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S-functions Presentation: The S-parameters for nonlinear components - Measure, Model, Verify, Simulate-

The document discusses S-functions, which are proposed as behavioral models for nonlinear components and applications, analogous to how S-parameters are used for linear components and applications. S-functions aim to simplify design and testing of nonlinear RF/microwave circuits by providing a uniform characterization approach, as S-parameters do for linear circuits. By extracting S-functions from a component, its nonlinear behavior can be modeled and its performance can be simulated, enabling more efficient system-level design and easier comparison to measurements during manufacturing testing. The document outlines benefits of the S-function approach and similarities to the established S-parameter methodology.

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S-functions “The S-parameters for nonlinear components” - Measure, Model, Verify, Simulate - An application in ICE March 2011
Outline ● Why S-functions? What is the impact? ● S-functions, the “S-parameters” for all nonlinear applications? ● S-functions: Key Benefits ● Theory: from S-parameters to S-functions ● Applicability and Assumptions of S-functions ● Confidence in S-functions ● S-function Extraction and Verification Tool ● Deployment of S-functions in ADS and MWO / VSS ● Strengths and Key Capabilities ● References ● Conclusion © 2011 2
Why S-parameters? DESIGN ● Complete characterization of a component in linear mode of operation ● Derive insertion loss, return loss, gain, … ● S-parameters enable system-level interpretation of behavior of the component ● Low – pass filtering, high reflective, ... ● S-parameters enable design in conjunction with other circuits TEST in Manufacturing ● S-parameters can be extracted for the designed circuit ● The S-parameters can be measured for the manufactured circuit and can be compared S-parameters close the characterization, design and test loop © 2011 3
S-parameter Design- and Test-Cycle for Linear Applications At the Foundry Design kit Design library Passive [S-parameter based] S-parameters Devices Semiconductor Manufacturer © 2011 4
S-parameter Design- and Test-Cycle for Linear Applications At the Semiconductor Manufacturer Design Chips S-parameters Design kit Design library [S-parameter based] Iterations almost completely eliminated Design Houses System Manufacturers © 2011 5
Beyond S-parameters??? ● S-parameters, the behavioural model for “linear” applications ● Components in linear mode of operation only ● Filters ● Transistors under small signal of excitation ● ... ● Their success is based on its uniform approach for linear RF and microwave problems both to measure and to simulate ● What about components in nonlinear mode of operation? ● No uniform approach for nonlinear RF and microwave problems ● There is a lot of “trial and error” or “measure – tweak” ● S-parameters are used mainly during device modelling in conjunction with a lot of model expertise to go from small-signal to large-signal © 2011 6
“Trial-Error” Design- and Test-Cycle for “Nonlinear” Applications At the Foundry Design kit Design library Modelling Devices (6 months) Small-Signal Large-Signal Load-Pull Mathematics... Semiconductor Manufacturer © 2011 7
“Trial-Error” Design- and Test-Cycle for “Nonlinear” Applications At the Semiconductor Manufacturer ● Models do not meet the needs of application ● To time costly to develop own models ● Wafer fabs cannot worry about specific problems Initial Chips DataSheet Design Eval Board Trial and Error Design Houses System Manufacturers © 2011 8
The Magic ... S-Parameters S- S-functions © 2011 9
The S-function Design- and Test-Cycle for Active Devices At the Foundry Design kit Design library [S-functions based (*)] Devices S-Functions Semiconductor Manufacturer (*) S-functions for different applications © 2011 10
The S-function Design- and Test-Cycle for Active Devices At the Semiconductor Manufacturer Improving S-functions with application-specific information Design Chips S-functions Design kit Design library [S-functions based] Reducing the number of iterations Design Houses System Manufacturers © 2011 11
Why S-functions? Adopting the S-parameter paradigm DESIGN ● “Complete” characterization of a component in nonlinear mode of operation for specific applications under a relevant set of conditions ● Derive “insertion loss”, “return loss”, “gain”, “mismatch”, conversion coefficients ● S-functions enable system-level interpretation of behaviour of the component ● Power- dependent Low – pass filtering, power conversions, … ● Ideal for dividers, multipliers and mixers ● S-functions enable design in conjunction with other circuits ● When the signals are limited to the relevant set of conditions TEST in Manufacturing ● S-functions can be extracted for the designed circuit ● The S-functions can be measured for the manufactured circuit and can be compared S-functions close the characterization, design and test loop © 2011 12
S-Functions, the “S-parameters” for nonlinear applications? ● S-Functions, the behavioural model for nonlinear applications ● Deal with a subset of nonlinear RF and microwave phenomena in a uniform way as a natural extension of S-parameters ● Will not solve “all” nonlinear problems S-parameters Linear Applications All Other Applications S-functions NonLinear (*) Applications ● Can be “measured” How to define the application boundary? ● Can be used for design in simulators ● Can be used for test to compare with realizations in simulator (*): Nonlinear behaviour determined by a small number (e.g. 2) of tones © 2011 13
S-Functions – Key Benefits S-Functions are for nonlinear applications ... ... what S-parameters are for linear applications ● Simplify the use of HF components and circuits ● Complement limited data sheets with more complete system-level models ● Complement evaluation boards, enabling upfront more realistic simulations ● Improve and speed up the design and test process ● Adequate replacement when classic models fail ● Simulate with a behavioural model, optimized for your design problem ● Same Look and Feel as S-parameters: measure, model, verify and simulate ● Verify the realized circuit with S-functions against the simulation during test ● Shorter time to market for component manufacturers and buyers © 2011 14
From S-parameters to S-functions S-parameters measured at fixed DC bias point S f  VDC f f IDC Keep signal small to f stay in a linear mode of operation S-parameters measured at different DC bias points Linear S V DC ; f  Nonlinear I DC V DC  Remark: for the sake of intuitive explanation, mathematics is not 100% correct © 2011 15
From S-parameters to S-functions f0 2f 0 3f 0 f0 A1  f 0  VDC B2 k f 0 k : 1... 3 ... f0 B1 k f 0 A2=0 50 k : 1... 3 ... f0 2f 3f 0 0 Simple model and “easy” to measure Nonlinear Bm n f 0=F mn V DC , f 0 ,∣a 1  f 0∣ Nonlinear I DC =H V DC , f 0 ,∣a 1  f 0 ∣ © 2011 16
