dec. 16, 2016 dac linearity improvement with …...2017/03/02 · using latin and magic squares...
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Gunma University Kobayashi Lab
DAC Linearity Improvement With Layout Technique
Using Latin and Magic Squares
Dec. 16, 2016
Dan YaoYifei Sun, Masashi Higashino, Takuya Arafuna, Haruo
Kobayashi
Gunma University
第7回電気学東京支部会栃木・群馬支所合同研究発表会足利工業大学 （2017/3/2,3）
ETG-17-85ETT-17-85
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Contents
l Research Objective
l Segment Type DA Converter
l Characteristic of Variation in Circuit Element
l Proposed Layout Method
- Magic Square
- Latin Square
l Summary
2017/3/4
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Contents
l Research Objective
l Segment Type DA Converter
l Characteristic of Variation in Circuit Element
l Proposed Method
- Magic Square
- Latin Square
l Summary
2017/3/4
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Research ObjectiveResearch Background l Requirements for electronic equipment -High speed -High precisionOur Approach l Improvement the linearity of a segmented DAC
-Unit current cells. -Layout based on Magic and Latin Squares
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Analog
DAC
Digital
Digital-to-Analog Converter
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Contents
l Research Objective
l Segment Type DA Converter
l Characteristic of Variation in Circuit Element
l Proposed Method
- Magic Square
- Latin Square
l Summary
2017/3/4
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Segment Type DAC Configuration
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Segmented DAC
ü Binary (Lower bits)
- Small circuit- Large glitch - Large mismatch effect & Large nonlinearity
ü Unary (Upper bits)
- Large circuit- Small glitch- Small mismatch effect & modest linearity
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Segment Type DAC (7-bit case)
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(0000100)
ex In case digital input =4
Regular layout of unit current cells
8I=I18I=I15 8I=I16
I14 I15 I16
I11 I12I10
I13
I1 I2 I4I3
I7 I8
I9
I5 I6
DECODER
DE
CO
DE
R
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Contents
l Research Objective
l Segment Type DA Converter
l Characteristic of Variation in Circuit Element
l Proposed Method
- Magic Square
- Latin Square
l Summary
2017/3/4
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Characteristic of Variation in Circuit Element
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Uni
t Cur
rent
Cel
lU
nit C
urre
nt C
ell
All unit current cellsI1,I2...I16 are NOT identical
Manufacturing variation
Systematic variations
Unit current value depends on its layout position
Linear error case
Quadratic error case
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Characteristic of Variation in Circuit Element
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Linear Error
Quadratic Error
Joint Errors
Uni
t Cur
rent
Cel
l Joint error case
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Contents
l Research Objective
l Segment Type DA Converter
l Characteristic of Variation in Circuit Element
l Proposed Method
- Magic Square
- Latin Square
l Summary
2017/3/4
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What is Magic Square ?
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• Classical mathematics• Origin from Chinese academia• “Constant sum” characteristics• Varieties of magic squares
Constant Sum Row, column, diagonal
Magic Square has good balanceto cancel the systematic mismatch effects of current cells
13/4216x16 Current Cells Layout
Current cell systematic error
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A: Magic square of the left figureB: 45 ° counterclockwise rotation
Even if one side is removed from the outside, it does not lose compatibility
u Concentric Magic Square
Random selection of current cells based on Magic Square layout
Current cell system
atic error
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16x16 Current Cell Layout Details
u Concentric Magic Square
l algorithm
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16x16 Current Cell Layout Details
u Concentric Magic Square
l algorithm
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16x16 Current Cell Layout Details
u Concentric Magic Square
l algorithm
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16x16 Current Cell Layout Details
u Concentric Magic Square
l algorithm
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18/42Simulation Results (Linear Error Case)
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u Concentric Magic Squareü Linear Error (Current Cell Systematic Mismatch)
Inte
gral
Non
-Lin
earit
y
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u Concentric Magic Square
ü Quadratic Error (Current Cell Systematic Mismatch)
Simulation Results (Quadratic Error Case)
Inte
gral
Non
-Lin
earit
y
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ü Joint Error
Magic square is better
u Concentric Magic Square
Linear >Quadratic case
Simulation Results (Joint Error Case)
Uni
t Cur
rent
Cel
lIn
tegr
al N
on-L
inea
rity
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ü Joint Error
Random Walk is better
u Concentric Magic Square
Linear < Quadratic case
Simulation Results (Joint Error Case)
Uni
t Cur
rent
Cel
l
Inte
gral
Non
-Lin
earit
y
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What is Latin Square ?
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Leonhard Euler(1707-1783)Swiss mathematician, physicist
l Each symbols occurring exactly once in each row and columnl In the Latin square , If the first row is(1,2,3,,,n) and the first column is (1,2,3,,,n), it is a standard Latin square
Example:
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Latin Square Layout Algorithm ualgorithml Latin Square
l Common Centroid
l Unary Layout
l Linear Error
l Quadratic Error
u Compare
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u Standard Latin squareü Linear Error
Simulation Results (Linear Error Case)
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Maximum
Latin Square:0.244
Common Centroid:0.197
Unary Layout:1.70
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u Standard Latin squareü Quadratic Error
Simulation Results (Quadratic Error Case)
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Maximum
Latin Square:0.0138
Common Centroid:0.0130
Unary Layout:0.0530
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Summary
l Research Objective
l Segment Type DA Converter
l Characteristic of Variation in Circuit Element
l Proposed Method
- Magic Square
- Latin Square
l Summary
2017/3/4
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Summary
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Unary DAC linearity improvement l Magic square layout -Linear error is larger, Magic square is suitable. -Quadratic error is larger, random walk is suitable.l Latin square layout -Latin square can improve selecting current cells of common centroid.
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Final Statement
温故知新Classical mathematics can contribute modern technology.