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Matsuzawa& Okada Lab.Matsuzawa& Okada Lab.

Numerical Analysis ofAsymmetric Differential Inductors

Masaki Kanemaru, Daisuke Imanishi, Kenichi Okada, and Akira Matsuzawa

Tokyo Institute of Technology, Japan

2008/12/18 M. Kanemaru, Tokyo Tech.

2


Contents

●Background

●Matrix-Decomposition Technique

●Simulation & Measurement Results

●Summary


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BackgroundMiniaturization of CMOS process→Difficulty of characterize on-chip inductors

Degradation of circuit performances

●On-chip differential inductorUsed for LC-VCO, differential LNA, Mixer…Mismatch between left and right halvesdegrades circuit performances.

Accurate modeling of on-chip symmetric inductor→ Extract of asymmetric parameters


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Symmetric inductor analysis

•3-port symmetric inductor analysis in various operation modes [1]-Circuit parameters are extracted by numerical optimization-Symmetry is assumed in the parameters

•Asymmetric properties are estimated from Y11 and Y22 [2]-The difference is involved in only difference in shunt parasiticcomponents

)Re()Im()Im(1)()(

)(2

diff

diffdiffdiffdiff

222113121123

1323

diff

diffdiff

ZZQZL

YYYYYYYY

IVZ

==∴

−−−+

==

　　ω

[1] K. Okada, et al., EuMC, Oct. 2007, pp. 520– 523. [2] Y. Aoki, et al., EuMC, Oct. 2007, pp. 339–342.


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Proposed methodby Matrix-Decomposition Technique

Extract π−type equivalent circuit3port S-parameter

port3(C.T.)

port1 port2

・Physically reliable parameters can be extracted. ・The mismatch can be accurately evaluated.


6


Contents

●Background



●Summary


7


Overviewsubcmeas YYY +=

vYYi meas

3

2

1

meas

3

2

1=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

vvv

iii

1 2

sub1 sub3 sub2

1 2

3

1 2

3

1 2

3

12

Yc: Inductor core

Ysub: Interlayer-dielectricand Si substrate

●All ports have common voltagesYc can be ignored → Ysub is calculated from Ymeas

●Yc is calculated from Ymeas and Ysub

●Zcore is derived from Yc by converting matrix


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Calculation of YsubVoltages of each port are equal

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

a

a

a

sub

a

a

a

c

a

a

a

meas

3

2

1

vvv

vvv

vvv

iii

YY

Y

meas33meas32meas31sub3 yyyy ++=

Ymeas

Yc

Ysub

→No current flows through zn

=0

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

sub3

sub2

sub1

sub00

0000

yy

yY




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Conversion of matrix Yc to Zcoresubsmeac YYY −= ′

Matrix Yc is converted into matrix Zcore

zcorez212

121core iZvZ =⎟

⎠⎞

⎜⎝⎛−

−= 　　zMjMjz

ωω

cY

⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛

−−=⎟

⎠⎞

⎜⎝⎛=

2

1

2

1z

32

31

2

1z i

iii

vvvv

vv

z

z

z

z iv 　

vYYi c

3

2

1

c

3

2

1=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

vvv

iii

Obtain converting matrix A and B

e.g.)1 2

1 23

z1 z2

123

1 23

z1 z2

12

Define Zcore by 2×2 matrix

⎟⎠⎞⎜

⎝⎛=⎟

⎠⎞⎜

⎝⎛

−−= 0

010

01

11

10

01 　　　　　 BA

BT can be A* AA*=I

BiiAvv == zz 　

1ccore *)( −= ABYZ

c

c

BYZAvBYZBiZAv

core

corecore

=

==


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Contents

●Background



●Summary


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Mismatch of ground loop

1

3

2

GND

1 2

GND

3

Even

Odd

Flux loss: Only half side Flux loss: Both sides

The inductance mismatch depends on the number of turns.

Each loss is different Mismatch

Each loss is almost equal Mismatch


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Simulation model

・Inductance mismatches are evaluated by the proposed method.・The mismatches are plotted as a function of ∆x.

x


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Simulation Result

∆x (µm)

00 50 100 150

2

4

6

8

10

12

L m

ism

atch

(%) 1 turn

2 turn

200

3 turn

・The mismatch of 2-turn is smaller than 1- and 3-turn ・Increasing ∆x, mismatch decreases


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Measurement

Line width：9µm, Line space:2µmInner diameter:100µm, Turn:3

0.18 µm Si-CMOS

AsymmetricSymmetric

VNA : 4port 10MHz-67GHzE8361A+N4421BH67(Agilent)

Probe : I67-D-GSGSG-150 (Cascade)I67-GSG-150 (Cascade)


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Measurement Result

1.00.5

0.6

0.7

0.8

Frequency [GHz]

Indu

ctan

ce [n

H]

0.5

0.6

0.7

0.8

Indu

ctan

ce [n

H]

10 20 1.0Frequency [GHz]

10 20

left-halfright-half

left-halfright-half

Mismatch1.5% 4.0%

Symmetric Asymmetric

・ Influence of asymmetric ground loop is extracted ・Other reasons to cause asymmetry exist


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Contents

●Background


● Simulation & Measurement Results

●Summary


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Summary

The numerical analysis using the matrix-decomposition technique is proposed

・Physically reliable parameter can be extracted ・The mismatch can be accurately evaluated

Proposed method is applied to 1-, 2-, and 3-turn differential inductors

Influence of asymmetric ground loop can be accurately extracted


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Q factor

AsymmetricSymmetric


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Extract Ymeas’

Ymeas

・Zshort and Yopen are removed by Open-Short de-embedding1

openshort1

openmeassmea )()( −−′ −−−= YZYYZ

1smeasmea−′′ = ZY