Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Numerical Analysis of Asymmetric Differential Inductors

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

Tokyo Institute of Technology, Japan

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

2

Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Contents

●Background

●Matrix-Decomposition Technique

●Simulation & Measurement Results

●Summary

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Background Miniaturization of CMOS process →Difficulty of characterize on-chip inductors

Degradation of circuit performances

●On-chip differential inductor Used for LC-VCO, differential LNA, Mixer… Mismatch between left and right halves degrades circuit performances.

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

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

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 parasitic components

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

)(2

diff

diff diffdiffdiff

222113121123

1323

diff

diff diff

Z ZQZL

YYYYYY YY

I VZ

==∴

−−− +

==

　　 ω

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

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Proposed method by 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.

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

6

Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Contents

●Background

●Matrix-Decomposition Technique

●Simulation & Measurement Results

●Summary

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

7

Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Overview subcmeas YYY +=

vYYi meas 3

2

1

meas

3

2

1 =

⎟⎟ ⎟

⎠

⎞

⎜⎜ ⎜

⎝

⎛ =

⎟⎟ ⎟

⎠

⎞

⎜⎜ ⎜

⎝

⎛ =

v v v

i i i

1 2

sub1 sub3 sub2

1 2

3

1 2

3

1 2

3

12

Yc: Inductor core

Ysub: Interlayer-dielectric and Si substrate

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

●Yc is calculated from Ymeas and Ysub ●Zcore is derived from Yc by converting matrix

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Calculation of Ysub Voltages of each port are equal

⎟⎟ ⎟

⎠

⎞

⎜⎜ ⎜

⎝

⎛ +

⎟⎟ ⎟

⎠

⎞

⎜⎜ ⎜

⎝

⎛ =

⎟⎟ ⎟

⎠

⎞

⎜⎜ ⎜

⎝

⎛ =

⎟⎟ ⎟

⎠

⎞

⎜⎜ ⎜

⎝

⎛

a

a

a

sub

a

a

a

c

a

a

a

meas

3

2

1

v v v

v v v

v v v

i i i

YY

Y

meas33meas32meas31sub3 yyyy ++=

Ymeas

Yc

Ysub

→No current flows through zn

=0

⎟⎟ ⎟

⎠

⎞

⎜⎜ ⎜

⎝

⎛ =

sub3

sub2

sub1

sub 00

00 00

y y

y Y

meas13meas12meas11sub1 yyyy ++=

meas23meas22meas21sub2 yyyy ++=

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Conversion of matrix Yc to Zcore subsmeac YYY −= ′

Matrix Yc is converted into matrix Zcore

zcorez 212

121 core iZvZ =⎟⎠

⎞ ⎜ ⎝ ⎛ −

−= 　　zMj Mjz

ω ω

cY

⎟ ⎠ ⎞

⎜ ⎝ ⎛=⎟

⎠ ⎞

⎜ ⎝ ⎛=⎟

⎠ ⎞

⎜ ⎝ ⎛

− −=⎟

⎠ ⎞

⎜ ⎝ ⎛=

2

1

2

1 z

32

31

2

1 z i

i i i

vv vv

v v

z

z

z

z iv 　

vYYi c 3

2

1

c

3

2

1 =

⎟⎟ ⎟

⎠

⎞

⎜⎜ ⎜

⎝

⎛ =

⎟⎟ ⎟

⎠

⎞

⎜⎜ ⎜

⎝

⎛ =

v v v

i i i

Obtain converting matrix A and B

e.g.) 1 2

1 23

z1 z2

1 23

1 23

z1 z2

12

Define Zcore by 2×2 matrix

⎟ ⎠ ⎞⎜

⎝ ⎛=⎟

⎠ ⎞⎜

⎝ ⎛

− −= 0

0 1 0

0 1

1 1

1 0

0 1 　　　　　 BA

BT can be A* AA*=I

BiiAvv == zz 　

1 ccore *)(

−= ABYZ c

c

BYZA vBYZBiZAv

core

corecore

=

==

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

10

Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Contents

●Background

●Matrix-Decomposition Technique

●Simulation & Measurement Results

●Summary

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

11

Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

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

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Simulation model

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

x

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Simulation Result

∆x (µm)

0 0 50 100 150

2

4

6

8

10

12

L m

is m

at ch

(% ) 1 turn

2 turn

200

3 turn

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

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Measurement

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

0.18 µm Si-CMOS

AsymmetricSymmetric

VNA : 4port 10MHz-67GHz E8361A+N4421BH67(Agilent)

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

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Measurement Result

1.0 0.5

0.6

0.7

0.8

Frequency [GHz]

In du

ct an

ce [n

H ]

0.5

0.6

0.7

0.8

In du

ct an

ce [n

H ]

10 20 1.0 Frequency [GHz]

10 20

left-half right-half

left-half right-half

Mismatch1.5% 4.0%

Symmetric Asymmetric

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

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Contents

●Background

●Matrix-Decomposition Technique

● Simulation & Measurement Results

●Summary

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

17

Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

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

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

18

Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Q factor

AsymmetricSymmetric

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

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Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

Extract Ymeas’ Ymeas

・Zshort and Yopen are removed by Open-Short de-embedding 1

openshort 1

openmeassmea )()( −−

′ −−