Abstract:
A method for accurately measuring the integral nonlinearity (INL) and differential nonlinearity (DNL) of an analog front end (AFE) system, such as an analog/digital converter (ADC), is provided. In particular, the method eliminates the need for well-calibrated equipment and an accurate signal source. Differing from conventional approaches, according to the invention, the INL of the AFE system is obtained by directly transferring the output of the AFE system rather than by accumulating the DNL. Therefore, the INL of the measured AFE system according to the invention is only slightly affected by inputted signal source.

Description:
FIELD OF INVENTION 
     The present invention relates to a method for measuring the nonlinearity of an analog front end (AFE) system, such as an analog/digital converter (ADC), and more in particular, to a method for measuring accurately the differential nonlinearity (DNL) and integral nonlinearity (INL) of an AFE system. 
     BACKGROUND OF INVENTION 
     With respect to the conversion characteristic of an AFE system, e.g., an ADC, the DNL and INL both are very important specifications. Conventional methods usually utilize an accurate signal source to first measure the DNL of an AFE system. Afterwards, the INL of the AFE system is obtained by accumulating the DNL of the AFE system. Related prior arts refer to the following: 
     1. U.S. Pat. No. 4,352,160; 
     2. U.S. Pat. No. 5,712,633; 
     3. “Mixed-signal Testing Tutorial Class Notes,” at European test conference, Rotterdam, on Apr. 19, 1993. 
     Hereinafter, the disadvantages of the conventional approaches will be described. 
     Note that an accurate signal source is necessary for the conventional approaches. When an inaccurate signal source is employed to measure the DNL and INL of an AFE system, it will introduce error into the DNL and INL. The DNL with little error induced by the inaccurate signal source may be permitted. However, the error of INL, which accumulates that of the DNL into a large value, can not be negligible. Therefore, only permissible DNL but no permissible INL can be obtained for an AFE system when an inaccurate signal source is employed to measure the nonlinearity of the AFE system. 
     Besides, shifted reference voltage existing in the signal source and/or poor-calibrated AFE system will induce D.C. drifts which makes the measured DNL diverge from accurate DNL. Furthermore, in conventional approaches, the computed INL of the AFE system by accumulating the inaccurate DNL will diverge from accurate INL more. 
     The foregoing and other state-of-the-art approaches for measuring the DNL and INL of an AFE system indicate the need for a new method of providing accurate DNL and INL measurements of the AFE system that can be implemented without the requisite of well-calibrated equipment and a high-accuracy signal source. It is also desirable that the measurements be immune to D.C. drifts induced by the signal source and/or AFE system. The present invention is directed toward satisfying the aforesaid need. In addition, the invention is to provide a method for measuring the INL of an AFE system by transferring from the output data of the AFE system rather than by accumulating the DNL. Further, the DNL of the AFE system is obtained by differentiating the INL. Therefore, the INL and DNL of the measured AFE system according to the invention both are only slightly affected by the accuracy of the inputted signal source slightly. 
     SUMMARY OF INVENTION 
     It is an objective of the invention to provide an improved method of measuring the DNL and INL of an AFE system, e.g., an analog/digital converter. 
     It is another objective of the invention to provide a method of measuring the DNL and INL of an AFE system that does not require well-calibrated equipment and a high-accuracy signal source. 
     It is another objective of the invention to provide a method of measuring the DNL and INL of an AFE system whereby the measurements are immune to D.C. drifts induced by the signal source and AFE system. 
     It is another objective of the invention to provide a method of measuring the DNL and INL of an AFE system whereby the measurements are affected slightly by the accuracy of inputted signal. 
     According to the invention, a method is provided for measuring an integral nonlinearity (INL) data and a differential nonlinearity (DNL) data of an analog front end (AFE) system corresponding to a predetermined ideal code. In a conversion of a signal by the AFE system, the signal is converted by the AFE system into N successive true codes at N corresponding successive coded steps. N successive ideal codes, based on to an ideal conversion of the signal by the AFE system, are computed at the N corresponding successive coded steps. Each of the N true codes includes a D.C. drift component contributed by a D.C. drift in the conversion, a signal component substantially contributed by the signal, a noise component contributed by a noise in the conversion and a harmonic distortion (HD) of the signal in the conversion. The N ideal codes includes the predetermined ideal code. The method is first to extract the noise component and HD component of each of the N true codes to obtain N error codes at the N coded steps. Afterwards, the method is to map each of the N error codes by one corresponding ideal code in accordance with the N coded steps. The method is then to average the error codes mapped by the predetermined ideal code to obtain the INL data. The method is then to differentiate the INL data with respect to the predetermined ideal code to obtain the DNL data. In the method, the noise and THD components, actually contributing the nonlinearity of the AFE system, are extracted, and then derived into the INL data. Afterwards, the DNL data is obtained by differentiating the INL data. Therefore, the method is implemented without the requisite of well-calibrated equipment. Moreover, the INL data and DNL data both are only slightly affected by the accuracy of the inputted signal: 
     The advantage and spirit of the invention may be understood by the following recitations together with the appended drawings. 
