generation means, which adds two sine-wave signals of the same frequency and the same voltage amplitude to form the output and controls the output voltage amplitude at any phase relationship between said two sine-wave signals by a phase control means, and an alternating-current voltage determination means, comprising  
           [0025]    a means by which, when the above-mentioned phase relationship is reversed so that the above-mentioned sine-wave signals are negated, the output voltage amplitude of the above-mentioned signal generator stays within a predetermined range and  
           [0026]    a means by which the amplification factor of the above-mentioned signal normalizer and the output voltage amplitude of the above-mentioned signal generator are each changed so that they are inversely proportional and a difference is obtained between the output voltage amplitude of the above-mentioned signal normalizer before the above-mentioned change and that after the above-mentioned change.  
           [0027]    In a sixth aspect of the invention, the signal generation means includes a means by which the output voltage amplitude of the above-mentioned signal generation means is amplified.  
           [0028]    In a seventh aspect of the invention, the above-mentioned adjustment means is a means whereby the voltage amplitude of at least one of the above-mentioned two sine-wave signals is controlled and comprises  
           [0029]    a means by which the amplification factor of the above-mentioned amplification means is determined and  
           [0030]    a means by which the output voltage amplification of the above-mentioned signal generation means that has been adjusted by the above-mentioned adjustment means is determined.  
           [0031]    In an eighth aspect of the invention, one of the above-mentioned two sine-wave signals is a synthetic signal of 2 or more sine-wave signals with the same frequency and the above-mentioned adjustment means is a means for controlling the voltage amplitude of the above-mentioned two or more sine-wave signals. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0032]    [0032]FIG. 1 is a drawing of the alternating-current voltage determination device and the signal generator of the prior art;  
         [0033]    [0033]FIG. 2 is a drawing showing a first example of the present invention;  
         [0034]    [0034]FIG. 3 is a drawing showing a second example of the present invention;  
         [0035]    [0035]FIG. 4 is a drawing showing a third example of the present invention; and  
         [0036]    [0036]FIG. 5 is a drawing showing a fourth example of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0037]    The following definitions are presented to provide a better understanding of the Figures in conjunction with the following detailed description of the invention.  
         [0038]    Definition of symbols  
         [0039]    [0039] 40 . Alternating-current voltage determination device  
         [0040]    [0040] 41 . Signal normalizer  
         [0041]    [0041] 42 . Analog-digital converter  
         [0042]    [0042] 80 . Alternating-current determination system  
         [0043]    [0043] 90 . Signal generator  
         [0044]    [0044] 91 . Reference generator  
         [0045]    [0045] 92 ,  93 . Direct signal synthesizers  
         [0046]    [0046] 94 . Phase control device  
         [0047]    [0047] 95 . Adder  
         [0048]    [0048] 96 . LPF  
         [0049]    [0049] 97 . Amplifier  
         [0050]    [0050] 98 . D/A converter  
         [0051]    The method and the device of the present invention are described below based on examples shown in the attached drawings. FIG. 2 shows the first example, which is the basic embodiment of the device of the present invention that uses the method of the present invention. This example is voltage determination system  20  for alternating current signals. It comprises signal generator  30 , which is the signal generation means, and alternating-current voltage determination device  40 .  
         [0052]    Signal generator  30  has reference generator  31 , two direct digital synthesizers  32  and  33  (DDS hereafter) that generate sine-wave signals, phase control device  34 , which is an example of a phase control means, adder  35 , which is an example of an addition means, and low-pass filter (LPF hereafter)  36 , which is an example of a filter means, and it is connected to alternating-current voltage determination device  40 .  
         [0053]    Reference generator  31  generates reference signals of frequency N·f (Hertz) where the output frequency f (Hertz) of signal generator  30  has been multiplied by a predetermined multiplying factor N and supplies these signals to the two DDS devices and phase control device  34 .  
         [0054]    The two DDS devices generate false sine waves of voltage amplitude A/2 and frequency f (Hertz) and after the outputs are added by adder  35 , the higher harmonic waves contained in the false sine waves are filtered by LPF  36  to obtain the output of signal generator  30 .  
         [0055]    Phase control device  34  has phase resolution N and is connected to the two DDS devices, so that the phase of the signals generated by each DDS is independently controlled.  
