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  • 2002 Agilent Technologies - Used with Permission

    Everything you've always wanted to know about Hot-S22 (but we're afraid to ask)

    Jan Verspecht

    Jan Verspecht bvba

    Gertrudeveld 151840 SteenhuffelBelgium

    email: contact@janverspecht.comweb: http://www.janverspecht.com

    Slides presented at the WorkshopIntroducing New Concepts in Nonlinear Network Design

    (International Microwave Symposium 2002)

  • Everything youve always wanted to know about

    Hot-S22(but were afraid to ask)

    Jan Verspecht

    Agilent Technologies

  • 2

    Purpose

    Convince people of a better Hot S22

    Show that technology is fun (sometimes)

  • 3

    Outline

    Introduction: What is Hot S22 ?

    Getting and interpreting experimental data

    Confront classic approaches with data

    Derivation of the extended Hot S22 theory

    Confront extended Hot S22 with data

    Conclusion

  • 4

    What is Hot S22 ?

    D.U.T. behavior is represented by pseudo-waves (A1, B1, A2, B2)

    Hot S22 describes the relationship between B2 and A2

    Valid under Hot conditions (A1 significant)

    D.U.T.A1 A2B1 B2

  • 5

    Experimental investigation

    Take a real life D.U.T. (CDMA RFIC amplifier)

    Apply an A1 signal

    Apply a set of A2s

    Look at the corresponding B2s

    Mathematically describe the relationship between the A2s and B2s

    Repeat for different A1s

  • 6

    Experimental set-up

    Large-Signal Network Analyzer(LSNA, formerly known as NNMS)

    RFIC

    A1 B1 B2 A2

    synth2synth1

    synth1 generates A1 synth2 generates a set of A2s

    LSNA measures all A1s, B1s, A2s, B2s

  • 7

    Interpretation of the data

    ? 0.3 ? 0.2 ? 0.1 0 0.1 0.2 0.3

    ? 0.3

    ? 0.2

    ? 0.1

    0

    0.1

    0.2

    0.3

    ? 0.75 ? 0.5 ? 0.25 0 0.25 0.5 0.75

    ? 0.75

    ? 0.5

    ? 0.25

    0

    0.25

    0.5

    0.75

    A2 (V) B2 (V)

    IQ-plots of the A2s and B2s for a constant A1(x-axis = real part, y-axis = imaginary part)

  • 8

    Phase normalization is good

    Normalize the phases relative to A1 P = ej.arg(A1)

    ? 0.3 ? 0.2 ? 0.1 0 0.1 0.2 0.3

    ? 0.3

    ? 0.2

    ? 0.1

    0

    0.1

    0.2

    0.3

    ? 0.6 ? 0.4 ? 0.2 0

    0

    0.2

    0.4

    0.6

    0.8

    A2.P-1 (V) B2.P-1 (V)

  • 9

    ? 1.25 ? 1 ? 0.75 ? 0.5 ? 0.25 0

    0

    0.25

    0.5

    0.75

    1

    1.25

    1.5

    Varying the amplitude of A1

    B2.P-1 (V)

    A1 increases

  • 10

    Varying the amplitude of A2

    Linear dependency versus A2

    ? 0.5 ? 0.25 0 0.25

    ? 0.6

    ? 0.4

    ? 0.2

    0

    0.2

    0.4

    ? 0.5 ? 0.25 0 0.25

    ? 0.5 ? 0.25 0 0.25

    ? 0.6

    ? 0.4

    ? 0.2

    0

    0.2

    0.4

    ? 0.5 ? 0.25 0 0.25

    ? 0.5 ? 0.25 0 0.25

    ? 0.6

    ? 0.4

    ? 0.2

    0

    0.2

    0.4

    ? 0.5 ? 0.25 0 0.25

    ? 1.3 ? 1.2 ? 1.1

    1.4

    1.45

    1.5

    1.55

    1.6

    1.65

    ? 1.3 ? 1.2 ? 1.1

    ? 1.3 ? 1.2 ? 1.1

    1.4

    1.45

    1.5

    1.55

    1.6

    1.65

    ? 1.3 ? 1.2 ? 1.1

    ? 1.3 ? 1.2 ? 1.1

    1.4

    1.45

    1.5

    1.55

    1.6

    1.65

    ? 1.3 ? 1.2 ? 1.1

    B2.P-1 (V)