    
    
     BRIEF DESCRIPTION OF THE APPENDED DRAWINGS 
     FIG. 1 is a flow chart illustrating a method of measuring the nonlinearity of an AFE system in accordance with the invention. 
     FIG. 2 shows the output of a 12-bits ADC applied by the sine waveform signal. 
     FIG. 3 is a zoom-in view showing the true codes of FIG. 2 without the D.C. drift components. 
     FIG. 4 shows the window function for windowing the data of FIG.  3 . 
     FIG. 5 shows the data of FIG. 3 after a transformation from time domain representation into frequency domain representation. 
     FIG. 6 shows the result of remaining noise in the frequency spectrum represented by FIG.  5 . 
     FIG. 7 shows the data of FIG. 6 after a transformation from frequency representation into time domain representation. 
     FIG. 8 shows the INL of the ADC vs. the corresponding ideal codes. 
     FIG. 9 shows the DNL of the ADC vs. the corresponding ideal codes. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     This present invention is to provide a method for measuring the INL and DNL of an AFE system such as an ADC. In general, the output of the AFE system can be distinguished into a signal component which represents the quantity substantially contributed by an inputted signal, a D.C. drift component which represents the quantity of D.C. drift in the output of the AFE system, a harmonic distortion component which represents the quantity of harmonic distortion induced by the AFE system, and a noise component which represents the quantity of noise. It is well known that the nonlinearity of the AFE system is substantially contributed by the harmonic distortion and noise components. In order to obtained the accurate nonlinearity of the AFE system, extraction of the harmonic distortion and noise components from the output of the AFE system is performed in the method according to the invention. 
     With respect to the investigation of a signal, there are two useful types of representations, i.e., time domain representation and frequency domain representation. By time domain representation, the digital output of the signal can be recorded easily. Otherwise, by frequency domain representation, a frequency spectrum analysis of the signal can be made, i.e., an actual signal spectrum and a noise spectrum from the analyzed signal can be separated from each other. Both types of representations are utilized in the method according to the invention. 
     FIG. 1 is a flow chart illustrating the method according to the invention. Hereinafter, a 12-bits ADC in a scanner is taken as an example of the AFE system to illustrate the method according to the invention. 
     Typically, the ADC has an analog input and a digital output. The method utilizes a function generator to generate a sine waveform signal. The sine waveform signal is applied to the ADC. In general, a conversion characteristic of the ADC is represented by N successive coded steps at a predetermined sampling rate. In the invention, the output of the ADC is recorded into N successive true codes with time domain representation corresponding to the N successive coded steps, respectively. The steps aforementioned are illustrated from step  1  to step  3  in FIG.  1 . In this case shown in FIG. 2, the output of the ADC is recorded at 32768 coded steps, i.e., the number of sampling points (N) is equal to 32768. It is noted that each of the N successive true codes includes a signal component (OUT signal ), a D.C. drift component (OUT DC ), a harmonic distortion component (OUT HD ) and a noise component (OUT noise ). 
     Based on an ideal conversion of the sine waveform signal by the ADC, N successive ideal codes are computed at the N corresponding successive coded steps. For the aforesaid is case shown in FIG. 2, 32768 successive ideal codes are computed corresponding to 32768 successive codes steps. 
     After the A.C. switch of the function generator is turned off, a D.C. signal is applied from the function generator to the ADC for a duration. The output of the AFE system is acquired and averaged to obtain a D.C. drift data (OUT DC ) which is substantially induced by shift reference voltages of the function generator and/or the ADC. The aforesaid steps are illustrated from step  4  to step  6  in FIG.  1 . 
     As illustrated in step  7  of FIG. 1, the D.C. drift data is subtracted from each of the N true codes, i.e., the OUT DC  is subtracted from the output of the ADC. A zoom-in view of the N true codes without the OUT DC  is shown in FIG.  3 . 
     As illustrated in step  8  of FIG. 1, the N true codes are transferred from time domain representation into frequency domain representation. The details of the transferring step is determined by whether a coherent relationship exists between the frequency of the sine waveform signal and the sampling frequency of the ADC with respect to the N coded steps. The coherent relationship is defined as follow: 
     
       
           F   signal   =F   sampling ×( M/N )  (1) 
       
     
     where F signal  is the frequency of the sine waveform signal, F sampling  is the sampling rate, and M is total cycle number of the sine waveform signal for measurement. 
     In the measurement, the phase difference between the starting point and the end point will induce an undesired D.C. drift. When the coherent relationship exists, the phase of the starting point of the measurement is equal to that of the end point of the measurement. By equation (1), the adequate F signal , F sampling , M and N can be chosen to minimize the D.C. drift induced by the phase difference. For example, the ideal F signal =24414.0625 Hz can be chosen to minimize the D.C. drift induced by the phase difference when F sampling =5 MHz, M=5 and N=1024. Under a coherent relationship, the transferring step is just a fast Fourier transformation (FFT) step. In practical application, F signal =24414 Hz, close to the ideal F signal =24414.0625 Hz, is made for the measurement easily when F sampling =5 MHz, M=5 and N=1024. However, in the aforesaid case, the D.C. drift induced by the phase difference only contributes within 0.02% of the full INL, so it is negligible. 