         [0056]    Alternating-current voltage detector  40  has signal normalizer  41  and A/D converter  42 , which is an alternating-current voltage detection means.  
         [0057]    Signal normalizer  41  has amplification factors of 1× and 10× and is placed in front of the input part of A/D converter  42 .  
         [0058]    The present invention is constructed as described above in the first example. The theory of obtaining the ratio of the amplification factor before changing the amplification ratio of above-mentioned signal normalizer  41  and the amplification factor after the change (simply amplification factor ratio hereafter) is described below:  
         [0059]    First, the amplification factor of signal normalizer  41  is set at 1×. The voltage amplitude of signals supplied from signal generator  30  through signal normalizer  41  to A/D converter  42  is determined by A/D converter  42  and the value that is obtained serves as V 1 . V 1  here is the voltage adjusted by signal generator  30  so that the determination is performed near the full-scale voltage of A/D converter  42 .  
         [0060]    Next, the amplification factor of signal normalizer  41  is set at 10×. The voltage amplitude of the signals that are output from signal generator  30  is converted to the inverse of the amplification factor of signal generator  41 , that is, {fraction (1/10)} th . Furthermore, the voltage amplitude of signals supplied from signal generator  30  through signal normalizer  41  to A/D converter  42  is determined by A/D converter  42  and the value that is obtained serves as V 2 . Unless there is a large difference in the true value of the amplification factor ratio of signal normalizer  41  in comparison to  10 , which is the apparent amplification factor ratio, as with V 1 , determinations of V 2  are performed near the full-scale voltage of A/D converter  42 .  
         [0061]    In this case, the true value of this amplification factor ratio is obtained by multiplying V 2 /V 1  by 10, which is the apparent amplification factor, in order to correct errors. The values V 1  and V 2  that are used here are determined near the full-scale voltage of A/D converter  42  and therefore, they are not affected by linearity errors of A/D converter  42  and the amplification factor ratio of signal normalizer  41  can be obtained. When the alternating-current voltage is determined, the amplification factor of signal normalizer  41  is controlled so that the voltage amplitude of the signals that are input to A/D converter  42  will be near the full-scale of A/D converter  42  and the signals that are input to A/D converter  42  are determined. The voltage of the alternating-current signals determined by calculation is obtained based on the true value of the voltage amplitude of these signals and the amplification factor ratio of signal normalizer  41 . Furthermore, determination errors by A/D converter  42  can be disregarded and therefore, determination errors in the amplification factor ratio depend on the accuracy of the output voltage amplitude of signal generator  30 .  
         [0062]    By means of the present invention, it is necessary to use alternating-current signals, the voltage amplitude of which varies in accordance with the number of amplification factors of the signal normalizer. The method in which multiple signal generators have voltage amplitudes of a fixed level is considered to be a simple method, but there are mathematical problems with the signal generator, and it is not easy to maintain the voltage amplitude of multiple signal generators at their respective predetermined ratio. Therefore, in this example, two signal sources are set up instead and the synthesis vector of these signal sources forms the output of the signal generator. The phase relationship of these signal sources is controlled and the voltage amplitude of the output signals is varied precisely.  
         [0063]    The theory of the method of the present invention is described in further detail below using mathematical formulas.  
         [0064]    As previously explained, signal generator  30  adds the output of the two DDS devices and the output signals of signal generator  30 , which represent the synthesis vector, control the phase difference between the two DDS devices and thereby vary the voltage amplitude of these signals.  
         [0065]    The phase difference θ of the two DDS devices in this example is held to the integral increase of 2π/N (rad) by phase control device  34 . The output signal voltage V c  devices of signal generator  30  is the synthesis vector of the signals that are output from the two DDS devices, and any value is obtained as this amplitude, depending on the phase difference θ, as shown in the following two formulas:  
                       v     c                 al       =         1   2        A                        j2π                 f                 t         +       1   2        A                        j        (       2                 π                 f                 t     +   θ     )                         =       1   2          A        (     1   +        jθ       )                 j2π                 f                 t                             formula                 1                               
 
