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    Mixed-Signal Systems-on-Chip:Architectures and Design Tools

    Alex Doboli, PhD

    Associate Professor

    Department of Electrical and Computer Engineering

    State University of New York, Stony Brook, NY 11794

    Email: [email protected]

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    The Wish List

    A new development paradigm that:

    Much more efficient design methodologies

    Higher Level Of Abstraction For Development

    Exploit design reusability & retargeting

    Frees Designers From Low Level Implementation Detail

    Produces Interoperable And Portable Designs

    Supports Reconfigurability Provides Extensive, and Extensible, Third-Party Device

    Libraries

    Is Self-Documenting

    Is scalable and extensible

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    Research, Entrepreneurial & Educational

    Challenges

    High-level AMS synthesis?

    Stephan Ohr, Synthesis proves to be Holy Grail

    for analog EDA, EE Times, 06/08/1999

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    Research, Entrepreneurial & Educational

    Challenges

    AMS design is art and less science

    Theory? Methodology? How to invent application-

    specific topologies & circuits?

    Architectures?

    Few CAD tools (mostly simulators: SPICE etc.)

    Transistor is not a switch! (modeling)

    Design usually at a low level (transistors, layout)

    Who will develop the architectures & tools?

    Who designs AMS systems? EE/CE/CS/all?

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    Presentation outline

    PSoC: embedded mixed-signal architecture

    Related research at Stony Brook

    Systematic methodology for ADC design Automated circuit modeling

    Education & training

    Conclusions

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    Embedded Mixed-Signal Architectures

    Cypress programmable PSoC mixed-signal SoC

    Main features: Hardware programmability

    Programmable analog blocks

    Programmable digital blocks

    Programmable interconnect

    Programmable I/Os

    Programmable clocks

    Selectable power supply

    Integration as an SoC

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    PSoC Mixed-Signal Architecture

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    Why PSoC-like architectures ?

    PSOC supports/helps:

    Design reusability & retargeting (library)

    Predictable performance (library of models)

    Frees designers from low level implementation(pre-characterized cells)

    Supports Reconfigurability

    Supports extensive, and extensible, third-partydevice libraries

    Is scalable and extensible (programmable

    transceivers, PLLs, software radio)

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    PSoC Mixed-Signal Architecture

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    PSoC Mixed-Signal Architecture

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    PSoC Mixed-Signal Architecture

    Analog blocks are programmable

    Programmable functionality (control registers) Programmable inputs & outputs

    Analog blocks of two types Continuous time blocks

    Switched capacitor blocks (type C and type D)

    Connected to programmable I/O ports

    Programmable interconnect

    Three kind of programmable interconnect

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    Programmable interconnect

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    Programmable CT blocks

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    Programmable SC blocks

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    PSoC Mixed-Signal Architecture

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    Some CAD related Issues

    Higher Level Of Abstraction For Development

    What behavioral descriptions are synthesizable? DAEs, TFs,SFGs?

    How do you correctly mix together continuous time and discretetime descriptions?

    What standard specification notations? VHDL-AMS, Verilog-A,

    MATLAB/SIMULINK, UML? Frees Designers From Low Level Implementation Details

    How do you synthesize a set of DAEs? (application-specifictopologies)

    Does the design work? (circuit modeling)

    CAD tools for transistor sizing and layout (Neoliniar CADENCE)

    Supports Reconfigurability Reconfigurable AMS architectures, reconfigurable ADCs, filters

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    VLSI System Design Laboratory(http://www.ece.sunysb.edu/~vsdlab)

    Lab director: Dr. Alex Doboli,

    Email: [email protected],

    Phone: 631-632-1611

    Lab expertise:

    Embedded mixed-signal systems

    CAD for system&circuit optimization

    Analog circuit modeling IP core integration

    Research funding (since 2001): NSF Center for Design of Analog

    and Digital IC

    AFRL

    NSF ITR DARPA, IBM, DAC, Cypress

    Academic results: 3 PhDs graduated

    3 MS graduated

    19 journal papers

    65 peer reviewedconference papers

    IC Developments: Rhapsody CADtool (ADC design)

