[introduction] we discussed how to be used shake will quantify sum of errors to input the statistical dependency between signal to raise ideal to quantify through breaking implement function. Alleged and ideal, it is to point to those who unite to ADC transfer function is had rank jump. In other words, ideal ADC has 0 DNL error. This kind shakes in applying in the radio receiver that needs tall SFDR, attach most importance to especially should.

We discussed how to be used shake will quantify sum of errors to input the statistical dependency between signal to raise ideal to quantify through breaking implement function. Alleged and ideal, it is to point to those who unite to ADC transfer function is had rank jump. In other words, ideal ADC has 0 DNL error. This kind shakes in applying in the radio receiver that needs tall SFDR, attach most importance to especially should.

In the article, we will discuss another when shake fundamental application, improve the SFDR of converter of real world A/D namely, for example AD6645, its meeting occurrence DNL is wrong. This kind shakes in applying in the radio receiver that needs tall SFDR now, attach most importance to especially should.
 
ADC static state and dynamic degree of linearity

Before begin, let us review the main limitation that raises ADC degree of linearity quickly above all. Although ADC uses different framework and circuit implementation, but they have two main nonlinear source: Sampling maintains (the coder part of S/H) circuit and ADC. S/H is nonlinear the part results from a such facts, namely it has finite changeover rate, and should be inputted be the high frequency signal that has big amplitude when, likelihood cannot enough follow quickly input. Lacking the S/H that shows enough changeover rate is a lot of ADC cannot offer prep above a crucial reason of the tall SFDR of bandwidth of signal of a few conspicuous. This also explained why of S/H nonlinear concern with frequency. S/H is in the trends of affirmatory ADC (or AC) respect of degree of linearity is having crucial effect.

Another nonlinear the source is ADC coder part. To given ADC is phasic, coder part basically processes dc signal, because it is located in after S/H. Accordingly, coder is nonlinear the static state that can cause a system (or dc) nonlinear. Below good case, nonlinear composition won’t change along with frequency. The feature with nonlinear static state depends on the DNL in ADC transfer function and INL (integral is nonlinear) error. Term ” the static state is nonlinear ” likelihood misnomer, because this is planted nonlinear composition affects dc signal not only, and still can reduce degree of linearity when processing communication signal.
 
Notice which are planted please nonlinear the type takes dominant place!

Another when the article should remember important thing is, to a lot of ADC, of S/H dispute linear main. Below this kind of circumstance, lack fidelity function meets harmonic be close to Nai Kui as the input this special frequency and drop quickly. If S/H is limitative element, cannot show improvement through exterior means ADC degree of linearity. But, certain ADC designs the front that has broadband, tall degree of linearity technically. This makes coder part is become nonlinear main. To this kind of ADC, we can be used shake the technology will improve ADC SFDR. In research this kind shakes before application, those who make us careful see transfer function of ADC static state introduce is nonlinear error.
 
Transfer function is nonlinear — determinism error

To understand a static state better nonlinear, what the transfer function that we show to in an attempt to 1 times introduces is nonlinear the error is exemple undertake study.

Graph 1.  Introduce nonlinear the transfer function give typical examples of the error [click picture enlarge] .

The gules curve in pursueing on expresses nonlinear 4 ADC, and blue curve states 4 ideal are answered. If we use afore-mentioned characteristic curves to digitlize the wave of 1.11 KHz sine with 4 MHz sampling, we will win a figure 2 medium the following weaveform.

Graph 2. The digitlizes wave of 1.11 KHz sine weaveform with 4 MHz sampling [click zoom] .

In the graph 2 in, green curve shows an input, and blue and gules curve are respectively ideal and nonlinear the output of transfer function. In connecting associate red curve, subtract blue curve, we can be not ideal to answer certainly those who introduce is nonlinear error. This by the graph 3 medium gules curves are shown.

Graph 3.  Indication blame ideal is answered those who introduce is nonlinear the graph of the error [click zoom] .

Transfer function is nonlinear the error that introduce is determinism error. This is meant, to given input voltage, the error is identical from beginning to end. For example, referenced graph 1, we observe 6 LSB (effective) the output that the input always brings about taller than good value 3 LSB. Behavior of this kind of determinism built dependency between input and mistake. If the input is in specific frequency, we predict the error is in the place of certain and specific frequency related to the input to have very strong frequency weight.