From S-parameters to S-functions Simple model and “easy” to measure Bm n f 0=F mn V DC , f 0 ,∣a 1  f 0∣ I DC =H V DC , f 0 ,∣a 1  f 0 ∣ ● AM-AM ● AM-PM ● Harmonic Distortion But not useful in the real world ● S-functions should be able to predict cascades Input contains harmonics !! “Easy” to measure .... not in reality f0 A1  k f 0 2f ● 0 3f 0 ● Harmonic distortion of source A2 l f 0 ● Imperfect match at input and output © 2011 17
From S-parameters to S-functions A1  k f 0 f0 2f 3f f0 0 0 B2 k f 0 2f 0 3f VDC 0 f0 k : 1... 3 ... B1 k f 0 A2 k f 0  ZL f0 f0 2f 3f 2f 3f 0 0 0 0 Bm n f 0=F mn V DC , f 0 ,∣a 1  f 0∣ I DC =H V DC , f 0 ,∣a 1  f 0 ∣ “Simple” model extension Bm n f 0=F mn V DC , f 0 ,∣a i  j f 0 ∣ , all phase comb of ai  j f 0 I DC =H V DC , f 0 ,∣a i  j f 0∣ , all phase comb of  ai  j f 0  © 2011 18
From S-parameters to S-functions Bm n f 0=F mn V DC , f 0 ,∣a i  j f 0 ∣ , all phase comb of ai  j f 0 I DC =H V DC , f 0 ,∣a i  j f 0∣ , all phase comb of  ai  j f 0  Huge number of combinations with sweeps in amplitude and phase © 2011 19
From S-parameters to S-functions What now ??? f0 f0 2f 0 3f 0 2f 3f 0 0 VDC A1  k f 0 B 2  k f 0 f0 B1 k f 0  f0 A2 k f 0  ZL f0 2f 3f 2f 3f 0 0 0 0 © 2011 20
From S-parameters to S-functions f0 f0 2f 0 3f 0 2f 3f 0 0 VDC A1  k f 0 B 2  k f 0 f0 B1 k f 0  f0 A2 k f 0  ZL f0 2f 3f 2f 3f 0 0 0 0 In many cases : A1  k f 0 , A2 k f 0  with k 1 SMALL Linearize equations in A1  k f 0 , A2 k f 0  with k 1 © 2011 21
From S-parameters to S-functions The intuitive approach f0 f0 2f 0 3f 0 VDC A1  f 0  B2  k f 0 f0 B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 © 2011 22
From S-parameters to S-functions f0 f0 2f 0 3f 0 2f 0 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 © 2011 23
From S-parameters to S-functions x2 f0 f0 2f 3f 2f 0 0 0 x2 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2  f 0  ZL f0 x2 2f 3f 0 0 LINEAR But with frequency conversion, like a mixer © 2011 24
From S-parameters to S-functions f0 f0 2f 0 3f 0 2f 3f 0 0 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 LINEAR Superposition © 2011 25
From S-parameters to S-functions f0 f0 2f 0 3f 0 2f 3f 0 0 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2 k f 0  ZL f0 2f 3f 2f 0 0 0 © 2011 26
From S-parameters to S-functions f0 f0 2f 0 3f 0 2f 3f 0 0 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2 k f 0  ZL f0 2f 3f 2f 3f 0 0 0 0 © 2011 27
From S-parameters to S-functions The Mathematical Approach Bm n f 0=F mn V DC , f 0 ,∣a i  j f 0 ∣ , all phase comb of ai  j f 0 I DC =H V DC , f 0 ,∣a i  j f 0∣ , all phase comb of  ai  j f 0  Linearization The S-functions * I DC =Sf 0001 V DC , A11 , A21 Sf 00ij V DC , A11 , A21  Aij Sfc 00ij V DC , A11 , A21  Aij * Bmn =Sf mn01 V DC , A11 , A21 Sf mnij V DC , A11 , A21 Aij Sfc mnij V DC , A11 , A 21 Aij “LSOP” Sf mnij “Tickle tone” m: output port with j 1 n: frequency at output port m i: input port with B mn≡B m n f 0  j: frequency at input port i with Aij ≡ Ai  j f 0  LSOP: large-signal operating point Sweep in strongly reduced LSOP © 2011 28
Sfc ??? f0 f0 2f 0 3f 0 2f 0 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 © 2011 29
Sfc ??? f0 f0 2f 0 3f 0 2f + df 0 VDC A1  k f 0 B2  k f 0 f0 df B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 df © 2011 30
Sfc ??? * A kl f0 f0 2f 0 3f 0 2f + df 0 VDC A1  k f 0 B2  k f 0 f0 df B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 df © 2011 31
How to extract S-functions? Select a LSOP and keep it constant * Bmn =Sf mn01 V DC , A11 , A21 Sf mnij V DC , A11 , A21  Aij Sfcmnij V DC , A11 , A 21  Aij constant constant constant Change the tickle tones Measure each time Aij , B mn Solve for the S-functions : Sf mnij LSOP , Sfc mnij  LSOP Select a new LSOP and repeat © 2011 32
Extract S-functions for a real device DC Bias f0 f0 or Large-Signal Tickling Source k f0 ZL Source DC Bias ● Repeat the following for all LSOPs of interest ● Select tickle tones Large-Signal ● Large enough to be detectable Source Tickling Source ● Small enough not to violate linearity assumption ● Measure incident and reflected waves for different tickle tones ● Model by solving for all Sf and Sfc ● Resulting into S-functions © 2011 33
S-functions for Real Devices with ZVxPlus Bias ZVxPlus Tickling Source Large-Signal Source © 2011 34
Extract S-functions for a simulated device Bias Settings Large-Signal Source Settings Tickling Source Settings Tickling Source Bias Bias Large-Signal Source © 2011 35
Assumptions of S-functions VDC v3 i3 a1 a2 DUT b1 b2 ` a 1 k f 0  , a 2 l f 0  with l , k ≠0,1 Is causing only a LINEAR perturbation on the NONINEAR behaviour Large-Signal Operating Point (LSOP) Tickle or probing tones a 1  f 0 , a 2  f 0 and v dc a 1 k f 0  , a 2 l f 0 with l , k ≠0,1 © 2011 36
The crucial question for S-functions S-parameters Linear Applications All Other Applications Some S-functions NonLinear Applications Mathematically well-defined To what applications does it apply? a 1 k f 0  , a 2 l f 0 with l , k 1 SMALL 20 dBc down from main tone BUT © 2011 37
Applicability of S-functions a1 a2 a3 DUT X DUT Y b1 b2 b3 Components Prediction ● Transistors ● Harmonic distortion ● Amplifiers ● AM – AM and AM – PM ● Dividers ● Source-pull ● Multipliers ● Load-pull ● Modulation behaviour (*) ● Intermodulation (*) : The component is assumed to be pseudo-static © 2011 38
S-functions in ICE(*) ● Sweepable Large-Signal Operating Point (LSOP) ● Auto or user-defined tickle signal level ● From simple push-the-button solution to access to expert-level details ● Visualization of component behaviour during data collection ● Easy model verification (no EDA tool required) ● Sanity checks included ● Easy export to and integration in Agilent™ ADS and AWR™ MWO ● Support for mismatched environments ● Harmonics generated by RF sources don't cause any problem ● Simple output prediction does not require EDA tool ● Export to and integration in other EDA tools on request ● Possible to extend the LSOP variables, e.g. temperature (*) Integrated Component Characterisation Environment © 2011 39
Confidence in S-functions ● Constantness of LSOP ● All Sf, and Sfc are assumed to be extracted at fixed LSOP ● e.g. variation in DC drain voltage due to changing current violates this assumption ● Interpolation capability of all Sf, and Sfc ● LSOP interleaving verification measurements ● Linearity assumption of tickle tones ● Model verification for different amplitude and phases of tickle tones Confidence Extract Measure through Simulate S-functions Verification © 2011 40
Confidence in S-functions through Verification ADS MWO ADS: Agilent Technologies Advanced Design Systems design software MWO: AWR Corporation's Microwave Office design software © 2011 41
S-functions for Real and Simulated Components / Circuits Measurements Simulations Data Collection on Real Devices On Virtual Devices using ICE (*) in Simulation Tool (ADS - MWO) Extraction S-functions S-functions Verifications Simulators S-functions Deployment (ADS - MWO) © 2011 42
S-functions Verification – Constantness of LSOP Select LSOP variable Variation on Filter for a LSOP variable drain bias voltage and value Variation on fixed input power © 2011 43
S-functions Verification – Interpolation Capability verify interpolation of b2 using independent set of measurements © 2011 44
