CN103795411A - SFDR testing method based on five-maximum-sidelobe-damping-window three-spectral-line interpolation - Google Patents

Abstract

The invention discloses an SFDR testing method based on five-maximum-sidelobe-damping-window three-spectral-line interpolation. Initialization setting of an SFDR testing program is completed, and sampling data are obtained through an ADC testing system; five maximum sidelobe damping windows are established, and sampling data are subjected to windowing FFT operation; a spectral line with the maximum amplitude and left and right spectral lines thereof are subjected to searching in FFT spectral lines for base waves and each harmonic wave, and the ratio of the difference of the amplitudes of the left and right spectral lines and the maximum spectral line amplitude is obtained; the mode of approximation by polynomial is used for obtaining the interpolation coefficients of the base waves and each harmonic wave; and finally, the correction amplitudes of the base waves and each harmonic wave are obtained through interpolation operation, the correction amplitudes are put into an ADC SFDR computational formula, and testing results are obtained. The ADC SFDR testing method based on five-maximum-sidelobe-damping-window three-spectral-line interpolation is provided for the first time. The method has the advantages that spectrum leakage and picket fence effect can be effectively restrained, and ADC SFDR is tested quickly and accurately.

Description

Based on the method for five maximum side lobe attenuation window three spectral line interpolation test SFDR

Technical field

The invention belongs to integrated circuit testing field, be specifically related to a kind of test ADC SFDR method, relate in particular to a kind of method based on five maximum side lobe attenuation window three spectral line interpolation test SFDR.

Background technology

Spurious Free Dynamic Range (Spurious-Free Dynamic Range, SFDR) be analog to digital converter (Analog-to-Converter, ADC) an important technical indicator, main ADC in the time that a very large signal exists can detect the ability of very little signal simultaneously.Fast Fourier transform (Fast Fourier Transformation, FFT) method is the method for the widely used a kind of ADC of test SFDR.But while adopting FFT method to test, be difficult to accomplish block synchronized sampling and complete cycle, the spectrum leakage causing thus and fence effect, cause the SFDR error that records larger.In order to reduce spectrum leakage, can adopt side lobe peak level window function little and that side lobe attenuation speed is large to process signal; Can carry out interpolation correction to result of calculation, i.e. windowed interpolation FFT method in order to reduce the error that fence effect causes.Its conventional window function has Hanning window, Blackman window, Blackman-Harris window etc.

How effectively suppressing spectrum leakage and fence effect is a problem in the urgent need to address in SFDR test.The impact of leakage can fall at present existing several different methods.Such as, adopt the rear relevant new method of sampling to suppress spectrum leakage, and recover test signal by signal reconstruction, in calculated in time domain signal power, thereby reduce the impact of fence effect on test result, but its realization is more complicated, error is larger; Or add Hanning window or Blackman-Harris window and suppress spectrum leakage, and revise the amplitude of first-harmonic and harmonic wave by two spectral lines within the scope of signal and harmonic energy are carried out to interpolation, it is better that it suppresses leakage effect, but SFDR test error is still larger.

Summary of the invention

In view of the deficiency of existing method of testing existence, object of the present invention aims to provide a kind of method based on five maximum side lobe attenuation window three spectral line interpolation test SFDR, the good window function of utility carries out truncation to time domain data, reduce the discontinuous effect of sampled data end points, reduce the impact of spectrum leakage; Interpolation algorithm based on three spectral lines further reduces fence effect, improves the accuracy of SFDR test.

The present invention is achieved through the following technical solutions:

Based on a method of five maximum side lobe attenuation window three spectral line interpolation test SFDR, comprise the following steps:

Step 1:SFDR test program arranges sinusoidal analog input signal frequency f _i, sample frequency f _s, need consider maximum harmonic order M and sampled data length N;

Described sample frequency f _s>=2f _i;

The integral number power that described sampled data length N is 2;

Step 2: based on ADC test macro with sample frequency f _sobtain the sampled data of N point length;

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

Wherein, in the time of m=1, f ₁, A ₁,

be respectively base wave frequency, amplitude and initial phase; In the time of m ≠ 1, f _m, A _m,

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

Step 3: five maximum side lobe attenuation windows of structure N point length, the sampled data of N point length is carried out to windowing FFT computing, obtain FFT spectral line X (k), k=0,1 ..., N, wherein FFT computing length is N;

The building method of five maximum side lobe attenuation window functions is:

$w\left(n\right)=\underset{l=0}{\overset{4}{\mathrm{\Σ}}}{(-1)}^l{c}_l\cos \left(\frac{2\mathrm{\πn}\·l}{N}\right)---\left(2\right)$

Wherein, c ₀=0.2734375, c ₁=0.4375, c ₂=0.0.21875, c ₃=0.0625, c ₄=0.0078125.

