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  • 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.

    5

    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.

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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.

    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.

    8

    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.

    9

    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.

    12

    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.

    15

    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.

    16

    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.

    19

    Matsuzawa & Okada Lab. Matsuzawa & Okada Lab.

    Extract Ymeas’ Ymeas

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

    openshort 1

    openmeassmea )()( −−

    ′ −−