                       |       v   .       ca                 l       |     =     |       1   2          A        (     1   +        jθ       )                       =         1   2        A          2        (     1   +     cos                 θ       )           =       1   2          A   ·   2        cos        θ   2                     =     A                 cos        θ   2                           formula                 2                               
 
         [0066]    When the amplification factor of signal normalizer  41  is 1× and the phase difference θ (rad) is θ1 (=0), the signals are input so that the maximum input voltage to A/D converter  42  is almost the full-scale voltage.  
         [0067]    The amplification factor of signal normalizer  41  is set at 1× and the phase difference θ is set at θ1. The voltage of the determination frequency component is calculated from the determination results of the A/D converter and this serves as V adc1 .  
               v   adc1     =       1   2          A        (     1   +          jθ   1         )                 formula                 3                               
 
         [0068]    Next, the amplification factor of signal normalizer  41  is set at 10× and the phase difference θ is set at θ2 (=2π·30/64). θ2 is selected so that the amplitude of the output of the detection device is {fraction (1/0)} th  that when the phase difference is set at θ1. When the output amplitude is 1 when the phase difference is set at θ1, the voltage amplitude of the signals that are output from signal generator  30  with the above-mentioned setting is 0.098017 from formula 2. The voltage of the determination frequency component is calculated from the determination results of the A/D converter and this serves as V adc2 .  
               v   adc2     =       g   nom          1   2          A        (     1   +          jθ   2         )                 formula                 4                               
 
         [0069]    The true value g nom  of the multiplication factor ratio when the multiplication factor of signal normalizer  41  is set at 10× is represented by the following formula:  
                       g   nom     =                    v   adc2          (     1   +        j0       )           v   adc1          (     1   +          j2                   π              ·     30   /   64             )                     ≅                  (     1   -     j                 10.15317       )            v   adc2       v   adc1                             formula                 5                               
 
         [0070]    Even though the amplification factor of signal normalizer  41  is set at either 1× or 10×, the maximum input voltage to A/D converter  42  is almost the full-scale voltage and therefore, the amplification factor ratio of signal normalizer  41  can be determined without any effect from the linearity error of A/D converter  42 . Determination accuracy is determined by the relative accuracy of the voltage amplitude of the signals that are output from signal generator  30  when the phase difference θ is set at θ1 and θ2. The output of signal generator  30  is controlled by the phase difference of the two DDS devices and therefore, the accuracy of the phase difference represents this relative accuracy. When the error in the phase is Δθ, the error in the voltage amplitude of the signals that are output from signal generator  30  is represented by the following 2 formulas:  
                 Δ                   v     c                 al           v     c                 al         =            jθ       1   +        jθ              (          jΔθ     -   1     )               formula                 6                     |       Δ                   v     c                 al           v     c                 al         |     ≅     Δθ     2        cos        (     θ   2     )                     (     ∵     Δθ      1       )                 formula                 7                               
 
