大豆营养成分A MASH111All-Digital Delta-Sigma Modulator
with Hybrid2nd-Order Shaped Dithering for Fractional-N Frequency Synthesizers
Jinbao Lan*1,Tao Liu1,Xingfa Huang2,Liang Li2,Yuxin Wang2
1Sichuan Institute of Solid State Circuits,Chongqing,400060,China
2Science and Technology on Analog Integrated Circuit Laboratory,Chongqing,400060,China
*Email:
Abstract—This work propos a hybrid2nd-order shaped dithering method for the MASH111all-digital delta-sigma modulator.The propod method injects a hybrid1st-order shaped dither signal into the2nd and3rd stages of the MASH111 delta-sigma modulator,enables it to avoid any tonal spur in its output quantization noi power spectrum,and at the same time alleviates the influence of the dither signal in the low frequency zone by hybridly shaping it to the2nd order. Keywords—Dither;MASH;delta-sigma modualtor;fractional-N frequency synthesizer.
I.I NTRODUCTION
Nowadays,the delta-sigma fractional-N frequency synthesizer is widely adopted in wireless transceiver chips. The block diagram of a typical delta-sigma fractional-N frequency synthesizer is shown in Fig.1,from which it is easy to find that the all-digital delta-sigma modulator is one of its key building blocks.Usually,the delta-sigma modulator quantizes the fraction part of the frequency control word (FCW)into integer and at the same time shapes the concomitant quantization noi to high frequency zone.The output(Y)of the delta-sigma modulator is a pudo-random number quence,which is ud to change the instantaneous division factor of the multi-modulus frequency divider,so as to achieve the desired long-term average fractional frequency
division.
Figure1.A typical delta-sigma fractional-N frequency synthesizer.
By now,many different delta-sigma modulator architectures have been propod for fractional frequency synthesis applications,among which the3rd-order multistage-noi-shaping architecture(MASH111DSM)is the most popular one[1].The schematic of a classical pipelined n-bit MASH 111DSM is shown in Fig.2.It consists of a cascade of three n-bit1st-order DSM’s and a delta path.The popularity of MASH 111DSM results from its following merits:(1)its circuit is quite simple,only a few adders and registers are needed;(2)it is unconditionally stable for any input in the range of[0,1), which avoids any output frequency gap resulting from modulator instability;(3)its output quantization noi is only 3rd-order shaped,so a relatively simple and easy4th-order pha-locked loop is enough to filter out the quantization noi that is pushed into the high frequency zone;(4)if its inner quantization nois(E1,E2and E3)are random enough to be approximated as white noi,then its output quantization noi power spectrum will be smooth and spur-free,which means that the synthesizer will not suffer from fractional
spurs.
is to ret the least-significant bit(LSB)of the n-bit error register in the first stage(S1)to1whenever the input X changes.This solution was first empirically found by the designers of[2]and was then mathematically verified by the work of[3,4].It was shown that after adopting this“retting LSB to1”solution,an N-bit MASH111DSM gains a guaranteed output quence length of2n+1and its output quantization noi power spectrum is totally spur-free. Except for the“retting LSB to1”method,dithering is another effective method to randomize the inner quantization nois.In the recent work of[5],the output bit stream of an m-bit linear feedback shift register(LFSR)is ud to replace the LSB’s of the inputs to the2nd and3rd stages of a MASH111 DSM,so as to achieve the goal of randomizing the quantization nois sufficiently without any influence on the DC input signal X.Fig.3shows a MASH111DSM adopting the“LFSR dithering”method of[5],in which the LFSR dither signal is inputted to the carry-in ports(Cin)of the2nd and3rd stages for simplifying the design process.The z-domain linear mathematical model of this MASH111DSM can be deduced as follows:
Y1(z)=X(z)+(1–z–1)E1(z)(1) Y2(z)=–z–1E1(z)+(1–z–1)E2(z)+X d(z)/2n(2) Y3(z)=–z–1E2(z)+(1–z–1)E3(z)+X d(z)/2n(3) =>Y(z)=z–2Y1(z)+(1–z–1)[z–1Y2(z)+(1–z–1)Y3(z)]
=z–2X(z)+(1–z–1)3E3(z)+(1–z–1)X d(z)/2n(4) Equation(4)shows that for the MASH111DSM of Fig.3, its output consists of three parts:the input signal with two clock periods delay z–2X(z),the3rd-order shaped quantization noi of the3rd stage(1–z–1)3E3(z)and the1st-order shaped dither signal(1–z–1)X d(z)/2n.The theoretical proof and experimental results of[5]both demonstrate that its propod dithering method is quite effective in avoiding tonal spurs and achieves a smooth3rd-order shaped output quantization noi power spectrum.However,as(4)indicates,the added dither signal is only1st-order shaped when it pass through the MASH111DSM,which increas the noi power level in the low frequency zone.As a result,the clo-in pha noi performance of the synthesizer will potentially be
degraded.
