Nonlinearity characterization and modelling Giovanni Ghione Dipartimento di

Nonlinearity characterization and modelling Giovanni Ghione Dipartimento di Elettronica Politecnico di Torino Microwave & RF electronics group NEWCOM WPR 3 Meeting – 6/9/04

Agenda n A glimpse on nonlinear models n Physics-based device-level models n Equivalent circuit & black-box device-level models n Vintage behavioral models: power series, Volterra, envelope n Advanced models: time-domain, frequency-domain, envelope n Characterization techniques (mainly loadpull…) n Aknowledgements NEWCOM WPR 3 Meeting – 6/9/04

Device models: from physical to behavioral NEWCOM WPR 3 Meeting – 6/9/04 From: D. Root et al. , IMS 2004 WME-4

Physics-based nonlinear modeling n Based on the solution of transport + Poisson equations on device volume n Mainly single-device, mixed-mode intensive n Often time-domain, Harmonic Balance LS simulation demonstrated but demanding (>10000 unknowns) order reduction techniques? n Potentially accurate, but NL operation can be a numerical killer (breakdown, direct junction conduction…) NEWCOM WPR 3 Meeting – 6/9/04

Example: LDMOS PA simulation From: Troyanovsky et al, SISPAD 1997 NEWCOM WPR 3 Meeting – 6/9/04

Circuit-oriented NL modelling n Equivalent circuit NL models: n Extensions of DC + small signal models with NL components n Ad hoc topologies for device classes: BJT, HBT, MESFETs, HEMTs, MOS, LDMOS… n Almost endless variety of topologies and component models from the shelf, many models proprietary n Empirical, semi-empirical, physics-based analytical varieties. n Pros: numerically efficient, accurate enough for a given technology after much effort and tweaking n Cons: not a general-purpose strategy, low-frequency dispersion (memory) effect modelling difficult NEWCOM WPR 3 Meeting – 6/9/04

NL equivalent circuit examples n. Bipolar: n. BJT: Ebers-Moll, Gummel-Poon n. HBT: Modified GP, MEXTRAM… n. FET: n. MOS: SPICE models, BSIM models… n. MESFET: Curtice, Statz, Materka, TOM… n. HEMT: Chalmers, COBRA… NEWCOM WPR 3 Meeting – 6/9/04

Example: the Curtice MESFET model NEWCOM WPR 3 Meeting – 6/9/04

Example: the HBT MEXTRAM model NEWCOM WPR 3 Meeting – 6/9/04

Black-box device-level modelling n Black-box models for circuit NL components: n Look-up-table, interpolatory (e. g. Root) n Static Neural Network based n Global black-box (“grey-box”) device-level (? ): n The Nonlinear Integral Model (University of Bologna) based on dynamic Volterra expansion + parasitic extraction n Potentially accurate, but computationally intensive NEWCOM WPR 3 Meeting – 6/9/04

Non-quasi static effects n Device level: low-frequency dispersion due to: n Trapping effects, surfaces, interfaces n Thermal effects n Amplifier level: n Bias effect (lowpass behavior of bias tees) n Thermal effect n Impact on device modelling pulsed DC and SS measurements NEWCOM WPR 3 Meeting – 6/9/04

Pulsed IV characteristics n Investigation of the device behaviour outside the SOA region n Pulsed measurement for exploiting thermal and traps effects n Different QP with the same dissipated power n Point out flaws of the fabbrication processes (e. g. passivation faults, uncompensated deep traps) n Allow the identification of the dispersive model contributions NEWCOM WPR 3 Meeting – 6/9/04

Pulsed IV: FET example NEWCOM WPR 3 Meeting – 6/9/04

System-level (behavioral) NL models n Classical & textbook results: n Power and Volterra series (wideband) models, frequency or time-domain n Envelope (narrowband) static models descriptive function n A sampler of more innovative techniques: n Dynamic time-domain models n Dynamic neural network models n Dynamic f-domain models scattering functions n Advanced envelope models NEWCOM WPR 3 Meeting – 6/9/04