Graph 3 can help you understand this kind of situation better. Below this kind of circumstance, error weaveform is not periodic completely; But, appearance meets wrong whole to repeat with regular means it seems that appear. Namely, input signal has twice inside a cycle repeat. The 2 harmonic point that this indicates to the error is being inputted has very strong weight. For better visualize this, this graph returns scale 2.22 KHz (2 harmonic) sine wave. If what you see, sine wave makes the trend of bodily form shape at error weaveform approximately.

Right nonlinear answer output to undertake fast Fourier alternates (FFT) , we get a picture 4 medium spectrum, show DC comes only among them 50 KHz limits.

Graph 4.  Show arrive from DC inside 50 KHz limits nonlinear the plot that answers output [click zoom] .

The main frequency weight that FFT result verifies 2 times to harmonic dispute linear is answered. Be worth what carry is, the frequency of main harmonic heft depends on the INL appearance of ADC. To the graph 1 is shown nonlinear (call arched INL sometimes) , 2 harmonic is main harmonic. To S form INL, 3 harmonic is the main frequency heft of the error. Concerned INL appearance is right D/A converter (DAC or digital-to-analogue converter) the discussion of the influence of spectrum, consult please the article.
 
Break the dependency between ADC error and input

If we add to the input relative to bigger random signal, make the integral input of ADC is in with uncertain means of ADC transfer function different rank jump between change, we can reduce determinism on certain level lack fidelity. This concept is shown 5 times like the graph.

Graph 5.  Indication ADC transfer function rank the fundamental picture that during jumping, ADC input changes. The picture is offerred by Analog Devices

Add random signal (or shake signal) hind, given the input always is not changeover is identical output n. Accordingly, although the input is constant, the error also can change along with time. For example, the consideration uses the input of 6 LSB at the graph 1 medium transfer function. If did not shake, the error is 3 LSB from beginning to end. Consider shaken case now. Shake suppose signal now and then be equal to 2 LSB. Be in 2 LSB place, nonlinear the error turns into 0. Because the error is in 0 and change between 3 LSB, because of this and did not shake photograph of become enamoured condition to compare, error average is reduced somewhat. This simple case was revealed shake how to eliminate input and nonlinear the dependency between the error, reduce determinism thereby lack fidelity. Shake come true through making the DNL error of converter comes from region or randomization this.
 
Communication system shakes technology

Shake the technology is particularly useful in communication system. To a lot of communication application, the input can be far the small signal under ADC full span. This small signal is used opposite a few ADC code. If these code show bigger DNL error, output will include the harmonic that showing lack fidelity.
Ask an attention, to full span (or big) signal, DNL error is in going up somehow is inherent and average. The reason is all code that big signal can implement ADC. Accordingly, fall when signal extent when coming to be worth 20 DB under full span, the ADC that has SFDR of 88 DBFS full span may offer the SFDR of 80 DBFS only. Below this kind of circumstance, shake the SFDR function that the technology may conduce to us maintaining ADC below low signal level. What should notice is, because input n is very small, we are OK will shake signal adds an input and ADC of won’t excessive drive.
 
ADC noise — are we to be in lose information?

You may ask: Is we join bigger noise in inputting signal to lose information? The answer is information appeared to be lost in time domain. However, handle a technology through choosing noise signal and signal appropriately, we can rebuild original message. A kind of solution is impair the excellence of shakes. Below this kind of circumstance, the figure 5 medium fundamental pictures compile the figure below instead (graph 6) .

Graph 6. Subtration shakes graph. The picture is offerred by Analog Devices

In subtration method, the noise that introduces an input adds output with contrary polarity, shake what systematic output carries moving noise to clear completely thereby. Another kind of when use in communication system interesting technology is to use frequency composition to need the tape noise besides signal bandwidth in place. The zonule of hundreds of KHz is wide to shaking signal normally enough. Of the noise outside the belt two likelihood the position is dc around or slightly under Nai Kui this special frequency (F S /2, among them F S is sampling frequency) . In can use at shaking one of areas of these two frequency are not used in the most communication system of the purpose. Below this kind of circumstance, can divide easily in output end filter shake.
 