         [0071]    The recent increased speed of digital hardware technology has made it easy to hold timewise errors, such as DDS jitters, etc., to 100 picoseconds or less. Therefore, sufficiently high phase accuracy is obtained in low frequency regions. When the DDS output signal frequency is set at 1 kHz and jitters at 100 picoseconds, the phase accuracy is 0.6 micro(rad). Consequently, when the amplification factor of signal normalizer  41  is set at 1×, the error in the voltage amplitude of the signals that are output from the signal generator is 0.3 ppm, and similarly, the error when the amplification factor is set at 10× becomes 3 ppm and it is possible to control the output voltage amplification of signal generator  30  with high accuracy.  
         [0072]    Although the amplification factor of signal normalizer  41  was set at 1× and 10× in the present example, the amplification factor is not limited to these examples and determinations of signal normalizer  41  with a combination of various amplification factors, such as 1× and 5×, 2× and 8×, etc., can be performed by setting the phase differences θ1 and θ2 between the DDS devices at the appropriate values.  
         [0073]    The method and the device of the present invention were described with the above-mentioned examples. However, errors are actually produced in the amplitude direction and the phase direction of each DDS device because of fluctuations in parts, etc., and this error is manifested as an error in the voltage amplitude that is input from signal generator  41 . This voltage amplitude is not as ideal as in formula 2. Therefore, it is necessary to reduce errors to the required accuracy or less by adding an adjustment means for correcting this error to the DDS.  
         [0074]    Voltage determination system  50  for alternating-current signals with an adjustment means is shown in FIG. 3 as a second example of the present invention in order to solve the above-mentioned problems Voltage determination system  50  comprises signal generator  60 , which is a signal generation means, and above-mentioned alternating-current voltage determination device  40 .  
         [0075]    Signal generator  60  has reference generator  61 , three DDS devices  62 ,  63 , and  64  that generate sine-wave signals, phase control device  65 , which is an example of a phase control means, adder  66 , which is an example of an addition means, LPF  67 , which is an example of a filter means, amplifier  68 , which is an amplification means, and two digital-analog converters (D/A converter hereafter)  69  and  70 , which are adjustment means, and is connected to alternating-current voltage determination device  40 .  
         [0076]    Reference generator  61  generates reference signals of frequency N·f (Hertz), in which the output frequency f (Hertz) of signal generator  60  is multiplied by a predetermined multiplication factor N and supplied to the three DDS devices as well as phase control device  65 .  
         [0077]    The three DDS devices generate false sine waves of voltage amplitude A/2 and frequency f (Hertz), and after these outputs are added by adder  66 , the higher harmonic waves contained in the false sine waves are filtered by LPF  67  and are voltage-amplified by amplifier  68  and then become the output of signal generator  60 . Moreover, D/A converter  69  is connected to DDS  62  and D/A converter  70  is connected to DDS  63  and voltage amplitude of the output signals of the corresponding DDS is controlled by the respective D/A converter.  
         [0078]    Phase control device  65  has phase resolution N and is connected to the three DDS devices so that the phase of the signals generated by each DDS is independently controlled.  
         [0079]    The theory of the method of the present invention will now be described.  
         [0080]    In the present example, the discrepancies in voltage amplitude and phase produced in the output signals of the two DDS devices that construct the output signals of signal generator  60 , that is, DDS  62  and  64 , are corrected and the error in the voltage amplitude produced in the output signals of signal generator  60  are corrected for determinations of the amplification factor ratio of signal normalizer  41 . In the present example, DDS  63  is also set up as a third DDS device in comparison to the 2 DDS devices of the first example in order to correct the discrepancy in the phase direction.  
         [0081]    Furthermore, the method of determining the amplification factor ratio of signal normalizer  41  is in no way different from that of the first example.  
         [0082]    The theory of the method of the present invention is described in further detail below using mathematical formulas:  
         [0083]    First, in order to correct the discrepancy in the amplitude direction between DDS  62  and DDS  64 , the phase difference θ is set at π in order to satisfy formula 2, with the phase difference between DDS  62  and DDS  64  being θ (rad). With respect to the error that is produced by the above-mentioned DDS devices, D/A converter  69  changes the voltage amplitude of the output signals of DDS  62  so that the error in the amplitude direction is corrected.  
         [0084]    Moreover, in order to correct the discrepancy in the phase direction between DDS  62  and DDS  64 , DDS  63  is controlled by the phase control device so that it always has a phase difference of π/2 with respect to DDS  62 . In this case, D/A converter  70  changes the voltage amplitude of the output signals of DDS  63  so that the error in the phase direction is corrected.  
         [0085]    Furthermore, the voltage amplitude of the signals that are output from signal generator  60  are determined by A/D converter  42  while adjusting the two D/A converters so that this voltage amplitude is at its minimum. Furthermore, this voltage amplitude cannot be detected by A/D converter  42  when it is less than the minimum resolution of A/D converter  42 , and therefore, the amplification factor of amplifier  68  is raised and errors produced by the DDS devices are corrected by further similar adjustment.  
         [0086]    Once this adjustment has been performed, an error will be made in the voltage amplitude of the signals that are output from signal generator  60  in accordance with the size of this residual error ε unless the output amplitude of signal generator  60  is zero. Consequently, D/A converters  69  and  70  must have sufficient resolution. When the voltage amplitude accuracy of the signals that are input to A/D converter  42  is Δca1 and the amplification factor of signal normalizer  41  is G nom , the number of bits M dac  necessary for the resolution of the two D/A converters is represented by the following formula:  
               M   dac     ≥       log   2          (       G   nom       Δ                 c                 al       )               formula                 8                               
 
         [0087]    For instance, when signal normalizer  41  with amplification factors of 1× and 10× is determined at an accuracy of 10 ppm, Δca1=10 ppm and G nom =10 and therefore, according to formula 9, a D/A converter having a resolution of 20 bits or more is necessary.  
         [0088]    When zero is detected during the adjustment of signal generator  60 , A/D converter  42  must detect changes in the voltage amplitude adjusted by the minimum resolution of the two D/A converters, and therefore, if the number of bits of A/D converter  42  is M adc , the amplification factor necessary for amplifier  68  G cal  is represented by the following formula:  
               G     c                 al       ≥       1     2     (       M   adc     -   1     )              1     Δ                 c                 al            G   nom               formula                 9                               
 