S-functions Verification – Linearity Assumption of Tickle Tones Large-Signal DC Bias f0 f0 or Large-Signal Tickling Source k f0 ZL Source Small-Signal for harmonics DC Bias DC Bias a 2 k f 0 Switching Amplifier design  L 2 f 0   L  k f 0  L 3 f 0 a 2 2 f 0  Still small signal? a 2 3 f 0 © 2011 45
ICEBreaker – Option S-function Verification Tool ICEBreaker Predicted Compare Dataset ICEBreaker Datasets Dataset ● Measured Data ● Using S-function ● Derived Quantities ● Realistic Sweep Plan ● Incident / Reflected Waves ● Under multi-harmonic Load-Pull ● Voltage and Current ● Absolute Error ● Relative Error © 2011 46
Generation of “S-function Predicted Dataset” in ICEBreaker Generate S-function based Dataset Compare Dataset and S-function based Dataset © 2011 47
Absolute Comparisons with S-function Predictions Quantity for which to compare measurement and Idc_out prediction ● Derived quantities ➢ Idc_out ➢ Gain ➢ Pdel_in ➢ Pdel_out ➢ PAE ➢ .. ➢ Frequency selection ● Basic quantities ➢ Incident waves ➢ Reflected waves ➢ Voltages / Currents ➢ Frequency selection Measurements S-function Prediction Absolute Error © 2011 48
Relative Comparisons with S-function Predictions b_out(3f0) ● Versus ➢ Harmonic index ➢ Harmonic refl Relative Error (dB) © 2011 49
Case Study(*): EPA120B-100P  EPA120B-100P • high efficiency heterojunction power FET • power output: + 29.0dBm typ. • power gain: 11.5dB typ. @ 12 GHz Real Device Virtual Device (*) : all results in this slide set are based on S-function extraction and deployment for this device © 2011 © 2009 - NMDG NV 50
Data Collection with ZVxPlus LSOP “tickle” sweep settings detailed detailed feedback feedback of LSOP on tickle for actual for actual measurement measurement © 2011 51
Expert Details If Desired @ Data Collection Summary Monitor RF and DC source settings Observe what happens at the DUT © 2011 52
S-functions Extraction S11 S12 S22 S21 meaningful complex ~3 dB compression conjugate © 2011 53
S-functions Verifications – Residual Error zoom in on zoom in tickling on result Number of measurements required to extract S-functions amplitude of complex error for measured and predicted b2 using extraction data © 2011 54
S-functions Verification – Interpolation Capability verify interpolation of b2 using independent set of measurements © 2011 55
S-functions Verifications – Constantness LSOP Select LSOP variable Variation on Filter for a LSOP variable drain bias voltage and value Variation on fixed input power © 2011 56
S-functions in ADS Acknowledgement: With the support from Agilent Technologies providing ADS licensing © 2011 57
S-functions Useage in Agilent ADS EPAClassAMediumPower.ael EPAClassAMediumPower.dsn Set of equations using FDD Values of all Sf, Sfc © 2011 58
S-functions Verification in ADS - Schematic ● Example: Harmonic Balance simulation with measured a1 and a2 spectra ● Excitation: Sweeping through a subset of LSOP points + tickle tones Measured incident waves S-function to be verified Measurements for model verification Access to measured data using DAC Sweeping through subset of LSOP and tickle tones © 2011 59
S-functions Verification in ADS - Frequency Domain Frequency = 2 GHz, VDC1= -1.3 V, VDC2= +2.0 V Measurements at different input powers than those which were used for S-functions model extraction! circles – measurements solid lines - simulations © 2011 60
S-functions Verification in ADS - Time Domain circles – measurements Frequency = 2 GHz, VDC1= -1.3 V, VDC2= +2.0 V, Pa1 = +10.0 dBm solid lines - simulations Saturation Pinch-off © 2011 61
S-functions in ADS – Modulation Prediction - Schematic Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pa1 = +0.0 dBm – Class C © 2011 62
S-functions in ADS – Modulation Prediction - Display Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pa1 = +0.0 dBm – Class C © 2011 63
S-functions in ADS – Source-Pull - Schematic Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pav = +1.0 dBm – Class C Reflection : -0.27 © 2011 64
S-functions in ADS – Source-Pull - Schematic Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pav = +1.0 dBm – Class C Complex Conjugate Measured Input Impedance © 2011 65
S-functions in MWO Acknowledgement: With the support from AWR providing MWO / VSS licensing © 2011 66
S-functions Usage in AWR MWO MDF file SUBCKT ID=S1 BIASTEE NET="SFUNC_Model" ID=X2 1 RF 2 & RF BIASTEE 2 DC DC ID=X1 PORT 3 P=2 Z=50 Ohm Model data 2 RF 1 1 RF & DC DC PORT_PS1 3 DCVS .. P=1 Z=50 Ohm ID=V2 .. V=6 V PStart=PinMin dBm 1.16226472890446E-16,-1.35308431126191E-16 PStop=PinMax dBm PStep=PinStep dB -3.15025783237388E-15,4.72191730160887E-15 DCVS ID=V1 9.71445146547012E-17,-2.37310171513627E-15 V=-1.8 V 1.51267887105178E-15,1.07899800205757E-15 -2.98198965520413E-15,1.59594559789866E-15 -5.759281940243E-16,-1.97758476261356E-16 -1.83880688453542E-15,1.92901250528621E-15 -5.06539254985228E-16,2.94209101525666E-15 -2.50494069931051E-15,-6.73072708679001E-16 -8.60422844084496E-16,2.65412691824451E-16 -2.019218126037E-15,2.7373936450914E-15 -2.28289609438548E-15,1.70870262383715E-15 1.08246744900953E-15,-6.78276879106932E-16 -1.02955838299224E-15,-1.31578775652841E-15 5.45570533194706E-16,3.99333344169861E-15 -3.62904151174348E-15,-1.74860126378462E-15 -2.00100352953925E-15,-5.68989300120393E-16 2.14975606760426E-15,-5.53376788836601E-16 -1.16226472890446E-15,-2.44942954807925E-15 2.08166817117217E-16,2.4980018054066E-15 1.04372118124342E-05,-1.36061371223614E-05 2.85882428840978E-15,3.11556336285435E-15 -2.15105711021124E-16,1.37390099297363E-15 9.71445146547012E-16,9.95731275210687E-16 -1.69309011255336E-15,2.33146835171283E-15 4.27435864480685E-15,3.3584246494911E-15 -1.08246744900953E-15,-8.60422844084496E-16 … 2D and 3D package data © 2011 67
S-functions Verification in MWO - Frequency Domain HBT UNER2 ID=X1 Mag1=0 Ang1=0 Deg Mag2=0 Ang2=0 Deg Mag3=0 Ang3=0 Deg Fo=2 GHz Zo=50 Ohm PORT _PS1 P=1 1 2 Z=50 Ohm PStart=-20 dBm BIAST EE 2 PStop=8 dBm ID=X2 PORT PStep=1 dB 3:Bias P=2 SUBCK T 2 RF 1 1 Z=50 Ohm RF & ID=S1 DC NET ="EPA_120_B " DC 3 DCVS ID=V1 V=DC2val V DCVS ID=V2 V=DC 1val V Po with swept Pin Gain and Phase with swept Pin 40 20 19.5 20 19 F0 18.5 DB(|LSSnm(PORT_2,PORT_1,1,1)|)[1,X] 0 18 Swept Power.AP_HB Ang(LSSnm(PORT_2,PORT_1,2,1))[1,X] (Deg) 17.5 Swept Power.AP_HB -20 17 150 2F0 -40 100 DB(|Pcomp(PORT_2,1)|)[1,X] (dBm) Swept Power.AP_HB 50 3F0 DB(|Pcomp(PORT_2,2)|)[1,X] (dBm) -60 Swept Power.AP_HB DB(|Pcomp(PORT_2,3)|)[1,X] (dBm) Swept Power.AP_HB 0 -80 -50 -20 -15 -10 -5 0 5 10 -20 -15 -10 -5 0 5 10 Power (dBm) Power (dBm) © 2011 68
S-functions Verification in MWO - Time Domain Vtime(V_METER.VM1,1)[*,T] (V) Itime(I_METER.AMP1,1)[*,T] (mA) HBTUNER2 Waveform Tests.AP_HB Waveform Tests.AP_HB ID=X1 Mag1=0 Ang1=0 Deg Mag2=0 Ang2=0 Deg Mag3=0 IV Ang3=0 Deg 250 Fo=2 GHz SUBCKT Zo=50 Ohm PORT_PS1 ID=S1 200 P=1 NET="EPA_120_B" 1 2 Z=50 Ohm PStart=-20 dBm BIASTEE 2 150 PStop=8 dBm ID=X2 PORT PStep=1 dB I_METER 3:Bias P=2 2 RF 1 1 ID=AMP1 Z=50 Ohm 100 RF & DC DC 50 3 V _METER DCVS ID =VM1 ID=V1 V=DC2val V 0 15 DCVS ID=V2 V=DC1val V 10 5 DB(|Pcomp(PORT_2,1)|)[1,X] (dBm) DB(|Pcomp(PORT_2,2)| )[1,X] (dBm) DB(|Pcomp(PORT_2,3)|)[1,X] (dBm) Waveform Tests.AP_HB Waveform Tests.AP_HB Waveform Tests.AP_HB0 0 0.2 0.4 0.6 0.8 1 Harmonics 40 Time (ns) 20 0 -20 -40 -60 -80 -20 -10 0 8 Power (dBm) © 2011 69