The continuous frequency spectrum of five maximum side lobe attenuation window functions is:

$\begin{array}{c}W\left(w\right)=0.2734375W_R\left(w\right)-0.21875[W_R(w-\frac{2\mathrm{\π}}{N})+W_R(w+\frac{2\mathrm{\π}}{N})]+0.109375[W_R(w-\frac{4\mathrm{\π}}{N})\\ +W_R(w+\frac{4\mathrm{\π}}{N})]-0.03125[W_R(w-\frac{6\mathrm{\π}}{N})+W_R(w+\frac{6\mathrm{\π}}{N})]\\ +0.00390625[W_R(w-\frac{8\mathrm{\π}}{N})+W_R(w+\frac{8\mathrm{\π}}{N})]\end{array}---\left(3\right)$

Wherein, W _r(w) be the frequency spectrum function of rectangular window:

$W_R\left(w\right)=\frac{\sin (\mathrm{wN}/2)}{\sin (w/2)}{e}^{-\mathrm{jw}\left(\frac{N-1}{2}\right)}---\left(4\right)$

Signal x (n) in (1) formula is processed with five maximum side lobe attenuation window functions, and ignore negative frequency-f _mthe secondary lobe impact of place's signal, the expression formula that obtains the discrete Fourier transform of signal after windowing is:

Wherein, W (.) is the frequency spectrum of five maximum side lobe attenuation window functions, Δ f=f _s/ N is discrete sampling interval, f _m=k _mΔ f is the frequency of 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 amplitude maximum is k _a, note a _m=k _a-k _m, have-0.5≤a _m≤ 0.5, a _mbe the interpolation coefficient of first-harmonic and each harmonic, try to achieve accurately a _mit is the key of Solve problems;

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 FFT spectral line, calculate the left and right difference of two spectral line amplitudes and the ratio of maximum spectral line amplitude;

If amplitude maximum in the energy range of m subharmonic is | X (k _m) |, about it, the amplitude of two spectral lines is | X (k _m-1) | and | X (k _m+ 1) |, note b _mfor:

$b_m=\frac{\left|X(k_m+1)\right|-\left|X(k_m-1)\right|}{\left|X\left(k_m\right)\right|}---\left(6\right)$

Step 5: the mode that adopts multinomial to approach obtains the interpolation coefficient computing formula of first-harmonic and each harmonic, and calculates the interpolation coefficient of first-harmonic and each harmonic;

By (5) formula substitution (6) Shi Ke get:

$b_m=\frac{\left|W(1-a_m)\right|-\left|W(-1-a_m)\right|}{\left|W(-a_m)\right|}---\left(7\right)$

Adopt the multinomial method of approaching, can obtain the interpolation coefficient computing formula of first-harmonic and each harmonic:

a _m＝1.38888889b _m-0.10716697b _m ³+0.01652307b _m ⁵-0.00302876b _m ⁷ (8)

Step 6: obtain the correction amplitude of first-harmonic and each harmonic by interpolation arithmetic, by its substitution ADC SFDR computing formula, obtain test result, ADC SFDR computing formula is:

$\mathrm{SFDR}=20{\log }_{10}\frac{{\mathrm{RMS}}_{\mathrm{signal}}}{{\mathrm{RMS}}_{\mathrm{spu}\_\max }}---\left(9\right)$

Wherein, RMS _signalfor the root-mean-square value of input signal fundametal compoment; RMS _{spu_max}for the root-mean-square value of maximum distortion harmonic component in sample waveform frequency spectrum or maximum spur signal.

In non-synchronous sampling situation, the maximum spectral line of amplitude and two of left and right spectral line thereof all have compared with amplitude, and illustrate and contain abundant and information actual spectral line correlation, therefore, and general | X (k _m-1) |, | X (k _m) | and | X (k _m+ 1) |, for amplitude correction, consider | X (k _m) | be maximum spectral line, in the time of weighted average, give larger weight.Can be obtained by formula (5): | X (k _m-1) |=0.5A _m| W (1-a _m) |, | X (k _m) |=0.5A _m| W (a _m) |, | X (k _m+ 1) |=0.5A _m| W (1-a _m) |, thereby have:

|X(k _m-1)|+2|X(k _m)|+|X(k _m+1)|＝0.5A _m[|W(-1-a _m)|+2|W(-a _m)|+|W(1-a _m)|] (10)