         [0089]    For instance, when A/D converter  42  having a resolution of 18 bits is used, M adc =18, and therefore, according to formula 10, the amplification factor necessary for amplifier  68  is approximately 7.6 times or higher.  
         [0090]    In the present example, the discrepancy of the amplitude direction and the phase direction produced by the DDS devices is eliminated by the D/A converter and the voltage amplitude of the signals that are output from signal generator  60  is brought to the ideal state shown in the first example. Nevertheless, using a high-resolution D/A converter during production of the device is not favorable in terms of cost. Therefore, a third example is presented with which the same determination accuracy is obtained, even if a low-resolution D/A converter is used.  
         [0091]    The third example in FIG. 4 is voltage determination system  80  of alternating-current signals and it comprises signal generator  90 , which is the signal generation means, and the above-mentioned alternating-current voltage determination device  40 .  
         [0092]    Signal generator  90  has reference generator  91 , two DDS devices  92  and  93  that generate sine waves, phase control device  94 , which is an example of a phase control means, adder  95 , which is an example of an addition means, LPF  96 , which is an example of a filter means, amplifier  97 , which is an amplification means, and D/A converter  98 , which is an adjustment means, and is connected to alternating-current voltage determination device  40 .  
         [0093]    Reference generator  91  generates reference signals of frequency N·f (Hertz) in which the output frequency f (Hertz) of signal generator  90  is multiplied by the predetermined multiplication factor N and supplies these signals to the two DDS devices and phase control device  94 .  
         [0094]    The two DDS devices generate false sine waves of voltage amplitude A/2 and frequency f (Hertz) and these outputs are added by adder  95 . Then the higher harmonic waves contained in the false sine waves are filtered by LPF  96  and the voltage is amplified by amplifier  97 . This becomes the output of signal generator  90 . Moreover, D/A converter  98  is connected to DDS  92  and the voltage amplitude of the output signals of DDS  92  is controlled by D/A converter  98 .  
         [0095]    Phase control device  94  has phase resolution N and is connected to the two DDS devices so that the phase of the signals generated by the respective DDS is independently controlled.  
         [0096]    The theory of the method of the present invention is described below:  
         [0097]    In the second example, a high-resolution D/A converter is set up as an adjustment means for error correction of the amplitude direction and the phase direction, but in the present example, a D/A converter is set up for the amplitude direction only and the phase direction is not adjusted. In addition, the resolution of the D/A converter for the amplitude direction is relatively low. When the frequency of the output signals of signal generator  90  is low, the error in the phase direction is very small when compared to the amplitude direction, but an error still remains in the phase direction. Furthermore, the adjustment accuracy of the amplitude direction is also insufficient and the signals that are output from signal generator  90  are not in the ideal state shown in the first example and a very small error vector (residual error hereafter) remains. Therefore, in the present example the residual error is determined and corrected by calculation and an amplification factor ratio of the same accuracy as in the second example can be obtained. Furthermore, the method of determining the alternating-current signal voltage is the same as in the above-mentioned example.  
         [0098]    The theory of the method of the present invention is described below in further detail using mathematical formulas:  
         [0099]    When the signals output from DDS  92  deviate from the ideal state by residual error ε, the voltage amplitude V cal  of the signals that are output from signal generator  90  is represented by the following formula with the phase difference between DDS  92  and DDS  93  as θ (rad). The residual error ε contains both amplitude and phase components and is a complex number in the following formula:  
                       v     ca                 l       =         (         1   2        A                +   ɛ     )               j2π                 f                 t         +       1   2        A                        j        (       2                 π                 f                 t     +   θ     )                         =       {         1   2          A        (     1   +        jθ       )         +   ɛ     }               j2π                 f                 t                             Formula                 10                               
 
         [0100]    When phase difference θ is set at π, there is residual error ε in the voltage amplitude of signals output from signal generator  90  and therefore, direct determinations can be performed. However, since residual error ε is a very small signal, amplifier  97  set up in signal generator  90  is set at a high amplification factor G cal  and the voltage amplitude of the signals that are input to A/D converter  42  is amplified considerably and determined, in order to reduce the effect of linearity error of A/D converter  42  when determining residual error ε. The true value g cal  of the amplification factor of this amplifier  97  must be pre-determined.  
         [0101]    In order to find this true value g cal  here, the amplification factor of amplifier  97  is set at 1×, the amplification factor of signal normalizer  41  is set at 1×, and the phase difference θ of signal generator  90  is set at π. D/A converter  98  is set up and the voltage amplitude of the signals that are output from signal generator  90  is adjusted so that the maximum input voltage is input to A/D converter  42 . The voltage value of the determination frequency component is calculated from the determination results of A/D converter  42 . The true value of this voltage at this time serves as V adcα .  
         [0102]    Moreover, the amplification factor of amplifier  97  is set at G ca1 . The voltage value of the determination frequency component is calculated from the determination results of A/D converter  42 . The true value of this voltage at this time serves as V adcβ . g cal  is found as in the following formula by determining these two values:  
               g     ca                 l       =       v     a                 d                 c                 β         v     a                 d                 c                 α                 formula                 11                               
 
         [0103]    Next, the residual error of the voltage amplitude of output signals of signal generator  90  is determined. For instance, the voltage value of the determination frequency component is determined by A/D converter  42  while D/A converter  98  is adjusted so that the voltage amplitude of the signals that are output from signal generator  90  is brought to a minimum. After this adjustment, the voltage value of the determination frequency component is calculated from the determination results of A/D converter  42 . The true value of this voltage at this time serves as V adcε .  
                       ν     a                 d                 c                 ɛ       =       {     ɛ   +       1   2          A        (     1   +          j                 π         )           }          g     c                 al                     =     ɛ   ·     g     c                 al                             formula                 12                               
 