S-functions in MWO – Modulation Prediction - Schematic DB(PWR_SPEC(TP.AMP Out,1000,0,10,0,-1,0,-1,1,0,4,0,1,0)) (dBm) DB(PWR_SPEC(TP.AMP In,1000,0,10,0,-1,0,-1,1,0,4,0,1,0)) (dBm) 16QAM System 16QAM System HBTUNER2 ID=DCBlock2 Mag1=0 Ang1=0 Deg Mag2=0 Ang2=0 Deg Mag3=0 ACPR SUBCKT Ang3=0 Deg Fo=2000 GHz 50 ID=S1 Zo=50 Ohm ISOL8R NET="EPA_120_B" ID=U1 1 2 R=50 Ohm LOSS=0 dB BIASTEE 2 ISOL=30 dB ID=X1 PORT 3:Bias P=2 2 RF RF & 1 1 Z=50 Ohm 0 DC DC PORT_PS1 3 DCVS P=1 ID=V3 Z=50 Ohm V=DC2val V PStart=-20 dBm PStop=8 dBm PStep=0.5 dB DCVS -50 ID=V1 V=DC1val V -100 -150 1.92 1.94 1.96 1.98 2 2.02 2.04 2.06 2.08 Frequency (GHz) VS A ID=M1 VA RNA ME="" VA LUE S=0 NA VG= PBA SE = -76 V e c to r S w e p t v a r ia b le S ig n a l SRC MEAS A n a ly z e r QAM_S RC G e n e r a l R e c e iv e r ID=A1 MO D=16-QA M (Gray) OUT LV L=-0.2 OLVLT Y P=Avg. Power (dB m) NL_ S AW GN RAT E=_DRA T E ID=S 1 BER ID=A3 CTRFRQ=2 GHz TP NET ="AMAM A MPM.AP_HB " PW R=-170 ID=5 SIMT YP=Harm onic Balanc e TP PLST Y P=Root Rais ed Cos ine ID=AMP In PW RT YP=Avg. Po wer, Sym bol (dBW ) VARNAME="PBA SE" ID=AMP Out ALPHA =0.35 NO SE=RF Budget only I VALUES=s tepped(-76,-40,2) LOSS=0 dB PLSLN= RFIF RQ= QAM_RX OUT FL="" ID=A 2 1 R D 2 BER IQ 3 C irc u it 5 4 B E R D e te c to r B a s e d A m p lifie r C h a n n e l N o is e 1 6 Q A M S o u rc e TP ID=RX Cons tellation 1 6 Q A M (G r a y ) S y s te m © 2011 70
S-functions in MWO – Load-Pull HBTUNER2 ID=DCBlock2 Mag1=0.8 Load Tuner (and bias) Ang1=40 Deg LP_Data_Low_Power Mag2=0 Ang2=0 Deg 1.0 Swp Max Mag3=0 0.8 -0.89 Ang3=0 Deg Fo=2 GHz 6 0. Zo=50 Ohm 0 . 2 4 . 1 2 PORT1 0 0 . 3 P=1 2 p8 0 p1: Pcomp_PORT_2_1_M_DB = -2.87 Z=50 Ohm PORT p7 4. Pwr=10 dBm 3:Bias P=2 p9 p2: Pcomp_PORT_2_1_M_DB = -2.65 SUBCKT 5. 0 2 RF 1 Z=50 Ohm 2 p6 1 ID=S1 0. RF & p10 p3: Pcomp_PORT_2_1_M_DB = -2.43 DC NET="SFUNC_Model" p5 DC 10. 0 BIASTEE p4: Pcomp_PORT_2_1_M_DB = -2.21 3 DCVS ID=X1 p4 ID=V2 10.0 V=7 V 4.0 p5: Pcomp_PORT_2_1_M_DB = -1.99 0.2 0.4 0.6 0.8 1.0 2.0 3.0 5.0 0 p3 p6: Pcomp_PORT_2_1_M_DB = -1.77 DCVS p2 ID=V1 .0 -10 p7: Pcomp_PORT_2_1_M_DB = -1.55 V=-0.6 V p1 -0 . 2 0 . p8: Pcomp_PORT_2_1_M_DB = -1.33 -5 0 . -4 p9: Pcomp_PORT_2_1_M_DB = -1.11 p10: Pcomp_PORT_2_1_M_DB = -0.89 0 . 3 4 - . 0 - 0 . 2 6 - . -0 8 Swp Min -1.0 -0. -2.87 LP_Data_High_Power S M wp ax 1.0 0 .8 25.93 6 0. .0 2 .4 0 p1: Pcomp_PORT _2_1_M_DB = 21.93 .0 3 p9 p8 p7 p6 p5 p2: Pcomp_PORT _2_1_M_DB = 22.33 p4 4 .0 2 p10 p3 5. 0 p3: Pcomp_PORT _2_1_M_DB = 22.73 0. p2 0 p4: Pcomp_PORT _2_1_M_DB = 23.13 1 0. p11 p5: Pcomp_PORT _2_1_M_DB = 23.53 10.0 0.4 0.8 3.0 0.2 0.6 1.0 2.0 4.0 5.0 p1 p6: Pcomp_PORT _2_1_M_DB = 23.93 0 0 . p7: Pcomp_PORT _2_1_M_DB = 24.33 - 10 p8: Pcomp_PORT _2_1_M_DB = 24.73 .2 -0 .0 .0 -5 p9: Pcomp_PORT _2_1_M_DB = 25.13 -4 0 p10: Pcomp_PORT _2_1_M_DB = 25.53 3. 4 - 0. - p11: Pcomp_PORT _2_1_M_DB = 25.93 0 2. .6 - -0 8 S M wp in -1.0 - 0. 21.93 © 2011 71
S-functions Strengths ● S-functions are completely public ● S-functions are transparent ● S-functions are connected into ADS and MWO and can be connected in other tools on request, e.g. Matlab ● S-functions are closely integrated with load-pull in general and especially with tuners from Focus Microwave ● S-functions extraction tool has a verification capability for LSOP constantness and interpolation capability, investigating quality of model, without needing a simulation tool ● The source- and load-pull software ICEBreaker from NMDG allows S- function verification, related to the linearity assumption ● Customers can explore the capabilities of S-functions via NMDG services © 2011 72
S-Functions - Key Capabilities ● Natural extension of S-parameters ● Reduce to S-parameters for small-signal excitation ● S-parameters are cascadeable, S-Functions are cascadeable too ● e.g. Transistors, amplifiers, dividers, multipliers ● Predict harmonic behaviour of components under different impedances ● Source – Pull ● Load – Pull ● Harmonic distortion, Waveforms ● Predict modulation behaviour of components under different impedances ● When no long-term memory effects ● Valid for multi-ports, applicable to differential components © 2011 73
References ● F. Verbeyst and M. Vanden Bossche, “VIOMAP, the S-parameter equivalent for weakly nonlinear RF and microwave devices”, published in the Microwave Symposium Digest of IEEE 1994 MTT-S International and published in the 1994 Special Symposium Issue of the MTT Transactions, vol. 42, no. 12, pp. 2531 – 2535. ● F. Verbeyst and M. Vanden Bossche, “VIOMAP, 16QAM and Spectral Regrowth: Enhanced Prediction and Predistortion based on Two-Tone Black-Box Model Extraction”, published in the Proceedings of the 45th ARFTG Conference, Orlando, June 1995 and winner of the “Best Conference Paper Award”. ● J. Verspecht and P. Van Esch, “Accurately characterizating of hard nonlinear behaviour of microwave components by the Nonlinear Network Measurement System: introducing the nonlinear scattering function,” Proc. International Workshop on Integrated Nonlinear Microwave and Millimiterwave Circuits (INMMiC), October 1998, pp.17-26. ● J. Verspecht, “Scattering functions for nonlinear behavioral modeling in the frequency domain,” IEEE MTT-S Int. Microwave Symp. Workshop, June 2003. ● J. Verspecht and D.E. Root “Polyharmonic Distortion Modeling,” IEEE Microwave Magazine, vol.7 no.3, June 2006, pp.44-57. ● D.E. Root, J. Horn, L. Betts, C. Gillease, and J. Verspecht, ”X-Parameters: The new paradigm for measurement, modeling, and design of nonlinear RF and microwave components,” Microwave Engineering Europe, December 2008, pp. 16-21. © 2011 74
Conclusion ● S-functions are a natural extension to S-parameters for nonlinear behaviour ● S-functions aren't much more complex than S-parameters ● S-functions are accurate when assumptions are not violated ● Linearity assumption ● S-function extraction is supported on R&S network analysers ● S-functions can be coupled into ADS and MWO ● S-functions can be used to compress or hide specifics of nonlinear circuits in ADS and MWO For more information info@nmdg.be www.nmdg.be © 2011 75
Explore the power of S-functions Send your device or circuit to NMDG ... ` … and NMDG sends you the S-functions Please contact NMDG at info@nmdg.be © 2011 76

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S-functions Presentation: The S-parameters for nonlinear components - Measure, Model, Verify, Simulate-

  • 1.
    S-functions “The S-parameters for nonlinear components” - Measure, Model, Verify, Simulate - An application in ICE March 2011
  • 2.
    Outline ● Why S-functions? What is the impact? ● S-functions, the “S-parameters” for all nonlinear applications? ● S-functions: Key Benefits ● Theory: from S-parameters to S-functions ● Applicability and Assumptions of S-functions ● Confidence in S-functions ● S-function Extraction and Verification Tool ● Deployment of S-functions in ADS and MWO / VSS ● Strengths and Key Capabilities ● References ● Conclusion © 2011 2
  • 3.
