CN103441762A - ADC dynamic parameter testing method based on Blackman window three-spectrum-line interpolation - Google Patents

Abstract

The invention discloses an ADC dynamic parameter testing method based on Blackman window three-spectrum-line interpolation. The method is based on digital signals acquired by an ADC testing system for testing and comprises the following steps: arranging a sample size and a sampling frequency by initialization; adding a Blackman window to a sample for FFT operation; for fundamental waves and sub-harmonic waves, searching an FFT spectral line for a spectral line with the greatest amplitude and two spectral lines at the left and at the right of the spectral line with the greatest amplitude, and calculating the ration of the amplitude difference between the left spectral line and the right spectral line to the greatest spectral line amplitude; obtaining the interpolation coefficient calculating formulas of the fundamental waves and the sub-harmonic waves by using a polynomial fitting method, and calculating the interpolation coefficients of the fundamental waves and the sub-harmonic waves; and obtaining an amplitude correction formula by using the polynomial fitting method, calculating the correction amplitude values of the fundamental waves and the sub-harmonic waves, and taking the correction amplitude values into an ADC main dynamic parameter calculating formula so as to obtain a testing result. The ADC dynamic parameter testing method based on the Blackman window three-spectrum-line interpolation is brought forward for the first time and has the following advantages: a testing error resulted from a frequency spectrum leakage can be effectively inhibited, and the ADC product dynamic parameters can be rapidly and accurately tested.

Description

A kind of method based on Blackman window three spectral line interpolation test ADC dynamic parameters

Technical field

The invention belongs to the integrated circuit testing field, be specifically related to a kind of test ADC dynamic parameter method, particularly a kind of method based on Blackman window three spectral line interpolation test ADC dynamic parameters.

Background technology

Flourish along with global IT application technology and industry, increase rapidly the demand of analog to digital converter (Analog-to-Converter, ADC), and the performance of ADC is also had higher requirement.The performance of ADC generally comprises static characteristic and dynamic characteristic, the static characteristic parameter mainly comprises DNL degree (Differential Non-Linearity, DNL) and integral nonlinearity degree (Integral Non-Linearity, INL), be mainly used to weigh transfer function departing from datum line.The static characteristic of ADC has the national regulation standard, and method of testing is comparative maturity also.Dynamic characteristic parameter is for being described in the transfer characteristic of ADC under the AC signal input condition, comprise signal to noise ratio (Signal to Noise Ratio, SNR), Spurious Free Dynamic Range (Spurious-Free Dynamic Range, SFDR), total harmonic distortion (Total Harmonic Distortion, THD), signal with noise distortion than (Signal to Noise And Distortion, SINAD), number of significant digit (Effective Number of Bits, EN0B) etc., can characterize better the performance of ADC.Therefore, these dynamic parameters are carried out to accurately test and seem particularly important.

The sample mode of ADC output digit signals has two kinds: relevant sampling and incoherent sampling.The sinusoidal analog input signal frequency of ADC and sampling clock frequency meet f _s* C=f _ibe relevant sampling during * N, wherein f _ifor the sinusoidal analog input signal frequency of ADC, f _sfor the sampling clock frequency, N is sampled data length, and the complete cycle number that C is the input signal that comprises in the sampled data length N requires C and the N integral number power that prime number and N are 2 each other.

Relevant sampling fast Fourier transform (Fast Fourier Transformation, FFT) method is a kind of ADC dynamic parametric test method commonly used, has the advantages such as precision is high, directly perceived, easy.But, in the reality test, in order to realize relevant sampling, remove and require test macro to meet f _s* C=f _ioutside * N, also require to overcome the noise of power supply noise and the generation of system peripherals circuit, make test macro can have incoherence unavoidably.For frequency, be f _isinusoidal input signal sampling, the output sampled data is not the desirable discrete data of simple sinusoidal input signal, but the discretization data that comprise sinusoidal input signal and various harmonic componentss cause the frequency spectrum of signal not only at f _ithere is a discrete spectrum at place, and with f _icentered by frequency band range in spectral line is arranged, and the each harmonic spectral line not necessarily just in time is positioned on the Frequency point of standard fft analysis, and may drop between two Frequency points.Therefore, inevitably there is spectral leakage in the dynamic parameter by FFT method test ADC.