    ISIS CAD tool

    (SoC integration)

    SoC design in0.18m process

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    VLSI System Design Laboratory(http://www.ece.sunysb.edu/~vsdlab)

    G. Gielen, R. Rutenber, Computer-Aided Design of

    Analog and Mixed-Signal Integrated Circuits,Proceedings of IEEE, Vol. 88, No. 12, pp. 1825-1852, 2000:

    Recently, a first attempt was presented towards the fullbehavioral synthesis of analog systems from (annotated)

    VHDL-AMS behavioral descriptions.

    A. Doboli, R. Vemuri, "Behavioral Modeling for High-Level

    Synthesis of Analog and Mixed-Signal Systems from

    VHDL-AMS", IEEE Transactions on CADICS, Vol. 22, No.

    11, 2003, pp. 1504-1520. (among the most downloadedpapers in 2005)

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    Rhapsody: Automated design

    of analog and mixed-signal systems

    Topology generation and

    system architecture selection:VHDL-AMS

    specifications:entity aaa is

    end entity;

    Performance

    evaluation

    Circuit and

    interconnect

    models

    Obtained

    performanceConstraint transformation,

    floorplanning and global routing

    Performance

    evaluation(simulation)

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    Rhapsody (snapshots)

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    Benefits

    Quality:- Complements SD toolbox (finding NTF and STF), Cadences

    NeoCircuit (transistor sizing) and NeoCell (layout generation)

    - Produces SD topologies customized to performance specificrequirements

    - less complex, better sensitivity to parameter variations, andlower power consumption

    - Finds 6x-10x more constraint-satisfying solutions thanCircuitExplorer (Synopsis) and NeoCircuit (Cadence)

    Effort:- Designs (including circuit sizing using NeoCircuit and layout using

    NeoCell) can be ready much faster- Designers can focus on more challenging issues, like system

    topology, selecting circuits

    - Can be used by less-experienced designers

    - Prototyping of new applications, e.g., reconfigurable SD ADC

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    Application-specific modulator topologies

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    Application-specific modulator topologies

    The topology is an SFG containing integrators and

    having all signal paths and coefficients of the signal

    paths defined

    A topology differs from another one in terms of

    the type of the integrator

    signal paths definition

    numerical coefficients of the signal paths

    For topology synthesis, they are the control

    parameters and uniquely determine a topology

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    Traditional modulator topologies

    3rd order Delta-Sigma modulator topologies(a) Chain of Integrators with Feedforward Summation

    (b) Chain of Integrators with Feedforward Summation and Local Feedback

    (c) Chain of Integrators with Distributed Feedback

    (d) Chain of Integrators with Distributed Feedback, DistributedFeedforward and Local Feedback

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    Previous work: I

    F. Medeiro, A. Verdu, A. Vazquez, Top-down Design of High

    Performance Delta-Sigma Modulators, Kluwer, 1999

    Designers have toselect anincompletetopology based onexperience

    Coefficient design

    is the only degreeof freedom to beexplored.

    Set integrator types

    Define signalpaths

    Explore coefficientvalues

    An incomplete

    topology is defined

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    Previous work: II

    K. Francken, G. Gielen, A High-level Simulation and Synthesis

    Environment for Delta-Sigma Modulators, IEEE Transactions on

    Computer Aided Design of Integrated Circuits and Systems, Vol. 22,

    No. 8, 2003, pp. 1049-1061.

    Selected incomplete topologies(or complete topologies) are

    stored in a library

    Given design specifications, suchas SNR and DR, the tool selects

    one with the smallest powerconsumption

    Save and selectoptimal solution

    Yes

    No

    Set integrator types

    Define signal paths

    Explore coefficientvalues

    MeetSpecification?

