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Nonlinearity characterization and modelling

Nonlinearity characterization and modelling. Giovanni Ghione Dipartimento di Elettronica Politecnico di Torino Microwave & RF electronics group. Agenda. A glimpse on nonlinear models Physics-based device-level models Equivalent circuit & black-box device-level models

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Nonlinearity characterization and modelling

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  1. Nonlinearity characterization and modelling Giovanni Ghione Dipartimento di Elettronica Politecnico di Torino Microwave & RF electronics group NEWCOM WPR3 Meeting – 6/9/04

  2. Agenda • A glimpse on nonlinear models • Physics-based device-level models • Equivalent circuit & black-box device-level models • Vintage behavioral models: power series, Volterra, envelope • Advanced models: time-domain, frequency-domain, envelope • Characterization techniques (mainly loadpull…) • Aknowledgements NEWCOM WPR3 Meeting – 6/9/04

  3. Device models: from physical to behavioral From: D.Root et al., IMS2004 WME-4 NEWCOM WPR3 Meeting – 6/9/04

  4. Physics-based nonlinear modeling • Based on the solution of transport + Poisson equations on device volume • Mainly single-device, mixed-mode intensive • Often time-domain, Harmonic Balance LS simulation demonstrated but demanding (>10000 unknowns) order reduction techniques? • Potentially accurate, but NL operation can be a numerical killer (breakdown, direct junction conduction…) NEWCOM WPR3 Meeting – 6/9/04

  5. Example: LDMOS PA simulation From: Troyanovsky et al, SISPAD 1997 NEWCOM WPR3 Meeting – 6/9/04

  6. Circuit-oriented NL modelling • Equivalent circuit NL models: • Extensions of DC + small signal models with NL components • Ad hoc topologies for device classes: BJT, HBT, MESFETs, HEMTs, MOS, LDMOS… • Almost endless variety of topologies and component models from the shelf, many models proprietary • Empirical, semi-empirical, physics-based analytical varieties. • Pros: numerically efficient, accurate enough for a given technology after much effort and tweaking • Cons: not a general-purpose strategy, low-frequency dispersion (memory) effect modelling difficult NEWCOM WPR3 Meeting – 6/9/04

  7. NL equivalent circuit examples • Bipolar: • BJT: Ebers-Moll, Gummel-Poon • HBT: Modified GP, MEXTRAM… • FET: • MOS: SPICE models, BSIM models… • MESFET: Curtice, Statz, Materka, TOM… • HEMT: Chalmers, COBRA… NEWCOM WPR3 Meeting – 6/9/04

  8. Example: the Curtice MESFET model NEWCOM WPR3 Meeting – 6/9/04

  9. Example: the HBT MEXTRAM model NEWCOM WPR3 Meeting – 6/9/04

  10. Black-box device-level modelling • Black-box models for circuit NL components: • Look-up-table, interpolatory (e.g. Root) • Static Neural Network based • Global black-box (“grey-box”) device-level (?): • The Nonlinear Integral Model (University of Bologna)  based on dynamic Volterra expansion + parasitic extraction • Potentially accurate, but computationally intensive NEWCOM WPR3 Meeting – 6/9/04

  11. Non-quasi static effects • Device level: low-frequency dispersion due to: • Trapping effects, surfaces, interfaces • Thermal effects • Amplifier level: • Bias effect (lowpass behavior of bias tees) • Thermal effect • Impact on device modelling  pulsed DC and SS measurements NEWCOM WPR3 Meeting – 6/9/04

  12. Pulsed IV characteristics • Investigation of the device behaviour outside the SOA region • Pulsed measurement for exploiting thermal and traps effects • Different QP with the same dissipated power • Point out flaws of the fabbrication processes (e.g. passivation faults, uncompensated deep traps) • Allow the identification of the dispersive model contributions NEWCOM WPR3 Meeting – 6/9/04

  13. Pulsed IV: FET example NEWCOM WPR3 Meeting – 6/9/04

  14. System-level (behavioral) NL models • Classical & textbook results: • Power and Volterra series (wideband) models, frequency or time-domain • Envelope (narrowband) static models  descriptive function • A sampler of more innovative techniques: • Dynamic time-domain models • Dynamic neural network models • Dynamic f-domain models  scattering functions • Advanced envelope models NEWCOM WPR3 Meeting – 6/9/04

  15. Recalling a few basics • PA single-tone test • PA two-tone test • PA modulated signal test • Intermodulation products, ACPR… NEWCOM WPR3 Meeting – 6/9/04