Recalling a few basics n. PA single-tone test n. PA two-tone test n. PA modulated signal test n. Intermodulation products, ACPR… NEWCOM WPR 3 Meeting – 6/9/04

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

Two-tone PA test n Rationale: two-tone operation “simulates” narrowband operation on a continuous band f 1 - f 2 PA NEWCOM WPR 3 Meeting – 6/9/04

Two-tone Pin-Pout NEWCOM WPR 3 Meeting – 6/9/04

Modulated signal test & ACPR NEWCOM WPR 3 Meeting – 6/9/04

Class A AB C two-tone test NEWCOM WPR 3 Meeting – 6/9/04 Fager et al, IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 39, NO. 1, JANUARY 2004, p. 24

Power series (PS) model n Strictly speaking an IO model for a memoryless NL system, often cascaded with a linear system with memory: NEWCOM WPR 3 Meeting – 6/9/04

Active device PS cascading s(t) u(t) w(t) FET transfer curve NEWCOM WPR 3 Meeting – 6/9/04

PS output with multi-tone excitation n Assume a multi-tone frequency-domain excitation: n Output: NEWCOM WPR 3 Meeting – 6/9/04

Single- and two-tone PS test n The PS approach correctly yields the small-signal harmonic and IMPn slope in small-signal, class A operation n It also gives an estimate of gain compression n The two-tone output with equal tone power yields: n Same IMPn power for right & left-hand side lines n IMPn power independent on line spacing ( can be artificially introduced through H) NEWCOM WPR 3 Meeting – 6/9/04

Single- and two-tone gain compression n The 2 -tone (modulated signal) Pin-Pout is not exactly the same as the single-tone n While the AM-AM curve is different, the AM-PM is almost the same (Leke & Kenney, MTT-S 96, TH 2 B-8) n Can be shown already with a PS model, assume: n the output power is: n Single-tone n Two-tone with IMP 3 NEWCOM WPR 3 Meeting – 6/9/04

Example NEWCOM WPR 3 Meeting – 6/9/04

Volterra series approach n In frequency domain, generalization of the PS approach: n Exact representation, but unsuited to true LS regime or strongly NL system due to the difficulty of characterizing high-order kernels n The time-domain version is a generalization of the impulse response NEWCOM WPR 3 Meeting – 6/9/04

Envelope modeling n 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 n (Complex) envelope representation of input and output signals, envelope slowly varying vs. carrier: n Static envelope model (G complex “descriptive function”): NEWCOM WPR 3 Meeting – 6/9/04

AM/AM and AM/PM distortion curves NEWCOM WPR 3 Meeting – 6/9/04

Static envelope models features n No information on harmonics and out-of-band spurs bandpass filtering implied, unsuited for circuit-level modeling n G can be identified from single-tone measurements but better fitted on two-tone measurements (see caveat on fitting function Loyka IEEE Trans. VT 49, p. 1982) n IM 3 intrinsically symmetrical and independent on tone spacing no memory (non quasi-static) effects modeled n Poor ACPR modeling in many realistic cases, performances deteriorate increasing channel bandwidth NEWCOM WPR 3 Meeting – 6/9/04

Some “novel” approaches n Modeling strategies have ups and downs in time, the last not necessarily the best one n Recent trends: n Revival on dynamic state-variable black-box (behavioral) models based on general system identification techniques n Steady interest and progress in neural network models n Progress in exploiting multi-frequency NL measurement tools n Search for better system-level envelope models, also on the basis of classical methods revisited and revamped (e. g. Volterra) NEWCOM WPR 3 Meeting – 6/9/04

Nonlinear Time Series (NTS) model n Idea: identify a standard state-variable model on the basis of measured input and output time series [Root et al. , Agilent]: NEWCOM WPR 3 Meeting – 6/9/04

Model identification: how? n NL model identification amounts to a nonlinear inverse scattering problem n Several theoretical methods available from dynamic system theory (Whitney embedding theorem, Takens’ theorem) which allow in principle to identify f as a smooth function n Once f is identified, the implementation in commercial simulators is straightforward n Problems: n n 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 n See D. Root et al, IMS 2003, paper WE 2 B-2 and references NEWCOM WPR 3 Meeting – 6/9/04