    Previous work: III

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    Previous work: III

    O. Bajdechi, G. Gielen, J. Huijsing, Systematic Design Exploration of

    Delta-Sigma ADCs, IEEE Transactions on Circuits and Systems I, Vol.

    51, No. 1, Jan 2004, pp. 86-95.

    A filter level exploration of the design space

    defined by abstract topology parameters

    implemented using the

    previous design flow

    Subject to sensitivityanalysis for yield

    possible designsolutions

    Several best solutions in

    terms of power consumption

    A li ti ifi d l t t l i

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    Application-specific modulator topologies

    Y. Wei, H. Tang, A. Doboli, "DATE06: Systematic Methodology

    for Designing Reconfigurable Delta Sigma Modulator

    Topologies for Multimode Communication Systems", invited

    paper, IEEE Transactions on CADICS, accepted for publication.

    H. Tang, H. Zhang, A. Doboli, "Refinement based Synthesis of

    Continuous-Time Analog Filters Through Successive DomainPruning, Plateau Search and Adaptive Sampling", IEEE

    Transactions on CAD of Integrated Circuits and Systems, Vol.

    25, No. 8, pp. 1421-1440, August 2006.

    H. Tang, A. Doboli, "High-Level Synthesis of Delta-Sigma

    Modulators Optimized for Complexity, Sensitivity and Power

    Consumption", IEEE Transactions on CAD of Integrated

    Circuits and Systems, Vol. 25, No. 3, pp. 597-607, March 2006.

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    Proposed synthesis methodology

    Define the solution space region with

    all the possible modulator topologies

    Formulate topology synthesis as an MINLP(Mixed-Integer Nonlinear Programming) problem

    Formulate the design requirements as

    symbolic cost functions and solve for the optimal solution

    Advantages:

    Global optimal solution is guaranteed

    The methodology is scalable

    The methodology could be fully automated

    G i t l f 3rd d d l t

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    Generic topology for 3rd order modulator

    adderthetofromtscoefficiendfeedforwarandfeedback:addertheinput tofromtscoefficiendfeedforwar:

    addertheoutput tofromtscoefficienfeedback:quantizertheinput to:

    integratortheofoutputthe:

    th

    jji

    th

    i

    th

    i

    th

    i

    iYtib

    iaY

    iY

    G i t l g f 3rd d d l t

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    Generic topology for 3rd order modulator

    Chain of Integrators with Feedforward Summation

    Generic topology for 3rd order modulator

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    Generic topology for 3rd order modulator

    Chain of Integrators with Distributed Feedback

    Generic topology for 3rd order modulator

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    Generic topology for 3rd order modulator

    Chain of Integrators with Feedforward Summation and Local Feedback

    Generic topology for 3rd order modulator

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    Generic topology for 3rd order modulator

    Chain of Integrators with Distributed Feedback,

    Distributed Feedforward and

    Local Feedback

    Generic topology

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    Generic topology

    (1)1,...,1,0,0

    1,...,1,,...,1,if,01,...,1,,...,1,if,0

    +=

    +==

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    Symbolic TF for generic topology

    Generalize the symbolic expressions for Delta-Sigma

    modulator of any order

    For example, the numerator and denominator

    of of Delta-Sigma modulator of order are:

    Solve the above equation using MATHEMATICA to

    obtain and

    dNTF

    nNTF

    N

    )(

    )(

    zE

    zV

    NTF = )(

    )(

    zU

    zV

    STF =

    N

    NN

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    =

    =

    +

    +

    +=

    N

    i

    N

    i

    KNN

    i

    iiiiiiiiiiii

    KK

    KN

    K

    i

    ii

    K

    N

    K

    K

    N

    K

    n

    ztttC

    tCCNTF

    K

    KKKK

    1 2

    21212211)......)1(

    ...()1(

    ),...,,(),...,,(),...,,(

    1

    1

    1

    0

    1

    KNN

    i

    N

    i

    N

    i

    iiiiiiiiiiii

    KK

    KN

    K

    N

    iii

    K

    N

    K

    N

    K

    N

    N

    j

    N

    j

    N

    jjjjjjjjjjjjj

    N

    ii

    KK

    KN

    N

    i

    N

    j

    N

    j

    jNjjNji

    K

    N

    N

    i

    Nii

    K

    N

    K

    N

    i

    N

    i

    N

    i

    iiiiiiiiiiii

    KK

    KN

    KN

    i

    ii

    K

    N

    N

    K

    K

    N

    K

    d

    ztttC

    tCCatttaC

    ttaCtaC

    tttCtCC

    NTF

    K

    KKKK

    K

    KKKK

    K

    KKKK

    =

    +

    + =

    =

    ++

    =

    +

    +

    =

    =

    +

    +

    ++

    ++++

    +++

    =

    ))......)1(

    ...()1()......

    ...()1(

    ...)......)1(...(()1(

    1 2

    21212211

    1 2

    21212211

    1 2

    2221

    1 2

    21212211

    ),...,,(),...,,(),...,,(

    1

    1

    1

    1

    1),...,,(),...,,(),...,,(1

    1

    ),1(),1(

    2

    2

    1

    1,

    1

    1

    1

    ),...,,(),...,,(),...,,(

    1

    1

    1

    0

    1

    S b li NTF d STF

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    Symbolic NTF and STF

    Complexity of growth of terms is roughly 4N!

    Generally, modulator order is kept below 6~8, thesymbolic expressions scale reasonably well

    MINLP is able to handle large number of

    constraints of different complexity

    Symbolic expressions for other combination of

    integrator types can be readily obtained viavariable substitution

    MINLP problem formulation

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    MINLP problem formulation

    By equating the symbolic TF to the desired TF,3(N+1) equations are obtained with (N+1)(N+2)

    unknowns

    Properties for the symbolic TF:

    All terms are nonlinear expressions of the defined

    coefficient variables No quadratic terms

    This mild nonlinear formulation is suitable to besolved by NLP

    To select the signal paths, binary variables aredefined, so MINLP

    MINLP formulation

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    MINLP formulation

    };1,0{),1(:

    ;0),(:

    ;0)(:

    ),(minimize

    =

    ii

    ii

    i

    ii

    wxsatisfyxtosubject

    wxxhtosubject

    xgtosubject

    wxxf

    Linear constraintsh

    are added considering the complexityof nonlinear product term

    Instead, we formulate h as:

    smallveryiswhereotherwise,0andif1 == iii wxxwx

    ii wxx

    Topology exploration flow

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    Topology exploration flow

    Initialize modulator order

    Initialize combination

    Initialize OSR

    Initialize MAG

    Generate NTF

    Generate and solveMINLP program

    Meet SNR, DR specification

    Save solution

    Go to next combination

    Optimal

    solution

    No

    Yes

    Yes

    SNR, DR specification

    Increaseorder

    More combinations

    IncreaseMAG

    IncreaseOSR

    YesYes YesYes

    No No NoOSR in

    range

    Order

    in range

    MAG in

    range

    Minimumsensitivity test

    Minimumpower test

    Minimumpath test

    Topology refinement

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    opo ogy e e e t

    Scaling => the voltage swings at the output of each

    integrator are within a certain range

    Nonideal blocks in Simulink

    Experiment: 3rd order modulator

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    p

    3rd order Delta-Sigma modulator

    DR>70db

    The topology is able to achieve DR=72db andSNR=67db

    5.1,32

    ,,5.1,3 max

    ==

    ===

    MAGOSR

    VUPN ref

    )6629.0529.1)(6685.0(

    )1994.1)(1(2

    2

    1+

    +=

    zzz

    zzzNTF

    Optimal topology

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    A. Minimum signal path (topology not unique)

    Optimal topology

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    p p gy

    B. Minimum sensitivity

    Sensitivity cost function values are 1.723 and 2.250respectively, with all (good case)

    L. Huelsman, Active and Passive Analog Filter Design, McGraw Hill, 1993

    0.1, ji

    j

    i

    q

    x

    P

    x SS

    Topology from Toolbox

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    Topology from Toolbox

    0.1, 334

    3

    3qt

    q

    a SSSensitivity cost function values is 4.454, with someterms larger than 1.0, e.g.