How effectively suppressing spectral leakage is a problem in the urgent need to address in the ADC dynamic parametric test.At present existing several different methods can frequency reducing be composed the impact of revealing.For example adopt based on time and frequency zone and calculate respectively signal energy and noise energy, but need to recover test signal by signal reconstruction, error is larger; After also can adopting sampling, relevant method improves measuring accuracy.Yet the effect of these methods inhibition spectral leakage is all not obvious, and realize comparatively complicated.

Summary of the invention

Deficiency in view of existing method of testing existence, purpose of the present invention aims to provide a kind of method based on Blackman window three spectral line interpolation test ADC dynamic parameters, utilize suitable window function to carry out truncation to time domain data, can significantly reduce the discontinuous effect of sampled data end points like this, weaken long scope spectral leakage, and interpolation algorithm can weaken the impact that fence effect brings.

The present invention is achieved through the following technical solutions:

A kind of method based on Blackman window three spectral line interpolation test ADC dynamic parameters comprises the following steps:

Step 1: gather the digital signal of ADC output by the ADC test macro, obtain the sampled data of N point length;

Step 2:ADC performance test program initialization arranges input simulation signal generator frequency f _i, sampling clock source frequency f _s, harmonic order M and collecting sample put big or small N;

Described collecting sample is put the integral number power that big or small N is 2;

Described sampling clock source frequency f _s>=2f _i;

Suppose that a single-frequency analog input signal x (t) is with sample frequency f _sthe discrete-time signal x (n) obtained through the ADC uniform sampling is:

Wherein, H is harmonic order; When M=1, f ₁, A ₁,

be respectively frequency, amplitude and the initial phase of first-harmonic; When M ≠ 1, f _m, A _m,

be respectively frequency, amplitude and the phase place of the inner M subharmonic produced of ADC analog-digital conversion process chips;

Step 3:ADC performance test program is carried out the FFT computing after sample point being added to the Blackman window function truncation of N point length, obtains the FFT spectral line;

Signal x (n) in (1) formula is added to the Blackman window function and carry out discrete sampling, the forms of time and space of establishing institute's windowed function is w (n), and its continuous frequency spectrum is W (2 π f), ignores negative frequency-f _mthe secondary lobe impact of place's signal, the expression formula that obtains the fast Fourier transform of this signal after windowing is:

Wherein, N is sampling number, Δ f=f _s/ N is frequency resolution, f _m=k _mthe frequency that Δ f is the M subharmonic, f _mbe difficult to just in time be positioned on the frequency of discrete spectral line, that is to say k _mit not generally integer.If from peak point k _mthe spectral line that near sampling obtains the amplitude maximum is k _a, note a=k _a-k _m, have-0.5<a<0.5, a is the interpolation coefficient of first-harmonic and each harmonic;

Step 4: first-harmonic and each harmonic are searched for to spectral line and two of the left and right spectral line thereof of amplitude maximum in the FFT spectral line, calculate the difference of the two spectral line amplitudes in left and right and the ratio of maximum spectral line amplitude;

If the difference of the b two spectral line amplitudes in maximum spectral line left and right that to be the M subharmonic corresponding and the ratio of maximum spectral line amplitude, expression formula is:

$b=\frac{X_{M+1}-X_{M-1}}{X_M}---\left(3\right)$

Step 5: adopt the method for fitting of a polynomial to obtain the interpolation coefficient computing formula of first-harmonic and each harmonic, and calculate the interpolation coefficient of first-harmonic and each harmonic;

According to (2) formula and (3) formula, can obtain the relation of a and b:

then adopt the method for fitting of a polynomial, can obtain the interpolation coefficient computing formula of first-harmonic and each harmonic:

a=0.7834267b-0.0777817b ³+0.0160200b ⁵-0.0033564b ⁷ (4)

Step 6: adopt the method for fitting of a polynomial to obtain the amplitude correction formula, and calculate the correction amplitude of first-harmonic and each harmonic in conjunction with the interpolation coefficient computing formula of above-mentioned first-harmonic and each harmonic;

In order to try to achieve more accurately the amplitude of first-harmonic and harmonic wave, by X _m-1, X _mand X _m+1for amplitude correction, consider X _mfor maximum spectral line, give larger weight when weighted average.By formula (2), can be obtained: X _m-1=0.5A _m| W (1-a) |, X _m=0.5A _m| W (a) |, X _m+1=0.5A _m| W (1-a) |, thus have:

X _M-1+2X _M+X _M+1=0.5A _M(|W(-1-a)1+2|W(-a)|+|W(1-a)|) (5)

