2nd Order CIFB Dither Chaotic Sigma Delta Modulator

by allenlu2007

 

前文主要 focus on MASH111 架構的 dither chaotic sigma delta modulator (DCSDM).

本文討論 2nd order chaotic sigma delta modulator (CSDM) 和 2nd order DCSDM.

 

General Form

首先考慮 2nd SDM CIFB (cascaded integrator feedback) form 如下圖。

STF = b D    (let z^-1 = D)

NTF = (1-aD)(1-bD)

以上的推導可用 Mason’s Gain Formula (MGF). 

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(A) 先從最普通 2nd order SDM 開始如下 (a=b=1).

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as expected, NTF has two zeros at origin.

STF = D  (D = z^-1)

NTF = (1-D)^2  

 

(B) 再來考慮 leaky integrator or exponential integrator (b=a)

First type (two leaky/exponential) integrator.  NTF 沒有 zero, 不考慮使用。

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(C) Second type (one leaky/exponential integrator + one integrator), (a=1)

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(D) Third type (one integrator + one leaky/exponential integrator), (b=1)

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Comparison

同樣考慮 DC = 0, 0.125, 0.25, 0.5, 0.75, 0.875 cases:

 

一般的 2nd order SDM: Type (A)

/Users/alu/work/matlab/simulink/sdm/sdm_mash211_v1.slx

結果都是 spurs, completed failed!

 

Type (C)

加上 aa=-1e-6;  K=0

DC=0

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DC=0.125

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DC=0.25

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DC=0.5

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DC=0.75

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DC=0.875

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Type C: Chaotic SDM:  aa=+0.05  K=0

DC=0

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DC=0.125

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DC=0.25

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DC=0.5

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DC=0.75

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DC=0.875 (explode!!)

 

Dither SDM:  aa=-1e-6  K=1-DC with HPF noise

DC=0

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DC=0.125

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DC=0.25

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DC=0.5

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DC=0.75

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DC=0.875

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Dither SDM:  aa=+0.0  K=1-DC with uniform random noise

DC=0

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DC=0.125

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DC=0.25

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DC=0.5

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DC=0.75

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DC=0.875

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Dither Chaotic SDM:  aa=+0.05  K=1-DC with uniform random noise

DC=0

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DC=0.125

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DC=0.25

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DC=0.5

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DC=0.75

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DC=0.875 (explode)

 

Dither Chaotic SDM:  aa=+0.05  K=1-DC with HPF noise

DC=0

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DC=0.125

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DC=0.25

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DC=0.5

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DC=0.75

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DC=0.875 (explode!)

In summary:  The best combination is cocktail DCSDM with uniform random noise!!

  

Type (D): Integrator first (b=1)

DC = 0, 0.125, 0.25, 0.5, 0.75, 0.875

Chaotic SDM (K=0, aa=+0.05)

DC=0

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DC=0.125

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DC=0.25

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0.5

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DC=0.75

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DC=0.875 (explode)

 

Dither Chaotic SDM (DCSDM) with uniform noise (K=1-DC; aa=+0.05)

DC=0

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DC=0.125

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DC=0.25

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DC=0.5

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DC=0.75

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DC=0.875 (explode)

 

In summary type C is better than type D, i.e. exponential integrator first seems to be better than later.

 

結論:

Type A:  SNR 最好 (NTF two zeros), 但 terrible spurs (periodical) at certain DC level (0, 0.125, …). 可以用少許 leaky integrator 改善 (aa=-1e-6), 或是 dithering 可改善,但仍有嚴重 spurs 問題。

Type B: SNR 最差 (NTF has no zero).  另外 dynamic range 嚴重收縮。不建議使用。

Type C: SNR 中間 (NTF has one zero).  aa=+0.05 仍有很大 spurs, 再加上 uniform noise dithering, 似乎可大幅改善 spurs.  Dynamic range 仍有收縮 (DC=0.875 failed, DC=0.75 OK).  目前似乎是最好的解法。

Type D: SNR 和 type C 相同。但 spurs 比 type C 大。加上 uniform noise dither 也可大幅改善 spurs.  Dynamic  range 亦收縮如同 type C.  

Uniform noise dithering 似乎比 HPF noise dithering 有效, not sure why? 我 check 了 random noise generate HPF (sdm_mash211_v3) and LPF (sdm_mash211_v4) 結果和 uniform random noise dither 效果類似。

 

Next Step

1. resonator type work better or worse?  Try CRFB 架構 later. 

2. how to saturation integrator 2nd –> 1st order to expand dynamic range??

   似乎 CIFF 才能用 saturation integrator 方法 extend DR.  CIFB 只要一個 integrator saturate 就掛掉。

請參考 sdm_ciff2_v1 simulation result.   It works for CIFF architecture.

3. Dither chaotic SDM doesn’t seem to go too far. 

 

 

 

 

 

 

 

 

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