     When the coherent relationship does not exist, the phase of the starting point is not equal to that of the end point in the measurement. In this case, undesired D.C. drift is introduced into the measurements. To solve the problem mentioned above, a windowing step is required. Therefore, in this case, the transferring step includes a windowing step and an FFT step. The data shown in FIG. 2 is just an example where the coherent relationship does not exist. As shown in FIG. 4, it is a window function utilized for windowing the N true codes without the OUT DC  whose zoom-in view is shown in FIG.  3 . After the FFT transformation, the N true codes are transferred into frequency domain representation, as shown in FIG.  5 . 
     In FIG. 5, by frequency domain representation, a signal spectrum and a noise spectrum from the sine waveform signal can be distinguished from each other. The signal spectrum represents the OUT signal  of the output of the ADC in frequency domain. The noise represents the quantity of the OUT HD  and OUT noise  of the output of the ADC in frequency domain. Based on an assumption that the noise on the signal spikes of the signal spectrum is equal to neighborhood, the signal spectrum can be filtered out and then the noise spectrum can be extracted, as shown in FIG.  6 . Afterwards, the extracted noise spectrum is transferred from frequency domain representation into time domain representation to obtain N successive error codes corresponding to the N successive coded steps, respectively, as shown in FIG.  7 . It is clear that the N error codes only include the OUT noise  and OUT HD  of the N true codes, i.e., the nonlinearity of the ADC can be derived from the N error codes. The steps aforesaid are illustrated from step  12  to step  13  in FIG.  1 . Step  13  is an inverse FFT step when the coherent relationship mentioned above exists. Otherwise, step  13  includes an inverse windowing step and an inverse FFT step when the coherent relationship mentioned above does not exist. The extraction of the noise spectrum from the sine waveform signal would introduce undesired nonlinearity. However, the aforesaid nonlinearity usually contributes slight quantity to the INL, so it is negligible. 
     Alternatively, the noise spectrum in FIG. 5 is filtered out and only the signal bin is extracted. By transferring the extracted signal spectrum from frequency domain representation into time domain representation, the OUT signal  can be obtained for the N true codes. Afterwards, by subtracting the OUT signal  of the N successive true codes from the N successive true codes without the OUT DC , N successive error codes contributed by the OUT noise  and OUT HD  of the N true codes can be obtained. The N error codes correspond to the N coded steps, respectively. The steps aforesaid are illustrated from step  9  to step  11  in FIG.  1 . Step  10  is an inverse FFT step when the coherent relationship mentioned above exists. Otherwise, the step  10  includes an inverse windowing step and an inverse FFT step when the coherent relationship mentioned above does not exist. 
     Afterwards, each of the N error codes is mapped by one corresponding ideal code in accordance with the N coded steps. Because the N ideal codes all locate within the full scale of resolution of the ADC (AFE system). Therefore, one ideal code may be found repeatedly in the N ideal codes. The N ideal codes can be summarized into a sequence of unrepeated ideal codes. To obtain an INL data corresponding to a predetermined ideal code included in the unrepeated ideal codes, all of the error codes mapped by the predetermined ideal code are averaged. By the aforementioned method, the unrepeated ideal codes vs. their corresponding INL data are rearranged and shown in FIG.  8 . It is noted that the scale of X-axis in FIG. 8 represents the full scale of resolution of the 12-bits ADC, i.e., the maximum scale of X-axis is equal to 4096. By differentiating the INL data with respect to the corresponding unrepeated ideal code, a DNL data of the corresponding unrepeated ideal code is obtained. The aforesaid steps are illustrated from step  14  to step  16 . A simple method for deriving the DNL(i) data of the ith ideal code existing in the unrepeated ideal codes is by subtracting the INL(i−1) from INL(i) data. Utilizing the aforementioned method, the result of the DNL data vs. the unrepeated ideal codes derived from the data of FIG. 8 is shown in FIG.  9 . 
     Differing from the conventional methods, the INL of an AFE system is generated from measured data by the method according to the invention. Therefore, the accuracy of the INL is permissible. Moreover, the DNL of the AFE system is obtained by differentiating the INL such that the accuracy of DNL is in the same order as that of the INL and is also permissible. 
     Also differing from the conventional method, the component induced by the D.C. drift is eliminated from the INL and DNL by the method according to invention. Therefore, the method is implemented without the requisite of well-calibrated equipment. 
     While the invention has been described in one presently preferred embodiment, it is understood that the words which have been used are words of description rather than words of limitation and that changes within the purview of the appended claims may be made without departing from the scope and spirit of the invention in its broader aspect.