    R. Schreier, The Delta-Sigma Toolbox 6.0,www.mathworks.com/matlabcentral/fileexchange, Nov 2003.

    Triple-mode continuous-time modulator

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    p

    270kHz14.5/87EDGE190kHz15/90GSM

    615kHz13/80CDMA2000

    1.92MHz11.5/70UMTSBandwidthDR (bits/dB)Mode

    Design

    Specifications

    484028, 325

    6448404

    9664483

    --128962

    GSM-EDGECDMA2000UMTS

    OSR

    OrderDesign

    parameters

    for possible

    candidates

    [1] R. Veldhoven, A Triple-Mode Continuous-Time Modulator With

    Switched-Capacitor Feedback DAC for a GSM/EDGE/CDMA2000/UMTSReceiver, JSSC, Dec 2003.

    Reconfigurable modulator topologies (1)

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    0.5917m10.5316m20.5878m3

    1.3013m2

    1.3009m1

    1.3944m3

    V

    0.0785m1

    0.0442m2

    0.0360m30.0013m3

    0.0024m2

    0.0069m1

    0.3420m1

    0.3605m2

    0.4008m3

    U

    0.1970m1

    0.1667m3

    0.1670m2

    0.7720m3

    0.1552m2

    0.1324m3

    0.1364m1

    0.6244m10.6585m2

    0.7987m1

    0.8988m2

    0.8762m3

    0.6274m1

    0.5261m30.5133m2

    0.4815m3

    0.5159m1,

    m2

    0.4815m3

    m20.5159m1,

    0.1533m3

    0.1467m2

    0.1200m1

    Topology opt1

    Generated topologies

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    U

    0.0206m3

    0.0342m1

    0.0324m2

    V

    0.0349m1

    1.3000m3

    1.2080m2

    0.4545m1

    0.5556m2

    0.5163m3

    0.4545m1

    m2,m3

    0.2222m1

    0.1829m3

    0.1769m21.3000m2,m3

    0.4500m1

    0.4000m1

    1.4765m10.5556m2

    0.5163m3

    1.3408m10.1545m1

    0.8655m2

    0.8000m3

    0.4789m2

    0.4771m3

    0.5706m1

    0.5143m2

    0.6009m3

    0.0941m2

    0.0836m3

    0.2647m1

    0.0108m1

    Topology opt2

    Design complexity

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    d : estimated design effortp : estimated power

    consumption reduction

    Np : # of signal paths

    Np,r: # of non-reconfigurable cells

    Nc,r : # of reconfigurable cells

    SNR degradation due to circuit noise

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    103

    102

    150

    100

    50

    0

    Frequency (f/fs)

    Spectrum

    (dB)

    Output spectrum comparison

    opt2, noise = 60dB[1], noise = 60dBopt2, noise = 70dB[1], noise = 70dB

    opt2, ideal[1], ideal

    40 35 30 25 20 15 10 5 010

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    Input amplitude [dB]

    SNR[dB]

    SNR comparison for different noise level

    opt2, ideal[1], idealopt2, noise = 60dB[1], noise = 60dBopt2, noise = 50dB[1], noise = 50dB

    Improvement as compared to the state-of-art design:

    3dB for the case of -60dB noise level

    5dB for the case of -50dB noise level

    Experiments

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    Experiments

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    Compare the triple-mode modulator with three

    single-mode modulators obtained with

    toolbox

    Design effort can be less than 1/3

    Complexity can be as less as 40%

    Power saving can be as large as 24.2%

    More robust to circuit nonidealities

    Experiments using PSoC

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    Implementation of a reconfigurable Delta-Sigma

    modulator using PSoC mixed-signal SoC

    Experiments using PSoC

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    Experiments using PSoC

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    Experiments using PSoC

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    Education & Training

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    Hugo De Man, System-on-Chip Design: Impact on Education and

    Research, IEEE Design & Test of Computers, July-Sept. 1999.