    Why S-parameters? DESIGN ● Complete characterization of a component in linear mode of operation ● Derive insertion loss, return loss, gain, … ● S-parameters enable system-level interpretation of behavior of the component ● Low – pass filtering, high reflective, ... ● S-parameters enable design in conjunction with other circuits TEST in Manufacturing ● S-parameters can be extracted for the designed circuit ● The S-parameters can be measured for the manufactured circuit and can be compared S-parameters close the characterization, design and test loop © 2011 3
  • 4.
    S-parameter Design- andTest-Cycle for Linear Applications At the Foundry Design kit Design library Passive [S-parameter based] S-parameters Devices Semiconductor Manufacturer © 2011 4
  • 5.
    S-parameter Design- andTest-Cycle for Linear Applications At the Semiconductor Manufacturer Design Chips S-parameters Design kit Design library [S-parameter based] Iterations almost completely eliminated Design Houses System Manufacturers © 2011 5
  • 6.
    Beyond S-parameters??? ● S-parameters, the behavioural model for “linear” applications ● Components in linear mode of operation only ● Filters ● Transistors under small signal of excitation ● ... ● Their success is based on its uniform approach for linear RF and microwave problems both to measure and to simulate ● What about components in nonlinear mode of operation? ● No uniform approach for nonlinear RF and microwave problems ● There is a lot of “trial and error” or “measure – tweak” ● S-parameters are used mainly during device modelling in conjunction with a lot of model expertise to go from small-signal to large-signal © 2011 6
  • 7.
    “Trial-Error” Design- andTest-Cycle for “Nonlinear” Applications At the Foundry Design kit Design library Modelling Devices (6 months) Small-Signal Large-Signal Load-Pull Mathematics... Semiconductor Manufacturer © 2011 7
  • 8.
    “Trial-Error” Design- andTest-Cycle for “Nonlinear” Applications At the Semiconductor Manufacturer ● Models do not meet the needs of application ● To time costly to develop own models ● Wafer fabs cannot worry about specific problems Initial Chips DataSheet Design Eval Board Trial and Error Design Houses System Manufacturers © 2011 8
  • 9.
    The Magic ... S-Parameters S- S-functions © 2011 9
  • 10.
    The S-function Design-and Test-Cycle for Active Devices At the Foundry Design kit Design library [S-functions based (*)] Devices S-Functions Semiconductor Manufacturer (*) S-functions for different applications © 2011 10
  • 11.
    The S-function Design-and Test-Cycle for Active Devices At the Semiconductor Manufacturer Improving S-functions with application-specific information Design Chips S-functions Design kit Design library [S-functions based] Reducing the number of iterations Design Houses System Manufacturers © 2011 11
  • 12.
    Why S-functions? Adoptingthe S-parameter paradigm DESIGN ● “Complete” characterization of a component in nonlinear mode of operation for specific applications under a relevant set of conditions ● Derive “insertion loss”, “return loss”, “gain”, “mismatch”, conversion coefficients ● S-functions enable system-level interpretation of behaviour of the component ● Power- dependent Low – pass filtering, power conversions, … ● Ideal for dividers, multipliers and mixers ● S-functions enable design in conjunction with other circuits ● When the signals are limited to the relevant set of conditions TEST in Manufacturing ● S-functions can be extracted for the designed circuit ● The S-functions can be measured for the manufactured circuit and can be compared S-functions close the characterization, design and test loop © 2011 12
  • 13.
    S-Functions, the “S-parameters”for nonlinear applications? ● S-Functions, the behavioural model for nonlinear applications ● Deal with a subset of nonlinear RF and microwave phenomena in a uniform way as a natural extension of S-parameters ● Will not solve “all” nonlinear problems S-parameters Linear Applications All Other Applications S-functions NonLinear (*) Applications ● Can be “measured” How to define the application boundary? ● Can be used for design in simulators ● Can be used for test to compare with realizations in simulator (*): Nonlinear behaviour determined by a small number (e.g. 2) of tones © 2011 13
  • 14.
    S-Functions – KeyBenefits S-Functions are for nonlinear applications ... ... what S-parameters are for linear applications ● Simplify the use of HF components and circuits ● Complement limited data sheets with more complete system-level models ● Complement evaluation boards, enabling upfront more realistic simulations ● Improve and speed up the design and test process ● Adequate replacement when classic models fail ● Simulate with a behavioural model, optimized for your design problem ● Same Look and Feel as S-parameters: measure, model, verify and simulate ● Verify the realized circuit with S-functions against the simulation during test ● Shorter time to market for component manufacturers and buyers © 2011 14
  • 15.
    From S-parameters toS-functions S-parameters measured at fixed DC bias point S f  VDC f f IDC Keep signal small to f stay in a linear mode of operation S-parameters measured at different DC bias points Linear S V DC ; f  Nonlinear I DC V DC  Remark: for the sake of intuitive explanation, mathematics is not 100% correct © 2011 15
  • 16.
    From S-parameters toS-functions f0 2f 0 3f 0 f0 A1  f 0  VDC B2 k f 0 k : 1... 3 ... f0 B1 k f 0 A2=0 50 k : 1... 3 ... f0 2f 3f 0 0 Simple model and “easy” to measure Nonlinear Bm n f 0=F mn V DC , f 0 ,∣a 1  f 0∣ Nonlinear I DC =H V DC , f 0 ,∣a 1  f 0 ∣ © 2011 16
  • 17.
    From S-parameters toS-functions Simple model and “easy” to measure Bm n f 0=F mn V DC , f 0 ,∣a 1  f 0∣ I DC =H V DC , f 0 ,∣a 1  f 0 ∣ ● AM-AM ● AM-PM ● Harmonic Distortion But not useful in the real world ● S-functions should be able to predict cascades Input contains harmonics !! “Easy” to measure .... not in reality f0 A1  k f 0 2f ● 0 3f 0 ● Harmonic distortion of source A2 l f 0 ● Imperfect match at input and output © 2011 17
  • 18.
    From S-parameters toS-functions A1  k f 0 f0 2f 3f f0 0 0 B2 k f 0 2f 0 3f VDC 0 f0 k : 1... 3 ... B1 k f 0 A2 k f 0  ZL f0 f0 2f 3f 2f 3f 0 0 0 0 Bm n f 0=F mn V DC , f 0 ,∣a 1  f 0∣ I DC =H V DC , f 0 ,∣a 1  f 0 ∣ “Simple” model extension Bm n f 0=F mn V DC , f 0 ,∣a i  j f 0 ∣ , all phase comb of ai  j f 0 I DC =H V DC , f 0 ,∣a i  j f 0∣ , all phase comb of  ai  j f 0  © 2011 18
  • 19.
    From S-parameters toS-functions Bm n f 0=F mn V DC , f 0 ,∣a i  j f 0 ∣ , all phase comb of ai  j f 0 I DC =H V DC , f 0 ,∣a i  j f 0∣ , all phase comb of  ai  j f 0  Huge number of combinations with sweeps in amplitude and phase © 2011 19
  • 20.
    From S-parameters toS-functions What now ??? f0 f0 2f 0 3f 0 2f 3f 0 0 VDC A1  k f 0 B 2  k f 0 f0 B1 k f 0  f0 A2 k f 0  ZL f0 2f 3f 2f 3f 0 0 0 0 © 2011 20
  • 21.
    From S-parameters toS-functions f0 f0 2f 0 3f 0 2f 3f 0 0 VDC A1  k f 0 B 2  k f 0 f0 B1 k f 0  f0 A2 k f 0  ZL f0 2f 3f 2f 3f 0 0 0 0 In many cases : A1  k f 0 , A2 k f 0  with k 1 SMALL Linearize equations in A1  k f 0 , A2 k f 0  with k 1 © 2011 21
  • 22.
    From S-parameters toS-functions The intuitive approach f0 f0 2f 0 3f 0 VDC A1  f 0  B2  k f 0 f0 B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 © 2011 22
  • 23.
    From S-parameters toS-functions f0 f0 2f 0 3f 0 2f 0 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 © 2011 23
  • 24.
    From S-parameters toS-functions x2 f0 f0 2f 3f 2f 0 0 0 x2 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2  f 0  ZL f0 x2 2f 3f 0 0 LINEAR But with frequency conversion, like a mixer © 2011 24
  • 25.