3.The MASH[5].
In this work,we propo a hybrid2nd-order shaped dithering method for MASH111DSM.The propod method not only keeps the outstanding randomization effect of the“LFSR dithering”method,but also reduces the influence of the added dither signal in the low frequency zone.In Section II the propod method will be explained in detail.In Section III experiment results of MASH111DSM’s using the three different quantization noi randomization methods will be demonstrated and their performance will be compared.Finally a conclusion is given in Section IV.一语定乾坤
II.H YBRID2ND-O RDER S HAPED D ITHERING
The schematic of a MASH111DSM with our propod hybrid2nd-order shaped dithering method is shown in Fig.4. Comparing with the“LFSR dithering”method of[5],we just add a few simple digital circuits to process the output bit stream of the m-bit LFSR before it is fed to the carry-in ports of the2nd and3rd DSM stages.The hybrid dither signal we finally get is:
X h(z)=(1–z–1)X d(z)+1/4+(1–z–1)E d(z)
=(1–z–1)[X d(z)+E d(z)]+1/4(5) Replacing the X d(z)of(4)with(5),we can get the output of our propod MASH111DSM as follows:
Y(z)=z–2X(z)+(1–z–1)3E3(z)+(1–z–1)X h(z)/2n
=z–2X(z)+(1–z–1)3E3(z)食品安全追溯制度
+(1–z–1)2[X d(z)+E d(z)]/2n+(1–z–1)*1/2n+2(6) Equation(5)and(6)actually reveal our key design idea. Firstly we u a simple differentiator to get the output of the m-bit LFSR1st-order shaped.As the differentiation result is a 2-bit signed number,which does not match the1-bit unsigned carry-in inputs of the2nd and3rd DSM stages,we then add1to it so as to eliminate its sign,and finally we u a2-bit1st-order DSM to compress the2-bit unsigned data quence into the usable1-bit1st-order shaped dither signal.Obviously,the dither signal we generated contains not only the LFSR output part X d(z)but also an extra quantization noi part E d(z). That’s the first reason why the propod dithering method is called“hybrid”.On the other hand,after passing through the delta path of the MASH111DSM,the injected1st-order shaped dither signal is differentiated once again,which makes it finally prent a2nd-order shaped power spectrum in the output of the MASH111DSM.The fact that the two differentiation operations happen at different gments of the propod DSM is referred as t
he cond reason for its being called“hybrid”.Another interesting characteristic of our propod DSM is that there ems to exist an extra component (1–z–1)*1/2n+2in its output,which results from the1we added for sign elimination.However,as1–z–1=0at DC and the added 1is constant and only contains power at DC,the component (1–z–1)*1/2n+2actually equals0,which means it does not influence the final output of the propod DSM.
广式蒸排骨的做法
S1
S2
III.P ERFROMANCE E VALUATION
In order to compare the performance of different DSM quantization noi randomization methods,we implement three17-bit MASH111DSM’s using Verilog HDL at the RTL level.The first DSM adopts the“retting to1”method of[2],the cond one adopts the“LFSR dithering”method of [5]and the third
十大洞天one adopts our propod hybrid2nd-order shaped dithering method.The LFSR’s in the last
two DSM’s are both7-bit wide.Thorough logic simulations are carried out for various input conditions,and220samples of each DSM output are collected and then analyzed with Discrete Fourier Transformation,assuming a sampling frequency of20MHz. The resultant discrete output quantization noi power spectra are then ud for performance comparison.
Fig.5and Fig.6are two examples of the enormous experiment results.They are picked out for demonstration becau their inputs are respectively0and0.5,which are both spur-prone input conditions for conventional MASH111DSM. Apparently,the three randomization methods all work well enough to avoid any tonal spur in their output quantization noi power spectra.And the“LFSR dithering”method and our propod hybrid dithering method are better than the “retting to1”method in the high frequency zone becau their output quantization noi power are about6dB lower, which implies their output quences are about4times as long as that of the“retting to1”method[4].In the low frequency zone,the influences of the added dither signals are obvious.As we have expected,the“LFSR dithering”method prents a1st-order shaped low-frequency dither noi and our propod hybrid dithering method prents a2nd-order shaped low-frequency dither noi.Moreover,it can be en that the low-frequency noi of our propod hybrid dithering method is much lower than that of the“LFSR dithering”method, which proves the superiority of our method.Figure5.The output quantization noi power spectra of the three MASH111
delta-sigma modulators for X=0.
Figure6.The output quantization noi power spectra of the three MASH
111delta-sigma modulators for X=0.5.
IV.C ONCLUSION
This paper has demonstrated that a hybrid1st-order shaped dither signal can be injected into the2nd and3rd stages of the MASH111delta-sigma modulator,which enables the modulator to avoid any tonal spur in its output quantization noi power spectrum,and at the same time the influence of the dither signal in the low frequency zone is alleviated by hybridly shaping it to the2nd order.
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