By formula (5), can be obtained $A_M=\frac{2(X_{M-1}+{2X}_M+X_{M+1})}{|W(1-a)+2|W(-a)|+|W(-1-a)|}---\left(6\right)$

When N is larger, formula (6) can be written as:

A _M=N ^-1(X _M-1+2X _M+X _M+1)v(a) (7)

The method that adopts multinomial to approach, can try to achieve the expression formula of v (a):

v(a)=2.1747990+0.5422966a ²+0.0886361a ⁴+0.0112150a ⁶ (8)

The amplitude correction formula that can obtain thus first-harmonic and harmonic wave is:

A _M=N ^-1(X _M-1+2X _M+X _M+1)(2.1747990+0.5422966a ²+0.0886361a ⁴+0.0112150a ⁶) (9)

Wherein, M is harmonic order, when M=1, and A ₁for corresponding fundamental voltage amplitude, when M ≠ 1, A _mamplitude for the M order harmonics; The interpolation coefficient that a is first-harmonic and each harmonic; X _mbe the amplitude of maximum spectral line in M subharmonic energy range, X _m-1and X _m+1amplitude for two spectral lines in left and right of corresponding maximum spectral line;

Step 7: the main dynamic parameter computing formula of the correction amplitude substitution ADC of first-harmonic and each harmonic is calculated to parameters, and show test results.The ADC dynamic parameter mainly comprises signal to noise ratio (SNR), sinad ratio (SINAD), number of significant digit (ENOB), Spurious Free Dynamic Range (SFDR) and total harmonic distortion (THD), and computing formula is:

$\mathrm{SNR}={20\log }_{10}\frac{{\mathrm{RMS}}_{\mathrm{signal}}}{{\mathrm{RMS}}_{\mathrm{noise}}}---\left(10\right)$

$\mathrm{SINAD}={20\log }_{10}\frac{{\mathrm{RMS}}_{\mathrm{signal}}}{{\mathrm{RMS}}_{(\mathrm{noise}+\mathrm{harmonic})}}---\left(11\right)$

$\mathrm{ENOB}=\frac{\mathrm{SINAD}-1.76\mathrm{dB}}{6.02}---\left(12\right)$

$\mathrm{SFDR}={20\log }_{10}\frac{{\mathrm{RMS}}_{\mathrm{signal}}}{{\mathrm{RMS}}_{\mathrm{spu}\_\max }}---\left(13\right)$

$\mathrm{THD}={20\log }_{10}\frac{{\mathrm{RMS}}_{\mathrm{harmonic}}}{{\mathrm{RMS}}_{\mathrm{signal}}}---\left(14\right)$

Wherein, RMS _signalroot-mean-square value for the fundametal compoment of sinusoidal analog input signal; RMS _noisefor the root-mean-square value sum of Nyquist Bandwidth with interior other spectrum components except DC component and harmonic component; RMS _{(noise+harmonic)}for nyquist frequency with the total root-mean-square value of interior whole other spectrum components (comprise harmonic component but containing DC component); RMS _harmonicroot-mean-square value sum for all harmonic components of comprising in the ADC output signal; RMS _{spu_max}root-mean-square value for maximum distortion component (except direct current).

The accompanying drawing explanation

Fig. 1 is the schematic diagram of the embodiment based on Blackman window three spectral line interpolation test ADC dynamic parameters provided by the invention.

Fig. 2 is the flow chart based on Blackman window three spectral line interpolation test ADC dynamic parameter algorithms provided by the invention.

Embodiment

Below in conjunction with accompanying drawing and case study on implementation, the present invention is further illustrated.The present invention is a kind of ADC dynamic testing method based on Blackman window three spectral line interpolations, and sample point comes from the ADC test macro.

As shown in Figure 1, the ADC test macro comprises high performance signal source 1, high-performance clock source 2, tested ADC daughter board 3, the control of the collection based on FPGA platform 4, high-speed interface 5 and PC 6.Its workflow is: with high performance signal source 1 and high-performance clock source 2, be input to tested ADC daughter board 3, collection based on FPGA is controlled platform 4 and is gathered the digital signal of tested ADC daughter board 3 outputs and be transferred to PC 6 by high-speed interface 5, and PC 6 operation ADC performance test programs also show ADC dynamic parametric test result.