    From S-parameters toS-functions f0 f0 2f 0 3f 0 2f 3f 0 0 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 LINEAR Superposition © 2011 25
  • 26.
    From S-parameters toS-functions f0 f0 2f 0 3f 0 2f 3f 0 0 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2 k f 0  ZL f0 2f 3f 2f 0 0 0 © 2011 26
  • 27.
    From S-parameters toS-functions f0 f0 2f 0 3f 0 2f 3f 0 0 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2 k f 0  ZL f0 2f 3f 2f 3f 0 0 0 0 © 2011 27
  • 28.
    From S-parameters toS-functions The Mathematical Approach Bm n f 0=F mn V DC , f 0 ,∣a i  j f 0 ∣ , all phase comb of ai  j f 0 I DC =H V DC , f 0 ,∣a i  j f 0∣ , all phase comb of  ai  j f 0  Linearization The S-functions * I DC =Sf 0001 V DC , A11 , A21 Sf 00ij V DC , A11 , A21  Aij Sfc 00ij V DC , A11 , A21  Aij * Bmn =Sf mn01 V DC , A11 , A21 Sf mnij V DC , A11 , A21 Aij Sfc mnij V DC , A11 , A 21 Aij “LSOP” Sf mnij “Tickle tone” m: output port with j 1 n: frequency at output port m i: input port with B mn≡B m n f 0  j: frequency at input port i with Aij ≡ Ai  j f 0  LSOP: large-signal operating point Sweep in strongly reduced LSOP © 2011 28
  • 29.
    Sfc ??? f0 f0 2f 0 3f 0 2f 0 VDC A1  k f 0 B2  k f 0 f0 B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 © 2011 29
  • 30.
    Sfc ??? f0 f0 2f 0 3f 0 2f + df 0 VDC A1  k f 0 B2  k f 0 f0 df B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 df © 2011 30
  • 31.
    Sfc ??? * A kl f0 f0 2f 0 3f 0 2f + df 0 VDC A1  k f 0 B2  k f 0 f0 df B1 k f 0  f0 A2  f 0  ZL f0 2f 3f 0 0 df © 2011 31
  • 32.
    How to extractS-functions? Select a LSOP and keep it constant * Bmn =Sf mn01 V DC , A11 , A21 Sf mnij V DC , A11 , A21  Aij Sfcmnij V DC , A11 , A 21  Aij constant constant constant Change the tickle tones Measure each time Aij , B mn Solve for the S-functions : Sf mnij LSOP , Sfc mnij  LSOP Select a new LSOP and repeat © 2011 32
  • 33.
    Extract S-functions fora real device DC Bias f0 f0 or Large-Signal Tickling Source k f0 ZL Source DC Bias ● Repeat the following for all LSOPs of interest ● Select tickle tones Large-Signal ● Large enough to be detectable Source Tickling Source ● Small enough not to violate linearity assumption ● Measure incident and reflected waves for different tickle tones ● Model by solving for all Sf and Sfc ● Resulting into S-functions © 2011 33
  • 34.
    S-functions for RealDevices with ZVxPlus Bias ZVxPlus Tickling Source Large-Signal Source © 2011 34
  • 35.
    Extract S-functions fora simulated device Bias Settings Large-Signal Source Settings Tickling Source Settings Tickling Source Bias Bias Large-Signal Source © 2011 35
  • 36.
    Assumptions of S-functions VDC v3 i3 a1 a2 DUT b1 b2 ` a 1 k f 0  , a 2 l f 0  with l , k ≠0,1 Is causing only a LINEAR perturbation on the NONINEAR behaviour Large-Signal Operating Point (LSOP) Tickle or probing tones a 1  f 0 , a 2  f 0 and v dc a 1 k f 0  , a 2 l f 0 with l , k ≠0,1 © 2011 36
  • 37.
    The crucial questionfor S-functions S-parameters Linear Applications All Other Applications Some S-functions NonLinear Applications Mathematically well-defined To what applications does it apply? a 1 k f 0  , a 2 l f 0 with l , k 1 SMALL 20 dBc down from main tone BUT © 2011 37
  • 38.
    Applicability of S-functions a1 a2 a3 DUT X DUT Y b1 b2 b3 Components Prediction ● Transistors ● Harmonic distortion ● Amplifiers ● AM – AM and AM – PM ● Dividers ● Source-pull ● Multipliers ● Load-pull ● Modulation behaviour (*) ● Intermodulation (*) : The component is assumed to be pseudo-static © 2011 38
  • 39.
    S-functions in ICE(*) ● Sweepable Large-Signal Operating Point (LSOP) ● Auto or user-defined tickle signal level ● From simple push-the-button solution to access to expert-level details ● Visualization of component behaviour during data collection ● Easy model verification (no EDA tool required) ● Sanity checks included ● Easy export to and integration in Agilent™ ADS and AWR™ MWO ● Support for mismatched environments ● Harmonics generated by RF sources don't cause any problem ● Simple output prediction does not require EDA tool ● Export to and integration in other EDA tools on request ● Possible to extend the LSOP variables, e.g. temperature (*) Integrated Component Characterisation Environment © 2011 39
  • 40.
    Confidence in S-functions ● Constantness of LSOP ● All Sf, and Sfc are assumed to be extracted at fixed LSOP ● e.g. variation in DC drain voltage due to changing current violates this assumption ● Interpolation capability of all Sf, and Sfc ● LSOP interleaving verification measurements ● Linearity assumption of tickle tones ● Model verification for different amplitude and phases of tickle tones Confidence Extract Measure through Simulate S-functions Verification © 2011 40
  • 41.
    Confidence in S-functionsthrough Verification ADS MWO ADS: Agilent Technologies Advanced Design Systems design software MWO: AWR Corporation's Microwave Office design software © 2011 41
  • 42.
    S-functions for Realand Simulated Components / Circuits Measurements Simulations Data Collection on Real Devices On Virtual Devices using ICE (*) in Simulation Tool (ADS - MWO) Extraction S-functions S-functions Verifications Simulators S-functions Deployment (ADS - MWO) © 2011 42
  • 43.
    S-functions Verification –Constantness of LSOP Select LSOP variable Variation on Filter for a LSOP variable drain bias voltage and value Variation on fixed input power © 2011 43
  • 44.
    S-functions Verification –Interpolation Capability verify interpolation of b2 using independent set of measurements © 2011 44
  • 45.
    S-functions Verification –Linearity Assumption of Tickle Tones Large-Signal DC Bias f0 f0 or Large-Signal Tickling Source k f0 ZL Source Small-Signal for harmonics DC Bias DC Bias a 2 k f 0 Switching Amplifier design  L 2 f 0   L  k f 0  L 3 f 0 a 2 2 f 0  Still small signal? a 2 3 f 0 © 2011 45
  • 46.
    ICEBreaker – OptionS-function Verification Tool ICEBreaker Predicted Compare Dataset ICEBreaker Datasets Dataset ● Measured Data ● Using S-function ● Derived Quantities ● Realistic Sweep Plan ● Incident / Reflected Waves ● Under multi-harmonic Load-Pull ● Voltage and Current ● Absolute Error ● Relative Error © 2011 46
  • 47.
    Generation of “S-functionPredicted Dataset” in ICEBreaker Generate S-function based Dataset Compare Dataset and S-function based Dataset © 2011 47
  • 48.
    Absolute Comparisons withS-function Predictions Quantity for which to compare measurement and Idc_out prediction ● Derived quantities ➢ Idc_out ➢ Gain ➢ Pdel_in ➢ Pdel_out ➢ PAE ➢ .. ➢ Frequency selection ● Basic quantities ➢ Incident waves ➢ Reflected waves ➢ Voltages / Currents ➢ Frequency selection Measurements S-function Prediction Absolute Error © 2011 48
  • 49.
    Relative Comparisons withS-function Predictions b_out(3f0) ● Versus ➢ Harmonic index ➢ Harmonic refl Relative Error (dB) © 2011 49
  • 50.
    Case Study(*): EPA120B-100P  EPA120B-100P • high efficiency heterojunction power FET • power output: + 29.0dBm typ. • power gain: 11.5dB typ. @ 12 GHz Real Device Virtual Device (*) : all results in this slide set are based on S-function extraction and deployment for this device © 2011 © 2009 - NMDG NV 50
  • 51.
    Data Collection withZVxPlus LSOP “tickle” sweep settings detailed detailed feedback feedback of LSOP on tickle for actual for actual measurement measurement © 2011 51
  • 52.
