How to Improve ADC Accuracy of DSP

introduction

TI's C2000 series DSP is widely used in industrial automation, motor control, and industrial production with its excellent performance and rich on-chip peripherals. TMS320F2812 is one of the outstanding performance in the C2000 series. F2812 integrates a 12-bit 16-channel digital/analog converter on the chip, and the theoretical accuracy can reach more than 0.1%. However, due to the existence of gain error (<5%) and offset error (<2%), the accuracy can only be around 5%, so the ADC must be calibrated.

The traditional method for ADC calibration is to input known standard voltages into two channels, determine the AD conversion curve based on the principle of two points determining a straight line, and use this to calibrate the conversion value. However, due to the influence of accidental factors in the calibration process, the accuracy of this calibration method can only reach about 3%. In response to this, a calibration method using the least squares method and linear regression is proposed. By analyzing and calculating multiple measurement points, the best fitting curve is found to minimize the overall mean square error.

The least square method is a data processing method proposed by Gauss in 1809 and widely used in multidisciplinary fields. The use of the least square method to estimate unknown parameters can effectively eliminate the influence of gross errors and systematic errors in measurement. Regression analysis was first proposed by British statistician Galton in 18*. Univariate linear regression is one of the statistical analysis methods that uses regression analysis in mathematical statistics to determine the quantitative relationship between two or more variables that are interdependent. It is widely used. Generally speaking, the equation of linear regression can be obtained by the least square method, and the straight line for y=bx+a can be calculated.

1. Correction principle and implementation scheme

The input and output of the ADC module of DSP are linear. Ideally, the input-output equation should be y=x. But in fact, the ADC module has gain error and offset error. The gain error is the deviation between the actual curve slope and the ideal curve slope, and the offset error is the deviation between the actual output value and the ideal output value (0 V) when the input is 0 V. The analog input voltage of F2812 ADC is 0~3 V, and the output is 0~4095. The corresponding relationship between analog input and digital output is: digital output value = 4095×(analog input value-reference voltage value)/3.0. The input/output characteristic curve of ADC module is shown in Figure 1.

Figure 1 ADC module input/output characteristic curve

The ADC of F2812 has 16 input channels. Since the error between channels is within ±0.2%, 6 channels can be selected as the calibration input terminals, and 6 unequal standard DC reference voltages can be input respectively. By defining the structure variables in the program to read the converted values, 6 sets of coordinate points on the input/output plane are obtained. Then, the data is processed using the least squares and univariate linear regression ideas to obtain the best fitting curve, which minimizes the sum of squares of the distances from each coordinate point to the best curve (the sum of squares of the residuals).

2 Least Squares Method and Univariate Linear Regression

2.1 Least Squares Principle

For a linear model, if there are t unmeasurable unknown quantities, theoretically, the functional relationship can be obtained by measuring the directly measured quantity that has a functional relationship with the t unknown quantities t times. However, since the measured data inevitably contains measurement errors, the results obtained must also contain certain errors. In order to improve the accuracy of the results obtained, the number of measurements can be increased to n (n>t) to use compensation to reduce the impact of random errors.

Gauss believed that when obtaining unknown parameters based on observed data, the most appropriate value of the unknown parameter should be such a value, that is, to select the parameter estimate that makes the model output as close to the observed data as possible, and the degree of closeness is measured by the sum of the squares of the difference between the model output and the data. This is the basic idea of ​​least squares. The principle of least squares method points out that the most accurate value should be obtained under the condition of minimizing the sum of squares of residual errors.

2.2 Principle of univariate linear regression

Univariate linear regression deals with the relationship between two variables, that is, if there is a linear relationship between two variables x and y, then through experiments and analysis of the obtained data, the function curve between the two is found. This is also the linear fitting problem often encountered in engineering.

3 Experimental plan and result analysis

3.1 Experimental plan

The experiment was completed using the F2812 development board and DSP debugging software CCS2.0. A stable signal source was used to generate 6 standard voltages, which were 0.2 V, 0.5 V, 1.0 V, 1.5 V, 2.0 V, and 2.5 V, and the input channels were selected as A0, A1, A2, B0, B1, and B2. The ADCL0 pin was connected to the analog ground of the circuit board, and the signal line connected to the analog input pin should avoid the digital signal line to reduce the interference of the digital signal on the analog signal. The input circuit is shown in Figure 2.

Figure 2 Input circuit [page]