Accompanying drawing 2 is depicted as the flow chart of test ADC dynamic parameter algorithm provided by the invention.The method based on Blackman window three spectral line interpolation test ADC dynamic parameters of preferred embodiment of the present invention, it comprises the following steps:

Step 1, frequency and amplitude according to actual samples condition setting sample point size, harmonic order and signal source and clock source, for avoiding spectral aliasing, should guarantee that the clock source frequency is more than or equal to the twice of signal source frequency, then enters step 2;

Step 2, the sample data that receives the collection control platform collection based on FPGA is carried out preliminary treatment, removes useless information, then enters step 3;

Step 3, add after the Blackman window function is done truncation and carry out the FFT computing pretreated sample data, then enters step 4;

Step 4, according to the relation of a and b: $b=\frac{\left|W(1-a)\right|-\left|W(-1-a)\right|}{\left|W(-a)\right|},0.5<a<0.5,$ And the method that adopts fitting of a polynomial obtains the expression formula of interpolation coefficient a, then enter step 5;

Step 5, according to a and A _mrelation: $A_M=\frac{2(X_{M-1}+{2X}_M+X_{M+1})}{\left|W(-1-a)\right|+2\left|W(-a)\right|+\left|W(-a)\right|},0.5<a<0.5,$ And adopt the method for fitting of a polynomial to obtain A _mcorrection formula, then enter step 6;

Step 6, find the amplitude X of first-harmonic and each harmonic corresponding maximum in the FFT spectral line _m, and the amplitude X of two spectral lines in left and right of the spectral line of corresponding maximum _m-1and X _m+1, and calculate revised first-harmonic and harmonic amplitude according to the amplitude correction formula, then enter step 7;

Step 7, utilize the computing formula of the amplitude substitution ADC dynamic parameter of revised first-harmonic and harmonic wave, and output test result.

The method based on Blackman window three spectral line interpolation test ADC dynamic parameters of the present invention's design, be the amplitude of utilizing three spectral line interpolation correction first-harmonics and harmonic wave, then according to the dynamic parameter computing formula, obtains test result.The present invention carries out windowing by the window function that adopts function admirable, carries out on this basis the interpolation correction, can reduce the incoherent error caused.Compare with double spectral line interpolation FFT algorithm commonly used, there is higher computational accuracy and practical value.The ADC dynamic parameter of test comprises SNR, SINAD, ENOB, SFDR and THD, can reflect the dynamic property of ADC comprehensively.

Therefore, the present invention has high accuracy, highly versatile, practical value advantages of higher.

Realize the function that in the technology before ADC on universal significance refers to the applying date, ADC can realize, contribution of the present invention mainly is to provide for ADC the method for reliable its dynamic parameter of test, but not other function of ADC, thereby do not do too much statement for the function of ADC.All being within the scope of the present invention of all method test ADC dynamic properties based on the present invention is based on Blackman window three spectral line interpolation test ADC dynamic parameters.

Than existing method, the present invention also has following beneficial effect:

1, test macro realization and the stable sampling difficulty that keeps being concerned with are very large, so the certain certainty of incoherent existence, and the present invention can suppress the incoherent spectral leakage of bringing, and optimizes and improve systematic function;

2, Blackman window function sidelobe performance is good, make edge, sampled signal two ends level and smooth gradually, reduce as far as possible discontinuous degree after making the input signal cycle continuation on border, thereby farthest suppress the spectral leakage phenomenon, improved the measuring accuracy of ADC dynamic parameter;

3, the amplitude based on three spectral line interpolation correction first-harmonics and harmonic wave, revise precision high, and test error is little, highly versatile.

ADC is the bridge of the connecting analog world and digital world, development along with computer, communication and microelectric technique, the application of ADC is more extensive, its performance quality is directly determining the performance of whole electronic system, test and evaluation to the dynamic property of the performance of ADC, particularly ADC requires to become increasingly conspicuous.Therefore, the method based on Blackman window three spectral line interpolation test ADC dynamic parameters that the present invention proposes has the very strong market competitiveness.

Finally explanation is, above embodiment is only unrestricted in order to technical scheme of the present invention to be described, although with reference to preferred embodiment, the present invention is had been described in detail, those of ordinary skill in the art is to be understood that, can modify or be equal to replacement technical scheme of the present invention, and not breaking away from aim and the scope of technical solution of the present invention, it all should be encompassed in the middle of claim scope of the present invention.