    Expert Details IfDesired @ Data Collection Summary Monitor RF and DC source settings Observe what happens at the DUT © 2011 52
  • 53.
    S-functions Extraction S11 S12 S22 S21 meaningful complex ~3 dB compression conjugate © 2011 53
  • 54.
    S-functions Verifications –Residual Error zoom in on zoom in tickling on result Number of measurements required to extract S-functions amplitude of complex error for measured and predicted b2 using extraction data © 2011 54
  • 55.
    S-functions Verification –Interpolation Capability verify interpolation of b2 using independent set of measurements © 2011 55
  • 56.
    S-functions Verifications –Constantness LSOP Select LSOP variable Variation on Filter for a LSOP variable drain bias voltage and value Variation on fixed input power © 2011 56
  • 57.
    S-functions in ADS Acknowledgement: Withthe support from Agilent Technologies providing ADS licensing © 2011 57
  • 58.
    S-functions Useage inAgilent ADS EPAClassAMediumPower.ael EPAClassAMediumPower.dsn Set of equations using FDD Values of all Sf, Sfc © 2011 58
  • 59.
    S-functions Verification inADS - Schematic ● Example: Harmonic Balance simulation with measured a1 and a2 spectra ● Excitation: Sweeping through a subset of LSOP points + tickle tones Measured incident waves S-function to be verified Measurements for model verification Access to measured data using DAC Sweeping through subset of LSOP and tickle tones © 2011 59
  • 60.
    S-functions Verification inADS - Frequency Domain Frequency = 2 GHz, VDC1= -1.3 V, VDC2= +2.0 V Measurements at different input powers than those which were used for S-functions model extraction! circles – measurements solid lines - simulations © 2011 60
  • 61.
    S-functions Verification inADS - Time Domain circles – measurements Frequency = 2 GHz, VDC1= -1.3 V, VDC2= +2.0 V, Pa1 = +10.0 dBm solid lines - simulations Saturation Pinch-off © 2011 61
  • 62.
    S-functions in ADS– Modulation Prediction - Schematic Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pa1 = +0.0 dBm – Class C © 2011 62
  • 63.
    S-functions in ADS– Modulation Prediction - Display Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pa1 = +0.0 dBm – Class C © 2011 63
  • 64.
    S-functions in ADS– Source-Pull - Schematic Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pav = +1.0 dBm – Class C Reflection : -0.27 © 2011 64
  • 65.
    S-functions in ADS– Source-Pull - Schematic Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pav = +1.0 dBm – Class C Complex Conjugate Measured Input Impedance © 2011 65
  • 66.
    S-functions in MWO Acknowledgement: Withthe support from AWR providing MWO / VSS licensing © 2011 66
  • 67.
    S-functions Usage inAWR MWO MDF file SUBCKT ID=S1 BIASTEE NET="SFUNC_Model" ID=X2 1 RF 2 & RF BIASTEE 2 DC DC ID=X1 PORT 3 P=2 Z=50 Ohm Model data 2 RF 1 1 RF & DC DC PORT_PS1 3 DCVS .. P=1 Z=50 Ohm ID=V2 .. V=6 V PStart=PinMin dBm 1.16226472890446E-16,-1.35308431126191E-16 PStop=PinMax dBm PStep=PinStep dB -3.15025783237388E-15,4.72191730160887E-15 DCVS ID=V1 9.71445146547012E-17,-2.37310171513627E-15 V=-1.8 V 1.51267887105178E-15,1.07899800205757E-15 -2.98198965520413E-15,1.59594559789866E-15 -5.759281940243E-16,-1.97758476261356E-16 -1.83880688453542E-15,1.92901250528621E-15 -5.06539254985228E-16,2.94209101525666E-15 -2.50494069931051E-15,-6.73072708679001E-16 -8.60422844084496E-16,2.65412691824451E-16 -2.019218126037E-15,2.7373936450914E-15 -2.28289609438548E-15,1.70870262383715E-15 1.08246744900953E-15,-6.78276879106932E-16 -1.02955838299224E-15,-1.31578775652841E-15 5.45570533194706E-16,3.99333344169861E-15 -3.62904151174348E-15,-1.74860126378462E-15 -2.00100352953925E-15,-5.68989300120393E-16 2.14975606760426E-15,-5.53376788836601E-16 -1.16226472890446E-15,-2.44942954807925E-15 2.08166817117217E-16,2.4980018054066E-15 1.04372118124342E-05,-1.36061371223614E-05 2.85882428840978E-15,3.11556336285435E-15 -2.15105711021124E-16,1.37390099297363E-15 9.71445146547012E-16,9.95731275210687E-16 -1.69309011255336E-15,2.33146835171283E-15 4.27435864480685E-15,3.3584246494911E-15 -1.08246744900953E-15,-8.60422844084496E-16 … 2D and 3D package data © 2011 67
  • 68.
    S-functions Verification inMWO - Frequency Domain HBT UNER2 ID=X1 Mag1=0 Ang1=0 Deg Mag2=0 Ang2=0 Deg Mag3=0 Ang3=0 Deg Fo=2 GHz Zo=50 Ohm PORT _PS1 P=1 1 2 Z=50 Ohm PStart=-20 dBm BIAST EE 2 PStop=8 dBm ID=X2 PORT PStep=1 dB 3:Bias P=2 SUBCK T 2 RF 1 1 Z=50 Ohm RF & ID=S1 DC NET ="EPA_120_B " DC 3 DCVS ID=V1 V=DC2val V DCVS ID=V2 V=DC 1val V Po with swept Pin Gain and Phase with swept Pin 40 20 19.5 20 19 F0 18.5 DB(|LSSnm(PORT_2,PORT_1,1,1)|)[1,X] 0 18 Swept Power.AP_HB Ang(LSSnm(PORT_2,PORT_1,2,1))[1,X] (Deg) 17.5 Swept Power.AP_HB -20 17 150 2F0 -40 100 DB(|Pcomp(PORT_2,1)|)[1,X] (dBm) Swept Power.AP_HB 50 3F0 DB(|Pcomp(PORT_2,2)|)[1,X] (dBm) -60 Swept Power.AP_HB DB(|Pcomp(PORT_2,3)|)[1,X] (dBm) Swept Power.AP_HB 0 -80 -50 -20 -15 -10 -5 0 5 10 -20 -15 -10 -5 0 5 10 Power (dBm) Power (dBm) © 2011 68
  • 69.
    S-functions Verification inMWO - Time Domain Vtime(V_METER.VM1,1)[*,T] (V) Itime(I_METER.AMP1,1)[*,T] (mA) HBTUNER2 Waveform Tests.AP_HB Waveform Tests.AP_HB ID=X1 Mag1=0 Ang1=0 Deg Mag2=0 Ang2=0 Deg Mag3=0 IV Ang3=0 Deg 250 Fo=2 GHz SUBCKT Zo=50 Ohm PORT_PS1 ID=S1 200 P=1 NET="EPA_120_B" 1 2 Z=50 Ohm PStart=-20 dBm BIASTEE 2 150 PStop=8 dBm ID=X2 PORT PStep=1 dB I_METER 3:Bias P=2 2 RF 1 1 ID=AMP1 Z=50 Ohm 100 RF & DC DC 50 3 V _METER DCVS ID =VM1 ID=V1 V=DC2val V 0 15 DCVS ID=V2 V=DC1val V 10 5 DB(|Pcomp(PORT_2,1)|)[1,X] (dBm) DB(|Pcomp(PORT_2,2)| )[1,X] (dBm) DB(|Pcomp(PORT_2,3)|)[1,X] (dBm) Waveform Tests.AP_HB Waveform Tests.AP_HB Waveform Tests.AP_HB0 0 0.2 0.4 0.6 0.8 1 Harmonics 40 Time (ns) 20 0 -20 -40 -60 -80 -20 -10 0 8 Power (dBm) © 2011 69
  • 70.