Play the ADC that we assume

Let us use a figure 1 medium transfer function will research this kind of technology. For this, the wave of 1.11 KHz sine that we use extent to be 7.5 LSB for 2 LSB and DC value to this ADC. What such input can carry out ADC is intermediate code. 0 Hz of prep above is omitted is like a graph to the output spectrum of 30 KHz limits 7 are shown.

Graph 7.  Another give typical examples of wave of 1.11 KHz sine pursues, 0 Hz of summary prep above reachs its spectrum range 30 KHz [clicks zoom] .

To this specific input, have a few different harmonic weight, but remain harmonic basically 2 times. the value changeover is decibel, we discover SFDR is 17.47 DBc. Shake for generation signal, we can use Matlab ” Randn ” function will arise have 2 LSB RMS (root mean square) broadband gauss noise. Application is the belt of 100 KHz to connect filter for central bandpass with 1.94 MHz, broadband noise is by changeover shake under the tape of F S /2 slightly. Shake following graphs show the spectrum of signal 8 times.

Graph 8.  Shake the spectrum of give typical examples of signal [click zoom] .

Because shake,the belt that signal is primitive noise is restricted version, we can use the following equality to shake certainly the variance of signal:
 
V A R I A N C E O Of D I T H E R = F I L T E R B And W I D W I D T H F S / 2  Noise Variance of × of _ _ _ _ _ _ _ _ Variance Of Dither=Filter Bandwidthfs/2 of variance of × No I S E
 
Era joins a number, we get:
 
4=0.2 of × of 4 = 0.2Variance Of Dither=100 KHz2 MHz of × of Va R I A N C E Of D I T H E R = 100 K H Z 2 M H Z _ _
 
Take the square root of this value, shake the RMS of signal is 0.45 LSB. Shaken peak peak value can estimate for 6.60.45 = 2.97 LSB (RMS gauss noise is multiplied it is peak peak value with 6.6 changeover) . Ask an attention, shaken peak peak value is enough small, ADC of won’t excessive drive. After application shakes, we obtain spectrum of the following output (graph 9) .

Graph 9.  Application shakes the output spectrum after RMS [click zoom] .

Can see, harmonic is being shown restrain. the value changeover is decibel, we obtain the SFDR of 27.9 DBc, with did not shake photograph of become enamoured condition than raising 10.43 DB. Shake restrain harmonic heft through distributing signal stray in background noise.
 
The test result of real world ADC — ADC3424

The graph below the 10 output spectrum that showed ADC3424 is inputted to 70 MHz.

Graph 10.  The output spectrum of the ADC3424 when 70 MHz is inputted. The picture is offerred by heart state apparatus

ADC3424 is offerred shake the function serves as in-house character. After shutting interior to shake, SFDR is 91 DBc. However, shake as interior be activationed, stray diffuses in background noise, and SFDR increases to 99 DBc.
 
Shake technical limitation

Can show those who improve ADC SFDR is proper shake level depends on the framework of specific ADC and other property. The improvement of SFDR still depends on the extent that inputs signal and shaken extent. Still should notice, exceed certain noise level, SFDR won’t show improvement possibly. It is with the AD6645 of Analog Devices exemple. This equipment uses multistage framework. To the ADC framework of this kind of type, DNL error is had repeat pattern, when and had swept ADC when the input inputting limits, there are a few aiguilles in DNL graph. The graph below 11 showed AD6645 inputs the DNL graph inside limits in one of fraction.

Graph 11.  AD6645 inputs the DNL graph inside limits in one of fraction. The picture is offerred by Analog Devices

To AD6645, aiguille every 512 LSB appear. Via the experiment discovery suits this of specific ADC shake n is peak value of 1024 LSB peak or 155 LSB RMS. Application is bigger shake won’t show the SFDR that improves AD6645. To this ADC, shaken peak peak value is equal to two DNL double what code is apart from between aiguille. But, we cannot conclude this is the general regulation of all multistage ADC.

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