    System architects/designers:

    Cross-disciplinary background: EE/CE/CS

    EE: signals, conversion techniques, impact of circuit

    nonidealities, and know how to tackle these

    CE: how HW & SW work together, abstraction levels,

    successive refinement, trade-off analysis

    CS: high-level description languages for systems, system and

    circuit modeling techniques, formal verification

    Education & Training

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    Curricula, textbooks, projects, lab material, exercises?

    A. Doboli and E. Currie

    Embedded Mixed-Signal Systems: A DesignersPerspective, due to be published in 2007.

    Conclusions

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    PSoC: embedded mixed-signal architecture

    Related research at Stony Brook

    Systematic methodology for ADC design Automated circuit modeling

    Education & training

    Automated Macromodeling

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    Produced macromodels:

    Structural

    No feedback dependencies (decoupled)

    Symbolically characterized nonlinear current

    sources

    Extensible, accuracy is controllable

    Insight into circuit

    Reusable

    Automated Macromodeling

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    f(vin)vin vout

    Black-box macromodel

    Vin1

    v3v2

    Vin2

    v1

    VbnM5

    M3 M4

    M2M1

    Circuit netlist Structural nonlinear macromodel

    id3nk

    k

    id1nk

    k

    iCdb3nk

    k

    iCdb1nk

    k

    id4nk

    k

    id2nk

    k

    iCdb4nk

    k

    iCdb2nk

    k

    id3nk

    k

    id4nk

    k

    iCsb3nk

    k

    iCsb4nk

    k

    id1nk

    k

    iCdb5nk

    k

    (sCgd4gmg4)

    vin2 v1

    gms4 C3(sCgd2gmg2)

    v2R3

    (sCgd3gmg3)

    vin1 v1

    gms3 R2C2

    V2

    V3

    C1 R1

    V1

    (sCgs3+gm3)

    vin1

    (sCgs4+gm4)

    vin2

    gmd3

    v2,eq

    gmd4

    v3,eq

    sCgd2

    v3,eq

    (R2,C2)

    Automated Macromodeling

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    v3

    sCgd2

    v3

    d3nki

    kd4nki

    k

    d5nki

    k

    d3nki

    kd1nki

    k

    d4nki

    kd2nki

    k

    v3

    (sCgd3gmg3)

    vin1

    gms3

    v1

    C2 R2

    v2

    (sCgd4gmg4)vin2

    gms4v1

    (sCgd2gmg2)v2

    C3 R3

    v1

    C1 R1

    k

    db5nkCC

    ksb4nkC

    ksb3nk

    Ck

    db3nk

    Ck

    db1nk

    Ck

    db2nk

    Ck

    db4nk

    (sCgs3+gmg3)vin1

    (sCgs4+gmg4)vin2

    gmd3v2

    gmd4

    Vin1

    v3v2

    Vin2v1

    VbnM5

    M3 M4

    M2M1

    Circuit netlist

    Automated Macromodeling

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    103

    104

    105

    106

    107

    108100

    90

    80

    70

    60

    50

    40

    Frequency [Hz]

    HD[d

    B]