    S-functions in MWO– Modulation Prediction - Schematic DB(PWR_SPEC(TP.AMP Out,1000,0,10,0,-1,0,-1,1,0,4,0,1,0)) (dBm) DB(PWR_SPEC(TP.AMP In,1000,0,10,0,-1,0,-1,1,0,4,0,1,0)) (dBm) 16QAM System 16QAM System HBTUNER2 ID=DCBlock2 Mag1=0 Ang1=0 Deg Mag2=0 Ang2=0 Deg Mag3=0 ACPR SUBCKT Ang3=0 Deg Fo=2000 GHz 50 ID=S1 Zo=50 Ohm ISOL8R NET="EPA_120_B" ID=U1 1 2 R=50 Ohm LOSS=0 dB BIASTEE 2 ISOL=30 dB ID=X1 PORT 3:Bias P=2 2 RF RF & 1 1 Z=50 Ohm 0 DC DC PORT_PS1 3 DCVS P=1 ID=V3 Z=50 Ohm V=DC2val V PStart=-20 dBm PStop=8 dBm PStep=0.5 dB DCVS -50 ID=V1 V=DC1val V -100 -150 1.92 1.94 1.96 1.98 2 2.02 2.04 2.06 2.08 Frequency (GHz) VS A ID=M1 VA RNA ME="" VA LUE S=0 NA VG= PBA SE = -76 V e c to r S w e p t v a r ia b le S ig n a l SRC MEAS A n a ly z e r QAM_S RC G e n e r a l R e c e iv e r ID=A1 MO D=16-QA M (Gray) OUT LV L=-0.2 OLVLT Y P=Avg. Power (dB m) NL_ S AW GN RAT E=_DRA T E ID=S 1 BER ID=A3 CTRFRQ=2 GHz TP NET ="AMAM A MPM.AP_HB " PW R=-170 ID=5 SIMT YP=Harm onic Balanc e TP PLST Y P=Root Rais ed Cos ine ID=AMP In PW RT YP=Avg. Po wer, Sym bol (dBW ) VARNAME="PBA SE" ID=AMP Out ALPHA =0.35 NO SE=RF Budget only I VALUES=s tepped(-76,-40,2) LOSS=0 dB PLSLN= RFIF RQ= QAM_RX OUT FL="" ID=A 2 1 R D 2 BER IQ 3 C irc u it 5 4 B E R D e te c to r B a s e d A m p lifie r C h a n n e l N o is e 1 6 Q A M S o u rc e TP ID=RX Cons tellation 1 6 Q A M (G r a y ) S y s te m © 2011 70
  • 71.
    S-functions in MWO– Load-Pull HBTUNER2 ID=DCBlock2 Mag1=0.8 Load Tuner (and bias) Ang1=40 Deg LP_Data_Low_Power Mag2=0 Ang2=0 Deg 1.0 Swp Max Mag3=0 0.8 -0.89 Ang3=0 Deg Fo=2 GHz 6 0. Zo=50 Ohm 0 . 2 4 . 1 2 PORT1 0 0 . 3 P=1 2 p8 0 p1: Pcomp_PORT_2_1_M_DB = -2.87 Z=50 Ohm PORT p7 4. Pwr=10 dBm 3:Bias P=2 p9 p2: Pcomp_PORT_2_1_M_DB = -2.65 SUBCKT 5. 0 2 RF 1 Z=50 Ohm 2 p6 1 ID=S1 0. RF & p10 p3: Pcomp_PORT_2_1_M_DB = -2.43 DC NET="SFUNC_Model" p5 DC 10. 0 BIASTEE p4: Pcomp_PORT_2_1_M_DB = -2.21 3 DCVS ID=X1 p4 ID=V2 10.0 V=7 V 4.0 p5: Pcomp_PORT_2_1_M_DB = -1.99 0.2 0.4 0.6 0.8 1.0 2.0 3.0 5.0 0 p3 p6: Pcomp_PORT_2_1_M_DB = -1.77 DCVS p2 ID=V1 .0 -10 p7: Pcomp_PORT_2_1_M_DB = -1.55 V=-0.6 V p1 -0 . 2 0 . p8: Pcomp_PORT_2_1_M_DB = -1.33 -5 0 . -4 p9: Pcomp_PORT_2_1_M_DB = -1.11 p10: Pcomp_PORT_2_1_M_DB = -0.89 0 . 3 4 - . 0 - 0 . 2 6 - . -0 8 Swp Min -1.0 -0. -2.87 LP_Data_High_Power S M wp ax 1.0 0 .8 25.93 6 0. .0 2 .4 0 p1: Pcomp_PORT _2_1_M_DB = 21.93 .0 3 p9 p8 p7 p6 p5 p2: Pcomp_PORT _2_1_M_DB = 22.33 p4 4 .0 2 p10 p3 5. 0 p3: Pcomp_PORT _2_1_M_DB = 22.73 0. p2 0 p4: Pcomp_PORT _2_1_M_DB = 23.13 1 0. p11 p5: Pcomp_PORT _2_1_M_DB = 23.53 10.0 0.4 0.8 3.0 0.2 0.6 1.0 2.0 4.0 5.0 p1 p6: Pcomp_PORT _2_1_M_DB = 23.93 0 0 . p7: Pcomp_PORT _2_1_M_DB = 24.33 - 10 p8: Pcomp_PORT _2_1_M_DB = 24.73 .2 -0 .0 .0 -5 p9: Pcomp_PORT _2_1_M_DB = 25.13 -4 0 p10: Pcomp_PORT _2_1_M_DB = 25.53 3. 4 - 0. - p11: Pcomp_PORT _2_1_M_DB = 25.93 0 2. .6 - -0 8 S M wp in -1.0 - 0. 21.93 © 2011 71
  • 72.
    S-functions Strengths ● S-functions are completely public ● S-functions are transparent ● S-functions are connected into ADS and MWO and can be connected in other tools on request, e.g. Matlab ● S-functions are closely integrated with load-pull in general and especially with tuners from Focus Microwave ● S-functions extraction tool has a verification capability for LSOP constantness and interpolation capability, investigating quality of model, without needing a simulation tool ● The source- and load-pull software ICEBreaker from NMDG allows S- function verification, related to the linearity assumption ● Customers can explore the capabilities of S-functions via NMDG services © 2011 72
  • 73.
    S-Functions - KeyCapabilities ● Natural extension of S-parameters ● Reduce to S-parameters for small-signal excitation ● S-parameters are cascadeable, S-Functions are cascadeable too ● e.g. Transistors, amplifiers, dividers, multipliers ● Predict harmonic behaviour of components under different impedances ● Source – Pull ● Load – Pull ● Harmonic distortion, Waveforms ● Predict modulation behaviour of components under different impedances ● When no long-term memory effects ● Valid for multi-ports, applicable to differential components © 2011 73
  • 74.
    References ● F. Verbeyst and M. Vanden Bossche, “VIOMAP, the S-parameter equivalent for weakly nonlinear RF and microwave devices”, published in the Microwave Symposium Digest of IEEE 1994 MTT-S International and published in the 1994 Special Symposium Issue of the MTT Transactions, vol. 42, no. 12, pp. 2531 – 2535. ● F. Verbeyst and M. Vanden Bossche, “VIOMAP, 16QAM and Spectral Regrowth: Enhanced Prediction and Predistortion based on Two-Tone Black-Box Model Extraction”, published in the Proceedings of the 45th ARFTG Conference, Orlando, June 1995 and winner of the “Best Conference Paper Award”. ● J. Verspecht and P. Van Esch, “Accurately characterizating of hard nonlinear behaviour of microwave components by the Nonlinear Network Measurement System: introducing the nonlinear scattering function,” Proc. International Workshop on Integrated Nonlinear Microwave and Millimiterwave Circuits (INMMiC), October 1998, pp.17-26. ● J. Verspecht, “Scattering functions for nonlinear behavioral modeling in the frequency domain,” IEEE MTT-S Int. Microwave Symp. Workshop, June 2003. ● J. Verspecht and D.E. Root “Polyharmonic Distortion Modeling,” IEEE Microwave Magazine, vol.7 no.3, June 2006, pp.44-57. ● D.E. Root, J. Horn, L. Betts, C. Gillease, and J. Verspecht, ”X-Parameters: The new paradigm for measurement, modeling, and design of nonlinear RF and microwave components,” Microwave Engineering Europe, December 2008, pp. 16-21. © 2011 74
  • 75.
    Conclusion ● S-functions are a natural extension to S-parameters for nonlinear behaviour ● S-functions aren't much more complex than S-parameters ● S-functions are accurate when assumptions are not violated ● Linearity assumption ● S-function extraction is supported on R&S network analysers ● S-functions can be coupled into ADS and MWO ● S-functions can be used to compress or hide specifics of nonlinear circuits in ADS and MWO For more information info@nmdg.be www.nmdg.be © 2011 75
  • 76.
    Explore the powerof S-functions Send your device or circuit to NMDG ... ` … and NMDG sends you the S-functions Please contact NMDG at info@nmdg.be © 2011 76