Dynamic Neural Network (DNN) model n Neural networks can provide an alternative to identify the NL dynamical system n 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 n Once trained the NN defines a “feedback” dynamic model and simply “is” the dynamic system n Very promising technique in terms of accuracy, CPU effectiveness and generality; easy implementation in circuit simulators. NEWCOM WPR 3 Meeting – 6/9/04

DNN result example NEWCOM WPR 3 Meeting – 6/9/04

F-domain dynamic behavioral models n The availability of Large-signal Network Analyzers (LSNA) have fostered the development of generalizations of the scattering parameter approach: NEWCOM WPR 3 Meeting – 6/9/04

Describing (scattering) functions n NL relationship between power wave harmonics in LS steady state (ij port & harmonics index) [Verspecht, IMS 2003]: NEWCOM WPR 3 Meeting – 6/9/04

Relationship with S parameters n Describing functions reduce to multifrequency Sparameters for a linear device (lowercase used for PW): n however, simplifications can be made (scattering functions model) if a 11 is the only “large” component superposition can be applied to the other terms. NEWCOM WPR 3 Meeting – 6/9/04

Frequency superposition n Normalization: NEWCOM WPR 3 Meeting – 6/9/04

Scattering function model n Introducing phase normalized variables one has the relationship [Verspecht, IMS 2003]: NEWCOM WPR 3 Meeting – 6/9/04

Scattering functions features n Also called large-signal scattering parameters n Directly measurable through a VNA n Effective in providing a model for a HB environment and for strongly nonlinear components n Can be used at a circuit level, providing interaction with higher harmonics; not an envelope model NEWCOM WPR 3 Meeting – 6/9/04

Envelope LS scattering parameters n Two-port extension of descriptive function concept, same features and limitations: NEWCOM WPR 3 Meeting – 6/9/04

Envelope models n Envelope models consider (narrowband) modulated signal “time varying spectrum” signals n Model purpose: relating input and output signal envelopes n Well suited to envelope circuit simulation techniques NEWCOM WPR 3 Meeting – 6/9/04

Limitations of static envelope models n IMD simmetry & independence on tone spacing n Both properties are not observed in practice owing to lowfrequency dispersion (memory) effects thermal, trap related, bias related (Pollard et al, MTTS-96, paper TH 2 B-5): NEWCOM WPR 3 Meeting – 6/9/04

Improving static models: simple solutions n Add a state-variable Z dependence (temperature, bias) [Asbeck IMS 2002, p. 135]; Z in turn depends (linearly or not) on the input variable: NEWCOM WPR 3 Meeting – 6/9/04

High-frequency dispersion n While low frequency (long memory) effects arise due to heating etc. , also high-frequency (short memory) phenomena can arise leading to highfrequency dispersion n This amount to an output sensitivity when the modulation bandwidth increases e. g. in next generation systems n General (usually, but not only) Volterra-based approaches have been suggested to overcome the static limitation NEWCOM WPR 3 Meeting – 6/9/04

Examples of low- and high-frequency dispersion LDMOS amplifier, from Ngoya et al. , BMAS 2003 NEWCOM WPR 3 Meeting – 6/9/04

More general approaches n In general, the descriptive function can be turned into a descriptive functional: n Volterra-based solutions, with slight variations: n Derivation from Dynamic Volterra Series [Ngoya et al MTTS Digest 2000] n Nonlinear Impulse Response Transient (NIRT) envelope model [Soury et al. MTT-S Digest 2002 paper WE 2 E-1] n Extracting memory effects from modified Volterra series [Filicori et al. , IEEE CAS-49, p. 1118 and IEEE Instr. & Meas. V. 53 p. 341] NEWCOM WPR 3 Meeting – 6/9/04

DC response DC (LF) regime Dynamic Volterra linearity n 1 st 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: amplitude Dynamic Volterra in a nutshell Volterra ss regime memory small-signal response NEWCOM WPR 3 Meeting – 6/9/04 frequency