    Comparison of HD2, HD3

    HD3, SPICEHD3, modelHD2, SPICE

    HD2, model

    Comparison of HD2, HD3

    Automated Macromodeling

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    vout

    Vin2

    v3

    RL CL

    CfRf

    v2

    Vin1

    v4

    v1

    M1 M2

    M6

    M8

    M9M7M5

    M3 M4

    Vbn

    Automated Macromodeling

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    vout

    d3nki

    kd4nki

    k

    d5nki

    kC

    ksb3nk

    Ck

    sb4nk

    Ck

    db5nk

    Ck

    db3nk

    Ck

    sb2nk

    Ck

    sb1nk

    d3nki

    k

    d1nki

    k

    v3

    d2nk

    ik d4nk

    ik Ck db2nk Ck

    db4nk

    d8nki

    kC

    ksb8nk

    Ck

    db9nk

    d9nki

    k

    d6nki

    kd7nki

    kC

    kdb6nk

    Ck

    db7nk

    gms3v1 (sCgd2)v3eq C2 R2(sCgd3gmg3)vin1

    vin1 Vin2 C1 R1(sCgs3+gmg3) (sCgs4+gmg4) gmd3 gmd4

    v2eq v3eq

    v1

    v2

    (sCgd2gmg2)v2

    (sCgd4gmg4)vin2 gms4v1

    (s(Cf+Cgd8)(1/Rf))v4eq C3 R3

    (sCgs8+gmg8)v4 C5 R5

    +1/Rfgmg6)v3(sCgs8)v5eq

    (s(Cgs6+Cf)

    v4

    C4 R4

    Automated Macromodeling

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    103

    104

    105

    106

    107

    108

    300

    250

    200

    150

    100

    50

    0 HD2 contribution

    Frequency [Hz]

    HD2

    [dB]

    M8M5M6

    M3,4M1,2HD2, modelHD2, SPICE

    Automated Macromodeling

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    vout

    Vin2

    v3

    RL CL

    CfRf

    v2

    Vin1

    v4

    v1

    M1 M2

    M6

    M8

    M9

    M7M5

    M3 M4

    Vbn

    Automated Macromodeling

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    103 104 105 106 107 108110

    100

    90

    80

    70

    60

    50

    40

    30

    20

    Frequency [Hz]

    H

    D[

    dB]

    HD3 comparison for twostage OpAmp

    SPICEmodel

    Automated Macromodeling

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    vo1

    Ck db3nk

    d7

    nk

    ikd3nk

    ik Ck db7nk

    Ck

    db9nk

    d11nki

    kd9nki

    kC

    kdb11nk

    d1nki

    k

    d3nki

    k

    d5nki

    k

    Ck

    sb1nk

    Ck

    sb3nk

    Ck

    db5nk

    Ck

    db1nk

    d13nki

    kd1nki

    kC

    kdb13nk

    v1

    gms3

    v1,eq(sCgd3gmg3)

    vin1

    sCgd9v3,eq R5 C5

    sCgd1vo1,eq

    (sCgd9gmg9)

    v5

    sCgs1v1,eq C3R3

    (sCgs3+gmg3)vin1

    (sCgs1+gm1)v3

    gmd3v5 R1

    gmd1vo1,eq C1

    v3

    (sCgd1gmg1) gms1v1 Ro1 Co1

    v5

    v3

    M13

    R

    Vo1 Vo2

    ClCl

    v1 v2

    v4v3

    v6

    Vin1 Vin2

    M1 M2

    M14

    M3

    M9

    M11 M6 M12

    M4

    M8

    M10

    M7

    v5

    VbpVcmfb

    Vbp

    VbnM5

    Automated Macromodeling

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    103 104 105 106 107 10890

    80

    70

    60

    50

    40

    30

    20

    10

    0

    Frequency [Hz]

    HD[

    dB]

    HD3 comparison for OTA

    HD3, SPICEHD3, model

    Automated Macromodeling

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    1 2 3 4 5 6 7 8

    0

    5

    10

    15

    20

    25

    30

    35

    40

    45

    50

    Number of iteration

    Error

    [%]

    complexity vs. accuracysinglestage, up to 100MHzsinglestage, up to 10MHztwostage, up to 100MHztwostage, up to 10MHz