  16. Single-tone PA test PA 3rd harmonics output intercept 1 dB compression point Output saturation power NEWCOM WPR3 Meeting – 6/9/04

  17. Two-tone PA test • Rationale: two-tone operation “simulates” narrowband operation on a continuous band f1- f2 PA NEWCOM WPR3 Meeting – 6/9/04

  18. Two-tone Pin-Pout NEWCOM WPR3 Meeting – 6/9/04

  19. Modulated signal test & ACPR NEWCOM WPR3 Meeting – 6/9/04

  20. Class AABC two-tone test Fager et al, IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 39, NO. 1, JANUARY 2004, p. 24 NEWCOM WPR3 Meeting – 6/9/04

  21. Power series (PS) model • Strictly speaking an IO model for a memoryless NL system, often cascaded with a linear system with memory: NEWCOM WPR3 Meeting – 6/9/04

  22. Active device PS cascading u(t) s(t) w(t) FET transfer curve NEWCOM WPR3 Meeting – 6/9/04

  23. PS output with multi-tone excitation • Assume a multi-tone frequency-domain excitation: • Output: NEWCOM WPR3 Meeting – 6/9/04

  24. Single- and two-tone PS test • The PS approach correctly yields the small-signal harmonic and IMPn slope in small-signal, class A operation • It also gives an estimate of gain compression • The two-tone output with equal tone power yields: • Same IMPn power for right & left-hand side lines • IMPn power independent on line spacing ( can be artificially introduced through H) NEWCOM WPR3 Meeting – 6/9/04

  25. Single- and two-tone gain compression • The 2-tone (modulated signal) Pin-Pout is not exactly the same as the single-tone • While the AM-AM curve is different, the AM-PM is almost the same (Leke & Kenney, MTT-S 96, TH2B-8) • Can be shown already with a PS model, assume: • then the output power is: • Single-tone • Two-tone • Two-tone with IMP3 NEWCOM WPR3 Meeting – 6/9/04

  26. Example NEWCOM WPR3 Meeting – 6/9/04

  27. Volterra series approach • In frequency domain, generalization of the PS approach: • Exact representation, but unsuited to true LS regime or strongly NL system due to the difficulty of characterizing high-order kernels • The time-domain version is a generalization of the impulse response NEWCOM WPR3 Meeting – 6/9/04

  28. Envelope modeling • The PS and Volterra models are general and wideband, i.e. they hold for any excitation  often in analog RF system the excitation is DC + a narrowband modulated signal • (Complex) envelope representation of input and output signals, envelope slowly varying vs. carrier: • Static envelope model (G complex “descriptive function”): NEWCOM WPR3 Meeting – 6/9/04

  29. AM/AM and AM/PM distortion curves NEWCOM WPR3 Meeting – 6/9/04

  30. Static envelope models features • No information on harmonics and out-of-band spurs  bandpass filtering implied, unsuited for circuit-level modeling • G can be identified from single-tone measurements but better fitted on two-tone measurements (see caveat on fitting function  Loyka IEEE Trans. VT49, p.1982) • IM3 intrinsically symmetrical and independent on tone spacing  no memory (non quasi-static) effects modeled • Poor ACPR modeling in many realistic cases, performances deteriorate increasing channel bandwidth NEWCOM WPR3 Meeting – 6/9/04

  31. Some “novel” approaches • Modeling strategies have ups and downs in time, the last not necessarily the best one • Recent trends: • Revival on dynamic state-variable black-box (behavioral) models based on general system identification techniques • Steady interest and progress in neural network models • Progress in exploiting multi-frequency NL measurement tools • Search for better system-level envelope models, also on the basis of classical methods revisited and revamped (e.g. Volterra) NEWCOM WPR3 Meeting – 6/9/04

  32. Nonlinear Time Series (NTS) model • Idea: identify a standard state-variable model on the basis of measured input and output time series [Root et al., Agilent]: NEWCOM WPR3 Meeting – 6/9/04

  33. Model identification: how? • NL model identification amounts to a nonlinear inverse scattering problem • Several theoretical methods available from dynamic system theory (Whitney embedding theorem, Takens’ theorem) which allow in principle to identify f as a smooth function • Once f is identified, the implementation in commercial simulators is straightforward • Problems: • system identification in the presence of noisy data • identification when the state space is large • building suitable sets of I/O data • providing a suitable numerical approximation to f • See D.Root et al, IMS2003, paper WE2B-2 and references NEWCOM WPR3 Meeting – 6/9/04