Dynamic Volterra – cntd. n 2 nd step: introduce an envelope representation of input and output into the dynamic Volterra series; one has: AM/AM – AM/PM NEWCOM WPR 3 Meeting – 6/9/04

Dynamic Volterra – cntd. n 3 rd step: identify the AM/AM and AM/PM response from two-tone (one-tone? ) measurements; identify the two transfer functions with two-tone measurements vs. tone spacing W and tone amplitude n Comments: the Dynamic Volterra Envelope approach still has problems when long-memory effects with highly nonlinear features are present; further modifications are suggested in Soury et al. MTT-S 2003 p. 795 NEWCOM WPR 3 Meeting – 6/9/04

Example from Ngoya et al. , BMAS 2003 NEWCOM WPR 3 Meeting – 6/9/04

Nonlinear Dynamic Measurements n. Amplifiers and two port devices n 50 Ohm fixed impedance systems n. Spectrum Analyzer based n. Power Meter based n. Load Pull systems n. Fundamental Load Pull n. Harmonic Load Pull n. Waveform Load Pull NEWCOM WPR 3 Meeting – 6/9/04

Spectrum Analyzer and PWM Based 1 - Pout measurement 2 - IM 3, ACPR measurement 3 - Gain measurement NEWCOM WPR 3 Meeting – 6/9/04

Load pull – Source pull n Load-pull procedure characterization of a device performance as a function of the load reflection coefficient, in particular the output power n Source pull same when changing the source reflection coefficient NEWCOM WPR 3 Meeting – 6/9/04

Class A Load-Pull theory (Cripps) NEWCOM WPR 3 Meeting – 6/9/04

Basics of Load Pull Example of Load Pull data Output Power [d. Bm] @ 1 d. B gain compression NEWCOM WPR 3 Meeting – 6/9/04 Power Added Efficiency (PAE) [%] @ 2 d. B gain compression

Comments on load pull contours n Ideally the loadpull measurement indicates the “maximum power” or “saturation power” for each load n In practice the power sweep is stopped up to a certain compression value (e. g. 1 or 2 d. B compression point) n Points having the same output power (curves in red) do not usually have the same gain NEWCOM WPR 3 Meeting – 6/9/04 Constant power curves Measured loads 2 d. B gain compression constant output power curves

Load Pull Systems n Power meter or scalar analyzer-based n only scalar information on DUT performances n economic n Vector receiver (VNA) n vector and more complete information on DUT performances n high accuracy, thanks to vector calibration n expensive n Time Domain Receiver (MTA) n Waveform capabilities n Complexity, high cost NEWCOM WPR 3 Meeting – 6/9/04

Passive Load Pull Systems I n. Passive loads n. Mechanical tuners n. Electronic tuners (PIN diode-based) Passive tuners Power Meter Power Sensor GS NEWCOM WPR 3 Meeting – 6/9/04 GL Power Sensor

Passive Load Pull Systems II n. Features n. Single or double slug tuners n. High repeatability of tuner positions n. Pre-characterization with a network analyzer, no real time load measurements n. High power handling NEWCOM WPR 3 Meeting – 6/9/04

Passive Load Pull Systems III Motors DUT Tuners NEWCOM WPR 3 Meeting – 6/9/04 Slab Line

Passive Load Pull Limits n Drawbacks n Load reflection coefficient limited in magnitude by tuner and test-set losses n This is true especially for harmonic tuning n higher frequency n optimum load on the edge of the Smith Chart n Pre-Matching using tuners or networks n To reach higher gamma while characterizing highly mismatched transistors NEWCOM WPR 3 Meeting – 6/9/04

Pre-Matching Tuners LOSS GL GL Networks LOSS NEWCOM WPR 3 Meeting – 6/9/04 GL

Real Time VNA based Load Pull Vector network analyzer-based system VECTOR INFO TUNABLE LOADS NORMAL VNA CAL LOSSES NEWCOM WPR 3 Meeting – 6/9/04

