Modelarea circuitelor electronice - Modelarea circuitelor electronice Simularea la nivel de circuit

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  • Modelarea circuitelor electronice  Simularea la nivel de circuit este costisitoare din punct de vedere al

    calculelor, în special dacă circuitul este mare şi necesită mai multe

    tipuri de analize (în timp, în frecvenţă, etc.).

     Alternativa: nivele ierarhic superioare de abstractizare în descrierea

    circuitului; utilizare modele compacte.

     Doi factori determină utilitatea modelului:

     eficient din punct de vedere al volumului şi complexităţii calculelor

     precizia (suficient de exact).

    Modelarea

    circuitelor

    • modelarea

    functiilor de

    performanta

    (statice)

    • modelarea

    functionala

    (dinamice)

  • Modelarea circuitelor electronice utilizand sisteme fuzzy

     Modelarea circuitelor electronice

     modelarea functiilor de performanta

     modelare SOTA

     modelarea functionala

     modelare FCOTA

     model Simulink

  • Modelarea functiilor de performanta ale unui circuit

    analogic

  • SOTA – Simple Operational Transconductance amplifier

      

       

       

          1cu;1;100

    0,75μcu;1;10

    0,5μcu;1;8

    μA20;70

    5656

    3434

    1212

    

    

    

    LWW,L

    LLW

    LLW

    IB

    •Parametrii

    • Functii de performanta:

    21 ii

    o

    vv

    v Avo

     

    BAvoGBW 

    PM

    cA

    Avo CMRR 

  • Procedura de

    modelare Design of

    experiment

    ! Metamodel (surrogate model); a model of the model

  •  Generally speaking, a metamodel, or a surrogate model, is a

    model of the model, i.e. a simplified model of an actual model

    of a circuit, system, or software like entity.

     A metamodel can be a mathematical relation or algorithm

    representing input and output relations.

     A model is an abstraction of phenomena in the real world; a

    metamodel is yet another abstraction, highlighting properties

    of the model itself.

    Metamodeling typically involves studying the output and input

    relationships and then fitting proper metamodels to represent

    that behavior.

    Metamodeling

  •  Once the metamodels are generated, the designer can conduct

    more extensive analyses of the circuit and use the same

    metamodel for different criteria to be optimized.

     The detailed simulation is significantly more time

    consuming than using the metamodel.

     The key points of metamodeling:

     accuracy - capability of generating the system response over the

    design space;

     efficiency - computational effort required for constructing the

    metamodel;

     transparency - capability of providing the information concerning

    contributions and variations of design variables and correlation

    among the variables;

     simplicity - simple methods should require less user input and be

    easily adapted to different problem.

    Metamodeling

  • Determinarea setului de parametric (DoE)

     LHS – Latin Hypercube Sample (+ Full Factorial Design)

    • Domeniul fiecarei variabile se imparte in K intervale (egale)

    • În fiecare interval se alege aleator o valoare.

    • Cele K valori ale fiecărui parametru sunt asociate în mod aleator cu cele

    K valori ale altui parametru ş.a.m.d. rezultand K vectori ai parametrilor.

    • LHS

    • 2 level Full Factorial Design – toate combinatiile posibile ale

    parametrilor, considerand numai valorile extreme (minim si maxim)

  • DoE

    9 /29

     For the design of the experiment it is necessary to generate those

    parameter combinations that fill the parameter space, in order to

    encompass all the regions in the parameter space.

     A good experimental design (ED) is essential to simultaneously reduce

    the possible effect of noise and bias error.

     It is recommended to construct an experimental design by combining

    multiple techniques for design experiment to reduce the risk of using a

    poor ED.

    LHS designs may leave out the boundary and the final model may lead to large

    extrapolation errors. To avoid this one should generate the experimental design by

    mixing the LHS design with a 2 level (or n level) full factorial design:

    1. Latin Hypercube sampling is used to generate a specified number of randomly

    distributed values for each parameter, these values being randomly permuted to

    obtain different parameter combinations.