         [0104]    Next, the amplification factor ratio of the signal normalizer is found. First, the amplification factor of amplifier  97  is set at 1×, the amplification factor of signal normalizer  41  is set at 1×, and the phase difference θ is set at θ1 (=0). The voltage value of the determination frequency component is calculated from the determination results of the A/D converter and this serves as V adc1 .  
               ν     adc                 1       =     ɛ   +       1   2          A        (     1   +          j                   θ   1           )                   formula                 13                               
 
         [0105]    Moreover, the amplification factor of signal normalizer  41  is set at 10× and phase difference θ is set at θ2 (=2π·{fraction (30/64)}). θ2 is selected so that the amplitude of the output of the determination device is {fraction (1/10)} th  that when the phase difference is set at θ1. When the output amplitude is  1 , when the phase difference is set at θ1, the output amplitude of the determination device with the above-mentioned setting is 0.098017 from formula 2. The voltage value of the determination frequency component is calculated from the determination results of the A/D converter. This serves as V adc2 .  
               ν     adc                 2       =       g   nom          {     ɛ   +       1   2          A        (     1   +          j                   θ   2           )           }               formula                 14                               
 
         [0106]    Here, g nom  is the true value of the amplification factor ratio when the amplification factor of signal normalizer  41  is changed from 1× to 10×.  
         [0107]    This amplification factor ratio g nom  from formulas 12, 13 and 14 is represented by the following formula:  
               g   nom     =         ν     adc                 2            (     1   +          j                   θ   1           )             ν     adc                 1            (     1   +          j                   θ   2           )       +         v     a                 d                 c                 ɛ         g     c                 al              (            j                   θ   1         -          j                   θ   2           )                   formula                 15                               
 
         [0108]    The determination error of residual error ε becomes the error in the amplification factor ratio determination of the signal normalizer in this example. The resolution of D/A converter  98  and the amplification factor of amplifier  97  that are needed to make the determination error of residual error ε sufficiently small can be estimated as follows:  
         [0109]    The main factor in the determination errors is the linearity error of A/D converter  42 . When this linearity error is generated at a constant rate δ to the full-scale voltage V adc     —     fs  of A/D converter  42 , this determination or measured value V adc     —     m  with respect to the true V adc  of the voltage amplitude of the signals that are input to A/D converter  42  is represented by the following formula 16.  
                       v     a                 d                   c_      m         =       v   adc     +       v     a                 d                 c_f                 s          δ                   =       v   adc          (     1   +         v     a                 d                 c_f                 s         v   adc          δ       )                           formula                 16                               
 
         [0110]    Here, the following relationship is established between the full-scale voltage of A/D converter  42  and each determination value. During determinations of V adc α , at most, approximately 1/G cal  of the full-scale voltage of A/D converter  42  is input to A/D converter  42 . Moreover, at most, the full-scale voltage of A/D converter  42  is input to A/D converter  42  during V adc β determinations. Furthermore, when the amplification factor of signal normalizer  41  is set at 1×, the phase difference θ is set at zero, and the amplification factor of amplifier  97  is set at 1×, the voltage that is approximately equal to the full-scale voltage of A/D converter  42  is input to A/D converter  42 .  
         [0111]    Consequently, the determination values V adcα-m , V adcβ     —m   , and V adcε     —m    of true values V adc α , V adcβ , and V adcε , respectively, are represented by the following 3 formulas:  
                     v     a                 d                 c                   α_      m         =                  v     a                 d                 c                 α            (     1   +         v     a                 d                 c_f                 s         v     a                 d                 c                 α            δ       )                   ≅                  v     a                 d                 c                 α            (     1   +       G     c                 al          δ       )                     formula                 17                       v     a                 d                 c                   β_      m         =                  v     a                 d                 c                 β            (     1   +         v     a                 d                 c_f                 s         v     a                 d                 c                 β            δ       )                   ≅                  v     a                 d                 c                 β            (     1   +   δ     )                     formula                 18                       v     a                 d                 c                   ɛ_      m         =                  v     a                 d                 c                 ɛ            (     1   +         v     a                 d                 c_f                 s         v     a                 d                 c                 ɛ            δ       )                   ≅                  v     a                 d                 c                 ɛ            (     1   +       A     ɛ                   G     c                 al              δ       )                     formula                                19                               
 