Real Time MTA based Load Pull Transition Analyzer based system VECTOR AND TD INFO REF SIGNAL TUNABLE LOADS TD CAL REQUIRED NEWCOM WPR 3 Meeting – 6/9/04

Active Load Active loop technique exp(j ) A C G a b = a·C·A·exp(j )·G NEWCOM WPR 3 Meeting – 6/9/04

Harmonic Load Pull n. Controlling the Load/Source condition at harmonic frequencies n. Wave-shaping techniques at microwave frequencies n. Great complexity of the system but potential improvement of the performance NEWCOM WPR 3 Meeting – 6/9/04

Passive harmonic Load Pull n A Tuner for each harmonic n Complex n Easy to change frequency n More harmonic load control n Harmonic Resonators within the slug n Only Phase control of the load n Difficult to change frequency NEWCOM WPR 3 Meeting – 6/9/04 Gf 0 G 2 f 0 Fundamental Harmonic

Active Harmonic Load Pull Politecnico di Torino implementation NEWCOM WPR 3 Meeting – 6/9/04

Four Loop Harmonic System Amplifier VNA Loop Unit Switching Unit Couplers DUT and Probe NEWCOM WPR 3 Meeting – 6/9/04

RF & BB Load Pull System n Exploit BB Load Pull: wide band analysis RF Frequency Test Set BB Frequency Test Set NEWCOM WPR 3 Meeting – 6/9/04

Load Pull and PA Design n Classical PA design information like: n Power Sweep n Optimum Loads n Load/Source Map based design n Active Real Time System Additional info n Gamma In n AM/PM conversion n Harmonic Load conditions n Time Domain Info NEWCOM WPR 3 Meeting – 6/9/04

Load Pull and PA Design n. Data set example NEWCOM WPR 3 Meeting – 6/9/04

Power Sweep and More 1 d. B compression Point Pout=26. 29 d. Bm Gain= 9. 72 d. B IM 3 R= -18. 34 d. Bc IM 3 L=-18. 50 d. Bc Eff=48. 07% NEWCOM WPR 3 Meeting – 6/9/04

Load Pull and PA Design COMBINING LP MAP INFORMATION TO OPTIMIZE POWER PERFORMANCES 12 d. B OUTPUT POWER @ 1 d. B GAIN COMPRESSION NEWCOM WPR 3 Meeting – 6/9/04 26 d. Bm POWER GAIN @ 1 d. B GAIN COMPRESSION

Load Pull and PA Design COMBINING LP MAP INFORMATION TO OPTIMIZE LINEARITY PERFORMANCES PAE @ 1 d. B GAIN COMPRESSION NEWCOM WPR 3 Meeting – 6/9/04 50% C/I 3 LEFT @ POUT = 24 d. Bm -28 d. Bm

Harmonic LP Example 2 nd Harmonic Load Plane PAE f: 3. 6 GHz NEWCOM WPR 3 Meeting – 6/9/04

TD Harmonic Source Pull Ids, A Instantaneous working point for different harmonic Gamma S 0. 2 PAE=65% 0. 18 PAE =55% 0. 16 PAE =51% 0. 14 Fundamental 0. 12 Freq: 1 GHz 0. 1 Gamma L fixed at 0. 08 1 GHz and at 2 GHz SII harm 0. 06 mag phase 149 0. 04 0. 21 88 0. 02 0. 65 0. 54 65 0 0 2 4 6 8 10 12 14 Vds, V NEWCOM WPR 3 Meeting – 6/9/04

TD Harmonic Source Pull PAE=65% 0. 2 12 10 8 0. 12 6 0. 08 4 0. 04 2 0 0. 4 NEWCOM WPR 3 Meeting – 6/9/04 0. 8 1. 2 time, ns 1. 6 Vds, V Ids, A 0. 16

Acknowledgements n. The presentation includes work from many colleagues from the Microwave & RF Group: n. Prof. Andrea Ferrero n. Prof. Marco Pirola n. Dr. Simona Donati n. Dr. Laura Teppati n. Dr. Vittorio Camarchia NEWCOM WPR 3 Meeting – 6/9/04