    2. Two-level full-factorial design is used to generate all possible parameter

    combinations, considering only the extreme values (minimum and maximum) for all

    parameter

  • Esantion al setului de date de antrenare

  • Structura modelului fuzzy Avo

    • Sistem fuzzy

    TS de ordin 1

  • Multimi fuzzy la intrare

    • 6 reguli

    • 6 mf pe fiecare

    variabila

  • Multimi fuzzy la iesire. Reguli

    •out1mf1=[-0.27907622925482 4.7336423208163 -0.22929012109304 -0.0028363221851113 45.49729161833]

    •out1mf2=[-0.11955049624726 10.308484211334 -0.23201470784719 0.00408876941051388 25.0003432748168]

    •out1mf3=[-0.50949884619065 5.4106958973798 -0.70345988469712 0.0282962177749871 52.5057718830839]

    •out1mf4=[-0.32603181267357 11.099093462894 -0.98934580658441 0.0138103461621346 37.5543179917034]

    •out1mf5=[-0.18956099089732 8.6928124102796 -0.96510752831766 0.016395396082041 33.7788736156701]

    •out1mf6=[-0.38682872084570 7.5633681369785 -1.3443012661576 -0.042937570643951 49.8212643120914]

    • Multimile fuzzy la iesire

    • Baza de reguli

  • Evolutia RMSE pe durata instruirii

    Suprapotrivire

    (overfitting)

    Suprapotrivire

    (overfitting)

  • RMSE pentru modelele fuzzy Funcţia

    de

    circuit

    Setul

    de date

    RMSE

    3 reguli 6 reguli 10 reguli

    antrenare verificare antrenare verif. antrenare verif.

    Avo

    450a+50v 1.85

    1.5

    1.15

    0.55

    1.6

    1.45

    0.7

    0.55

    700a+150v 1.39

    1.27

    1.16

    1.05

    1.29

    1.18

    1.06

    0.93

    1.21

    1.15

    1.00

    0.93

    GBW

    [KHz]

    450a+50v 178

    132

    176

    115

    130

    88

    124

    84

    106

    83

    79

    64

    700a+150v 205

    156

    142

    89

    155

    142

    80

    58

    145

    140

    68

    65

    PM [o]

    450a+50v 0.142

    0.115

    0141

    0.115

    0.115

    0.110

    0.079

    0.056

    0.116

    0.108

    0.084

    0.073

    700a+150v 0.116

    0.096

    0.063

    0.040

    0.102

    0.090

    0.054

    0.033

    0.98

    0.090

    0.050

    0.036

    CMRR

    450a+50v 101735

    95640

    61735

    46408

    72200

    70100

    61735

    46408

    700a+150v 107279

    80529

    72116

    35201

    36800

    33400

    27823

    43875

    75311

    75188

    30750

    30706

    • RMSE este dependenta de ordinul de marime

    al functiei modelate  

    K

    k

    k d k yy

    K 1

    21

  • Comparație model fuzzy – simulare Spice

    Funcţia de

    circuit

    EPM [%]

    instruire verificare

    Avo 1,375 1,278

    GBW 2,645 1,921

    PM 0,049 0,0398

    CMRR 3,04 4,67

    •EPM – eroarea procentuala

    medie

  • Suprafetele generate de modelele fuzzy

  • Modelarea functională a unui circuit analogic

  • Procedura de modelare

  • FCOTA – Folded Cascode OTA

  • Colectarea datelor

    necesare modelarii

  • Structura modelului fuzzy

  • Antrenare

    Evoluţia erorilor la antrenarea sistemului fuzzy

    amplificare(frecvenţă, temperatură) pentru circuitul FCOTA.

  • Reguli

  • Suprafetele generate de modelele fuzzy

    • Sistemul fuzzy

    dupa antrenare

    • Sistemul fuzzy

    initial

  • Comparatie model fuzzy – simulare Spice

  • Modelul functional fuzzy

  • Implementare Simulink

  • Rezultate -1

  • Rezultate - 2

  • Exercitiu

    31 /29

    Graficele cu evolutia erorilor pentru

    instruirea cu ANFIS a unor sisteme fuzzy

    sunt prezentate in figurile alaturate.

    Caracterizati procesul de instruire si realizati

    o recomnadare referitoare la obtinerea unui

    sistem fuzzy final optim, pastrand aceeasi

    configuratie a slf si a setului de date.