         [0112]    The determination value G cal     —m    of g cal  from formulas 17 and 18 is represented by the following formula:  
                       g     c                 a                 l                 _i                 n       =                  v     a                 d                 c                   β_      m           v     a                 d                 c                   α_      m                       =                    v     a                 d                 c                 β         v     a                 d                 c                 α                1   +   δ       1   +     G     c                 al              δ                 ≅                        g     c                 al            (     1   +   δ   -       G     c                 al          δ       )                          (       ∵     δ        &lt;&lt;        1       ,       G     c                 al          δ        &lt;&lt;        1       )                           ≅                        g     c                 al            (     1   -       G     c                 al          δ       )                          (     ∵       G     c                 al          1                   )                       formula                 20                               
 
         [0113]    εm to which the error of residual error ε has been added from formulas 12, 19 and 20 is represented by the following formula:  
                       ɛ   m     =                  v     a                 d                 c                   ɛ_      m           g     c                 a                 l                   _      m                       =                      ɛ          1   +       A     ɛ                   G     c                 al              δ         1   -       G     c                 al          δ                 (       ∵         A     ɛ                   G     c                 al              δ        1       ,         G     c                 al          δ        1       )                       ≅                ɛ        (     1   +       A     ɛ                   G     c                 al              δ     +       G     c                 al          δ       )                   =                ɛ   +       A                  G     c                 al              δ     +     ɛ                   G     c                 al          δ                   =                ɛ   +   Δɛ                         formula                 21                               
 
         [0114]    The effect of the determination error Δε of residual error ε increases with a reduction in the voltage amplitude of signals output from signal generator  90 . Therefore, only the error of signal generator  90  when the phase difference θ is θ2 should be considered. When the voltage amplitude of the signals that are output from signal generator  90 , that is, output from amplifier  97 , is V ca1 , the magnitude Δca1 of the determination error of residual error ε to the magnitude |V ca1 | of this voltage amplitude from formulas 2 and 21 is represented by the following formula:  
                       Δ                 cal     =                Δɛ     |     v     ca                 l       |                   =                      A                  G     ca                 l              δ     +     ɛ                   G     ca                 l          δ         A                   cos        (       θ   2     /   2     )                       =                  (       1     G     ca                 l         +       ɛ   A          G     ca                 l           )        δ        1                  cos        (       θ   2     /   2     )                         ≅                  (       1     G     c                 al         +       ɛ   A          G     ca                 l           )        δ                   G   nom                           formula                 22                               
 
         [0115]    Based on the above-mentioned formula, the linearity error of A/D converter  42  is clearly determined from amplification factor Gca1of amplifier  97  and the magnitude (ε/A) of residual error ε. When the determination error of residual error ε is small, the magnitude of residual error ε should be reduced by raising the amplification factor of amplifier  98  and increasing the resolution of D/A converter  98 . In order to minimize the determination error of residual error ε, the values within parentheses in the above-mentioned formula are minimized or the following formula is satisfied:  
               |     1     G     c                 al         |     =     |       ɛ   A          G     c                 al         |             formula                 23                               
 
         [0116]    Furthermore, in the following formula there is a correlation between the number of bits M dac  of D/A converter  98  and the magnitude of the residual error ε (ε/A):  
               ɛ   A     =     1     2     M     d                 a                 c                   formula                 24                               
 
         [0117]    The following formula is obtained from formulas 23 and 24:  
           G   ca1   2 =2 M   dac   formula 25  
         [0118]    Formula 22 can be represented by the following formula when formula 25 is established.  
                     Δcal   ≅                  2     G   cal          δ                   G   nom                   =                2          ɛ   A          δ                   G   nom                   =                  2     (     1   -       M   dac     /   2       )          δ                   G   nom                           formula                 26                               
 
         [0119]    For instance, when an 18-bit A/D converter  42  is used, the ratio δ of the linearity error is  
       δ   =         2       2       M   adc     -   1         ≅     11        [   ppm   ]                               
 
         [0120]    if the linearity error is due to a quantization error of A/D converter  42 . When signal normalizer  41  having an amplification factor of 1× and 10× is to be determined at an accuracy of 10 ppm, G nom =10 and Δ cal =10 ppm and therefore,  
                     G   cal     =       2      δ                   G   nom       Δcal                 =       2   ·     11        [   ppm   ]       ·   10       10        [   ppm   ]                     =   22                 formula                 27                       M     d                 a                 c       =                2          log   2          (     g   cal     )                     =                2          log   2          (   22   )                     ≅              9                 formula                 28                               
 