Can be obtained by formula (10) $A_m=\frac{2\left[\right|X(k_m-1)|+2|X\left(k_m\right)|+|X(k_m+1)\left|\right]}{\left|W(1-a_m)\right|+2\left|W(-a_m)\right|+\left|W(-1-a_m)\right|}---\left(11\right)$

In the time that N is larger, formula (11) can be written as:

A _m＝N ^-1[|X(k _m-1)|+2|X(k _m)|+|X(k _m+1)|]v(a _m) (12)

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

v(a _m)＝2.03174603+0.36840247a _m ²+0.03539572a _m ⁴+0.00246120a _m ⁶ (13)

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

A _m＝N ^-1[|X(k _m-1)|+2|X(k _m)|+|X(k _m+1)|](2.03174603+0.36840247a _m ²

(14)

+0.03539572a _m ⁴+0.00246120a _m ⁶)

Wherein, m is harmonic order, in the time of m=1, and A ₁for the fundamental voltage amplitude of revising, in the time of m ≠ 1, A _mit is the correction amplitude of m subharmonic.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of the embodiment based on five maximum side lobe attenuation window three spectral line interpolation test SFDR provided by the invention.

Fig. 2 is the flow chart based on five maximum side lobe attenuation window three spectral line interpolation test SFDR 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 method based on five maximum side lobe attenuation window three spectral line interpolation test SFDR, and sample data comes from ADC test macro.

As shown in Figure 1, ADC test macro comprises simulation signal generator 1, band pass filter 2, clock source 3, tested ADC daughter board 4, data acquisition system 5 and MATLAB routine analyzer 6.Its workflow is: simulation signal generator 1 is input to tested ADC daughter board 4 by band pass filter 2 and clock source 3, and data acquisition system 5 gathers the digital signal that tested ADC daughter board 4 is exported, and is tested SFDR parameter and is shown test results by MATLAB routine analyzer 6.

The attached flow chart that Figure 2 shows that test ADC SFDR provided by the invention.The method based on five maximum side lobe attenuation window three spectral line interpolation test SFDR of preferred embodiment of the present invention, it comprises the following steps:

Step 1, according to frequency and the amplitude of actual samples condition setting sample data size, the maximum harmonic order that needs consideration and analog sine input signal, sampling clock, for avoiding spectral aliasing, should guarantee that sampling clock frequency is more than or equal to the twice of analog sine frequency input signal, then enters step 2;

Step 2, ADC test macro collecting sample data;

Step 3, constructs five maximum side lobe attenuation window functions and sample data is carried out to windowing FFT computing, then enters step 4:

Step 4, according to a _mwith b _mrelation:

-0.5≤a _m≤ 0.5, the mode that adopts multinomial to approach obtains interpolation coefficient a _mexpression formula, then enter step 5;

Step 5, according to a _mwith A _mrelation: $A_m=\frac{2\left[\right|X(k_m-1)|+2|X\left(k_m\right)|+|X(k_m+1)\left|\right]}{\left|W(1-a_m)\right|+2\left|W(-a_m)\right|+\left|W(-1-a_m)\right|},$ -0.5≤a _m≤ 0.5, the method that adopts multinomial to approach obtains A _mcorrection formula, then enters step 6;

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

Step 7, utilizes the computing formula of the amplitude substitution ADC SFDR of revised first-harmonic and harmonic wave, and outputs test result.

The method based on five maximum side lobe attenuation window three spectral line interpolation test SFDR of the present invention's design, is the amplitude of utilizing three spectral line interpolation correction first-harmonics and harmonic wave, then obtains test result according to SFDR computing formula.The present invention carries out windowing by five maximum side lobe attenuation window functions of function admirable, carries out on this basis interpolation correction, can reduce the asynchronous error causing.Compared with conventional double spectral line interpolation FFT algorithm, there is higher computational accuracy and practical value.

The ADC realizing in universal significance refers to the function that in the technology before the applying date, ADC can realize, and contribution of the present invention is mainly to provide for ADC the method for reliable its SFDR of test, but not other function of ADC, thereby do not do too much statement for the function of ADC.All method test ADC SFDR based on the present invention is based on five maximum side lobe attenuation window three spectral line interpolation test SFDR are all within the scope of the present invention.

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

1, test macro is realized and is stablized and keeps synchronized sampling difficulty very large, therefore the certain certainty of asynchronous existence, in the time carrying out non-synchronous sampling, the spectrum leakage of fundametal compoment will have a strong impact on harmonic component, between harmonic component, also can there is mutual leakage, and the present invention can effectively suppress spectrum leakage and fence effect, optimize and improve systematic function;

2, the side lobe attenuation speed of five maximum side lobe attenuation windows is fast, thereby length scope is leaked with prestissimo decay, significantly reduces distant place and the at a distance spectrum leakage of Frequency point.In addition, the side lobe peak level of five maximum side lobe attenuation windows is low, can better suppress the impact of leakage, has improved the measuring accuracy of SFDR;

3, utilize Polynomial Approximation Method to solve the numerical problem of correction algorithm, simplified the realization of algorithm;

4, carry out the amplitude of interpolation correction first-harmonic and harmonic wave based on three spectral lines, revise precision high, test error is little, highly versatile.