Claims (3)

1. the method based on Blackman window three spectral line interpolations tests ADC dynamic parameters is characterized in that comprising the following steps:

Step 1: gather the digital signal of ADC output by the ADC test macro, obtain the sampled data of N point length;

Step 2:ADC performance test program initialization arranges input simulation signal generator frequency f _i, sampling clock source frequency f _s, harmonic order M and collecting sample put big or small N; Described collecting sample is put the integral number power that big or small N is 2; Described sampling clock source frequency f _s>=2f _i;

Step 3:ADC performance test program is carried out the FFT computing after sample point being added to the Blackman window function truncation of N point length, obtains the FFT spectral line;

Step 4: first-harmonic and each harmonic are searched for to spectral line and two of the left and right spectral line thereof of amplitude maximum in the FFT spectral line, calculate the difference of the two spectral line amplitudes in left and right and the ratio of maximum spectral line amplitude;

Step 5: adopt the method for fitting of a polynomial to obtain the interpolation coefficient computing formula of first-harmonic and each harmonic, and calculate the interpolation coefficient of first-harmonic and each harmonic;

Step 6: adopt the method for fitting of a polynomial to obtain the amplitude correction formula, and calculate the correction amplitude of first-harmonic and each harmonic in conjunction with the interpolation coefficient computing formula of above-mentioned first-harmonic and each harmonic;

Step 7: the main dynamic parameter computing formula of the correction amplitude substitution ADC of first-harmonic and each harmonic is calculated to parameters, and show test results.The ADC dynamic parameter mainly comprises signal to noise ratio snr, sinad ratio SINAD, number of significant digit ENOB, Spurious Free Dynamic Range SFDR and total harmonic distortion THD, and computing formula is:

$\mathrm{SNR}={20\log }_{10}\frac{{\mathrm{RMS}}_{\mathrm{signal}}}{{\mathrm{RMS}}_{\mathrm{noise}}}---\left(1\right)$

$\mathrm{SINAD}={20\log }_{10}\frac{{\mathrm{RMS}}_{\mathrm{signal}}}{{\mathrm{RMS}}_{(\mathrm{noise}+\mathrm{harmonic})}}---\left(2\right)$

$\mathrm{ENOB}=\frac{\mathrm{SINAD}-1.76\mathrm{dB}}{6.02}---\left(3\right)$

$\mathrm{SFDR}={20\log }_{10}\frac{{\mathrm{RMS}}_{\mathrm{signal}}}{{\mathrm{RMS}}_{\mathrm{spu}\_\max }}---\left(4\right)$

$\mathrm{THD}={20\log }_{10}\frac{{\mathrm{RMS}}_{\mathrm{harmonic}}}{{\mathrm{RMS}}_{\mathrm{signal}}}---\left(5\right)$

Wherein, RMS _signalroot-mean-square value for the fundametal compoment of sinusoidal analog input signal; RMS _noisefor the root-mean-square value sum of Nyquist Bandwidth with interior other spectrum components except DC component and harmonic component; RMS _{(noise+harmonic)}comprise harmonic component for nyquist frequency with interior whole other spectrum components but do not contain the total root-mean-square value of DC component; RMS _harmonicroot-mean-square value sum for all harmonic components of comprising in the ADC output signal; RMS _{spu_max}for the root-mean-square value of maximum distortion component except direct current.

2. the method based on Blackman window three spectral line interpolations tests ADC dynamic parameters according to claim 1, it is characterized in that: the interpolation coefficient computing formula of described first-harmonic and each harmonic is:

a=0.7834267b-0.0777817b ³+0.0160200b ⁵-0.0033564b ⁷ (6)

Wherein, the interpolation coefficient that a is first-harmonic and each harmonic, and-0.5<a<0.5; The difference that b is the two spectral line amplitudes in maximum spectral line left and right in the energy range that first-harmonic and each harmonic are corresponding and the ratio of maximum spectral line amplitude.

3. the method based on Blackman window three spectral line interpolation test ADC dynamic parameters according to claim 1 and 2, is characterized in that, the amplitude correction formula of described first-harmonic and harmonic wave is:

A _M=N ^-1(X _M-1+2X _M+X _M+1)(2.1747990+0.5422966a ²+0.0886361a ⁴+0.0112150a ⁶) (7)

Wherein, M is harmonic order, when M=1, and A ₁for corresponding fundamental voltage amplitude, when M ≠ 1, A _mamplitude for the M order harmonics; The interpolation coefficient that a is first-harmonic and each harmonic; X _mbe the amplitude of maximum spectral line in M subharmonic energy range, X _m-1and X _m+1amplitude for two spectral lines in left and right of corresponding maximum spectral line.

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