    A2.P-1 (V)

  • 11

    Data interpretation as loadpull

    Increasing amplitude of A1

  • 12

    Classic S-parameter description

    B2 = S21 (|A1|).A1+ S22.A2

    ? 1.25 ? 1 ? 0.75 ? 0.5 ? 0.25 0 0.25

    0

    0.5

    1

    1.5B2.P-1 (V)

  • 13

    Simple Hot S22 description

    B2 = S21(|A1|).A1+ S22(|A1|).A2

    ? 1.25 ? 1 ? 0.75 ? 0.5 ? 0.25 0 0.25

    0

    0.5

    1

    1.5B2.P-1 (V)

  • 14

    Model linearity & squeezing

    We look for a mathematical model which is linear (superposition valid) squeezes

    Squeezing implies that the phase of A2.P-1

    matters

    We need different coefficients for the real and the imaginary part of A2.P-1

    More elegant expression results when using A2.P-1 and its conjugate

  • 15

    Mathematical expression

    B2.P-1 = S21(|A1|).A1 .P-1 + S22(|A1|).A2 .P-1 + R22(|A1|).conjugate(A2 .P-1)

    B2 = S21(|A1|).A1+S22(|A1|).A2+ R22(|A1|).P2.conjugate(A2)

  • 16

    Extended Hot S22

    B2 = S21(|A1|).A1+ S22(|A1|).A2+ R22(|A1|).P2.conjugate(A2)

    ? 1.25 ? 1 ? 0.75 ? 0.5 ? 0.25 0 0.25

    0

    0.5

    1

    1.5

    B2.P-1 (V)

  • 17

    Quadratic Hot S22

    Further improvement is possible by using a polynomial in A2 and conj(A2)

    E.g.: quadratic Hot S22B2 = F.P + G.A2+ H.P2.conj(A2) +

    K.P-1.A22 + L.P3.conj(A2)2 + M.P.A2.conj(A2)

    Note the presence of the P factors(theory of describing functions)

  • 18

    Comparison (highest A1 amplitude)

    ? 1.4 ? 1.3 ? 1.2

    1.4

    1.5

    1.6

    1.7

    ? 1.4 ? 1.3 ? 1.2

    1.4

    1.5

    1.6

    1.7

    ? 1.4 ? 1.3 ? 1.2

    1.4

    1.5

    1.6

    1.7

    ? 1.4 ? 1.3 ? 1.2

    1.4

    1.5

    1.6

    1.7

    ? 1.4 ? 1.3 ? 1.2

    1.4

    1.5

    1.6

    1.7

    ? 1.4 ? 1.3 ? 1.2

    1.4

    1.5

    1.6

    1.7

    ? 1.4 ? 1.3 ? 1.2

    1.4

    1.5

    1.6

    1.7

    ? 1.4 ? 1.3 ? 1.2

    1.4

    1.5

    1.6

    1.7

    B2.P-1 (V)

    ClassicS22

    SimpleHot S22

    ExtendedHot S22

    QuadraticHot S22

  • 19

    Residuals

    ? 25 ? 20 ? 15 ? 10 ? 5 0 5

    ? 50

    ? 45

    ? 40

    ? 35

    ? 30

    Relative Error(dB) S22

    SimpleHot S22

    ExtendedHot S22

    QuadraticHot S22

    Amplitude of A1 (dBm)

  • 20

    Conclusion

    An accurate Hot S22 exists

    It has a coefficient for the conjugate of A2.P-1

    It can accurately be measured

    It describes the relationship between A2 and B2 under large-signal excitation

  • 21

    More information

    More detailed information on this kind of measuring and modeling techniques:

    http://users.skynet.be/jan.verspecht

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