Along with speed and the precision of ADC constantly promote, High Speed High Precision ADC is as the important module in analog-digital blended signal system, and general at leading-edge field ever-growing uses such as space, military affairs, medical treatment, its performance quality is directly determining the performance of its application system.SFDR is the important performance parameter of ADC, and it is responsible for characterizing the distortion index of whole system.Therefore the method based on five maximum side lobe attenuation window three spectral line interpolation test SFDR 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 the present invention is had been described in detail with reference to preferred embodiment, 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 departing 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 (4)

1. the method based on five maximum side lobe attenuation window three spectral line interpolation test SFDR, is characterized in that comprising the steps:

Step 1:SFDR test program arranges sinusoidal analog input signal frequency f _i, sample frequency f _s, need consider maximum harmonic order M and sampled data length N;

Step 2: based on ADC test macro with sample frequency f _sobtain the sampled data of N point length;

Step 3: five maximum side lobe attenuation windows of structure N point length, and the sampled data of N point length is carried out to windowing FFT computing, and obtain FFT spectral line X (k), k=0,1 ..., N, wherein FFT computing length is N;

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 FFT spectral line, obtain the left and right difference of two spectral line amplitudes and the ratio of maximum spectral line amplitude;

Step 5: the mode that adopts multinomial to approach obtains the interpolation coefficient computing formula of first-harmonic and each harmonic;

Step 6: obtain the correction amplitude of first-harmonic and each harmonic by interpolation arithmetic, by its substitution ADC SFDR computing formula, obtain test result, ADC SFDR computing formula is:

$\mathrm{SFDR}=20{\log }_{10}\frac{{\mathrm{RMS}}_{\mathrm{signal}}}{{\mathrm{RMS}}_{\mathrm{spu}\_\max }}---\left(1\right)$

Wherein, RMS _signalfor the root-mean-square value of input signal fundametal compoment; RMS _{spu_max}for the root-mean-square value of maximum distortion harmonic component in sample waveform frequency spectrum or maximum spur signal.

2. the method based on five maximum side lobe attenuation window three spectral line interpolation test SFDR according to claim 1, is characterized in that: in step 3, the building method of five described maximum side lobe attenuation window functions is:

$w\left(n\right)=\underset{l=0}{\overset{4}{\mathrm{\Σ}}}{(-1)}^l{c}_l\cos \left(\frac{2\mathrm{\πn}\·l}{N}\right)---\left(2\right)$

Wherein, c ₀=0.2734375, c ₁=0.4375, c ₂=0.21875, c ₃=0.0625, c ₄=0.0078125; N is the length of window function; N=0,1 ..., N-1.

3. the method based on five maximum side lobe attenuation window three spectral line interpolation test SFDR according to claim 1, is characterized in that: in step 5, the interpolation coefficient computing formula of described first-harmonic and each harmonic is:

a _m＝1.38888889b _m-0.10716697b _m ³+0.01652307b _m ⁵-0.00302876b _m ⁷ (3)

Wherein, a _mbe m subharmonic interpolation coefficient ,-0.5≤a _m≤ 0.5;

in formula, | X (k _m) | be the amplitude of maximum spectral line in m subharmonic energy range, | X (k _m-1) | and | X (k _m+ 1) | be the amplitude of two spectral lines in left and right of corresponding maximum spectral line.

4. the method based on five maximum side lobe attenuation window three spectral line interpolation test SFDR according to claim 1, is characterized in that: in step 6, the amplitude correction formula of described first-harmonic and harmonic wave is:

A _m＝N ^-1[|X(k _m-1)|+2|X(k _m)|+|X(k _m+1)|](2.03174603+0.36840247a _m ²+0.03539572a _m ⁴

(4)

+0.00246120a _m ⁶)

Wherein, a _mit is m subharmonic interpolation coefficient; | X (k _m) | be the amplitude of maximum spectral line in m subharmonic energy range, | X (k _m-1) | and | X (k _m+ 1) | be the amplitude of two spectral lines in left and right of corresponding maximum spectral line; In the time of m=1, A ₁for the fundamental voltage amplitude of revising, in the time of m ≠ 1, A _mit is the correction amplitude of m subharmonic.

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