  34. Dynamic Neural Network (DNN) model • Neural networks can provide an alternative to identify the NL dynamical system • In DNNs (see Ku et al, MTT Trans. Dec. 2002, p. 2769) the NN is trained with data sequences including the input / output and their time derivatives • Once trained the NN defines a “feedback” dynamic model and simply “is” the dynamic system • Very promising technique in terms of accuracy, CPU effectiveness and generality; easy implementation in circuit simulators. NEWCOM WPR3 Meeting – 6/9/04

  35. DNN result example NEWCOM WPR3 Meeting – 6/9/04

  36. F-domain dynamic behavioral models • The availability of Large-signal Network Analyzers (LSNA) have fostered the development of generalizations of the scattering parameter approach: NEWCOM WPR3 Meeting – 6/9/04

  37. Describing (scattering) functions • NL relationship between power wave harmonics in LS steady state (ij port & harmonics index) [Verspecht, IMS2003]: NEWCOM WPR3 Meeting – 6/9/04

  38. Relationship with S parameters • Describing functions reduce to multifrequency S-parameters for a linear device (lowercase used for PW): • however, simplifications can be made (scattering functions model) if a11 is the only “large” component  superposition can be applied to the other terms. NEWCOM WPR3 Meeting – 6/9/04

  39. Frequency superposition • Normalization: NEWCOM WPR3 Meeting – 6/9/04

  40. Scattering function model • Introducing phase normalized variables one has the relationship [Verspecht, IMS2003]: NEWCOM WPR3 Meeting – 6/9/04

  41. Scattering functions features • Also called large-signal scattering parameters • Directly measurable through a VNA • Effective in providing a model for a HB environment and for strongly nonlinear components • Can be used at a circuit level, providing interaction with higher harmonics; not an envelope model NEWCOM WPR3 Meeting – 6/9/04

  42. Envelope LS scattering parameters • Two-port extension of descriptive function concept, same features and limitations: NEWCOM WPR3 Meeting – 6/9/04

  43. Envelope models • Envelope models consider (narrowband) modulated signal  “time varying spectrum” signals • Model purpose: relating input and output signal envelopes • Well suited to envelope circuit simulation techniques NEWCOM WPR3 Meeting – 6/9/04

  44. Limitations of static envelope models • IMD simmetry & independence on tone spacing • Both properties are not observed in practice owing to low-frequency dispersion (memory) effects  thermal, trap related, bias related (Pollard et al, MTTS-96, paper TH2B-5): NEWCOM WPR3 Meeting – 6/9/04

  45. Add a state-variable Z dependence (temperature, bias) [Asbeck IMS2002, p.135]; Z in turn depends (linearly or not) on the input variable: Improving static models: simple solutions NEWCOM WPR3 Meeting – 6/9/04

  46. High-frequency dispersion • While low frequency (long memory) effects arise due to heating etc., also high-frequency (short memory) phenomena can arise leading to high-frequency dispersion • This amount to an output sensitivity when the modulation bandwidth increases  e.g. in next generation systems • General (usually, but not only) Volterra-based approaches have been suggested to overcome the static limitation NEWCOM WPR3 Meeting – 6/9/04

  47. Examples of low- and high-frequency dispersion LDMOS amplifier, from Ngoya et al., BMAS 2003 NEWCOM WPR3 Meeting – 6/9/04

  48. More general approaches • In general, the descriptive function can be turned into a descriptive functional: • Volterra-based solutions, with slight variations: • Derivation from Dynamic Volterra Series [Ngoya et al MTT-S Digest 2000] • Nonlinear Impulse Response Transient (NIRT) envelope model [Soury et al. MTT-S Digest 2002 paper WE2E-1] • Extracting memory effects from modified Volterra series [Filicori et al., IEEE CAS-49, p.1118 and IEEE Instr. & Meas. V.53 p.341] NEWCOM WPR3 Meeting – 6/9/04

  49. Dynamic Volterra in a nutshell DC response small-signal response • 1st step: from the conventional Volterra series extract a modified series in the instantaneous deviations x(t)-x(t-t); truncate the series to the first term; one has: DC (LF) regime amplitude Dynamic Volterra linearity Volterra ss regime memory frequency NEWCOM WPR3 Meeting – 6/9/04

  50. Dynamic Volterra – cntd. AM/AM – AM/PM • 2nd step: introduce an envelope representation of input and output into the dynamic Volterra series; one has: NEWCOM WPR3 Meeting – 6/9/04

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