         [0121]    from formulas 25 and 26.  
         [0122]    In the end, the amplification factor of amplifier  97  should be 22 times and the resolution of D/A converter  98  should be 9 bits or more. On the other hand, a D/A converter having a resolution of 20 bits or higher is needed in the second example under the same conditions.  
         [0123]    Although in the second example, the determinations are performed while controlling as much as possible the error of the signal normalizer, in the present example, there is an advantage in that when compared to the second example, the resolution needed for the D/A converter used in adjustments is a relatively low-bit resolution in order to determine the error in the signal normalizer and to perform determinations while making corrections using this value, and therefore, a system can be constructed less expensively.  
         [0124]    By means of the third example, the alternating-current voltage determination device can be constructed with high accuracy and inexpensively. The fourth example is shown in FIG. 5 as an example of using these advantages. This example is LCR meter  100 , and it comprises signal generator  101 , alternating-current voltage determination device  110 , differential amplifier  109 , current-voltage converter  102 , switches  103  and  104 , terminals  105  and  106  connecting the object to be determined  120 , control device  107 , and display device  108 .  
         [0125]    Signal generator  101  is connected to switch  103  and the signals generated by signal generator  101  are supplied to switch  104  or terminal  105 .  
         [0126]    Alternating-current voltage determination device  110  has A/D converter  111  and signal normalizer  112  set up in front of A/D converter  111 . Alternating-current voltage determination device  110  is connected to switch  104  and receives signals supplied from either switch  103 , differential amplifier  109  that obtains the potential difference between terminal  105  and terminal  106 , or current-voltage converter  102  connected to terminal  106 .  
         [0127]    Control device  107  is connected to and controls signal generator  101 , A/D converter  111 , signal normalizer  112 , and switches  103  and  104 , as shown by the broken line. Moreover, control device  107  has an electronic calculation function and calculates the values of data obtained from A/D converter  111  and outputs these values to display device  108  connected to control device  107  and displays the determination results to the user of the LCR meter.  
         [0128]    LCR meter  100  has the following effects because of the above-mentioned structure:  
         [0129]    First, in order to determine the amplification factor ratio of signal normalizer  112 , switches  103  and  104  are made so that the signals from signal generator  101  are directly supplied to alternating-current voltage determination device  110  to obtain the same state as the structure shown in the third example. The amplification factor ratio is determined by the same procedure as shown for the third example. Again, when briefly explained, corrections are made so that the error of signal generator  101  is brought to a minimum and the error that still remains is determined by A/D converter  111 . This serves as Vε. With respect to each amplification factor of signal generator  112 , the voltage amplitude of the output signals of signal generator  101  is adjusted so that the voltage amplitude of the signals supplied from signal generator  101  through signal normalizer  112  to A/D converter  111  becomes the full scale of A/D converter  111  and the voltage amplitude of the signals supplied to A/D converter  111  is determined by A/D converter  111 . The determination value at this time serves as V n . However, n is an integer of 1 or higher and the maximum is the number of amplification factors of signal normalizer  112 . Control device  107  obtains the true value of the amplification factor ratio of signal normalizer  112  by calculation from the determined Vε and Vn.  
         [0130]    Furthermore, A/D converter  111  performs successive determinations at a predetermined time interval, and therefore, phase information is actually simultaneously obtained. Consequently, the true value of the amplification factor ratio of signal normalizer  112  can be obtained as a complex number containing a phase component and not a real number that is simply an amplitude component.  
         [0131]    Next, in order to determine the impedance of an object to be determined, switch  103  is made so that the output signals of signal generator  101  are supplied to object  120  to be determined. Furthermore, the voltage of signals from differential amplifier  109  and the current converted to voltage displacement by current-voltage converter  102  are determined by alternating-current voltage determination device  110 . Voltage and current are continuously determined and the phase difference between voltage and current is also simultaneously obtained by calculation based on the voltage and current obtained by determination. Control device  107  obtains the impedance of the object to be determined by calculation from the current and phase difference and the amplification factor ratio of signal normalizer  112  that has already been obtained.  
         [0132]    The impedance of the object to be determined can be determined at a predetermined accuracy by a device that uses the above-mentioned method of the present invention.  
         [0133]    Furthermore, the method and the device of the present invention can be applied to any determination system that determines the magnitude of the input level, such as the increase or decrease in the error, in accordance with the input level of an A/D converter, etc. A network analyzer and the like represents an ideal example.  
         [0134]    As previously explained in detail, the present invention is constructed and has the effects as described above. Therefore, the ratio of the amplification factor before the amplification factor of the signal normalizer was changed and the amplification factor after the change is determined at a predetermined accuracy. Therefore, when the determination device has a signal normalizer for the purpose of reducing the linearity error, the error-reducing effect of this signal normalizer can be appropriately obtained with this determined amplification factor.  
         [0135]    Moreover, a signal normalizer is used and therefore, it is possible to keep the circuit scale from becoming larger in accordance with the determination frequency.  
         [0136]    Furthermore, the present invention is constructed so that inexpensive parts can be used and therefore, cost is reduced.