Large-Signal Measurements Going beyond S-parameters

Transcription

1 Large-Signal Measurements Going beyond S-parameters Jan Verspecht, Frans Verbeyst & Marc Vanden Bossche Network Measurement and Description Group Innovating the HP Way

2 Overview What is Large-Signal Network Analysis? Instrument Hardware Calibration Aspects Application Examples Conclusion Page 2

3 Part 1 What is Large-Signal Network Analysis? Instrument Hardware Calibration Aspects Application Examples Conclusion Page 3

4 Large-Signal Network Analysis? Put a DUT in realistic large-signal operating conditions Completely and accurately characterize the DUT behavior Analyze the network behavior using these measurements Page 4

5 Different Data Representations are used D.U.T. Physical Quantity Sets I ( t 1 ) I ( t 2 ) Travelling Waves (A, B) V 1 ( t) V 2 ( t) TUNER Voltage/Current (V, I) D.U.T. Representation Domain A 1 ( f ) A 2 ( f ) Frequency (f) TUNER Time (t) B 1 ( f ) B 2 ( f ) Envelope Presently limited to periodic signals and periodically modulated signals Page 5

6 Waves (A, B) versus Current/Voltage (V, I) A = V + Z 2 c I V = A + B B = V Z 2 c I I = A B Z c Typically Z c = 50 Ω Page 6

7 Signal Class: CW Signals 2-port DUT under periodic excitation E.g. transistor excited by a 1 GHz tone with an arbitrary output termination All current and voltage waveforms are represented by a fundamental and harmonics DC Freq. (GHz) Spectral components X h = complex Fourier Series coefficients of the waveforms Page 7

8 CW: Time Domain and Frequency Domain x( t ) H = Re h= 0 X h e j 2π hf t X h = 2f f 1 0 x( t ) e j 2π hf t dt f = 1/ period = fundamental frequency Page 8

9 Example: Time Domain V/I Representation Time (ns) Time (ns) Page 9

10 Signal Class: Modulated Signals Periodically modulated version of the previous case e.g. transistor excited by a modulated 1 GHz tone (modulation period = 10 khz) DC khz Freq. (GHz) Spectral components X hm Page 10

11 Modulation: Time and Frequency Domain x( t ) H = Re h = 0 + M m = M X hm e j 2π ( h f C + m f M ) t X hm = lim T 1 T T T x( t ) e j 2π ( hfc + m fm ) t dt f f C M = = carrier frequency modulation frequency Page 11

12 Modulation: Envelope Domain x( t ) H = Re h= 0 X h ( t ) e j 2π hf c t X h ( t ) = M m= M X hm e j 2π mf M t Page 12

13 Modulation: Time and Envelope Domain B 2 (Volt) Fundamental envelope 3rd harmonic envelope Time (normalized) Page 13

14 Modulation: Frequency Domain Incident signal (a1) dbm 1.9 GHz 3.8 GHz 5.7 GHz Transmitted signal (b2) dbm Reflected signal (b1) dbm IF freq (MHz) IF freq (MHz) IF freq (MHz) Page 14

15 Modulation: 2D Time Domain B 2 (Volt) t S (normalized) t F (normalized) x2d( tf, ts ) Re H + M = x( t) = x2 ( f t, f t) D c M h= 0 m= M X hm e j 2π ( ht F + m t S ) Page 15

16 Part 2 What is Large-Signal Network Analysis? Instrument Hardware Calibration Aspects Application Examples Conclusion Page 16

17 Hardware: Historical Overview Markku Sipila & al.: 2 channel scope with one coupler at the input (14 GHz) Kompa & Van Raay: 2 channel scope with VNA test-set + receiver Lott: VNA test set + receiver (26.5 GHz) Kompa & Van Raay: test-set with MTA (40 GHz) Verspecht & al.: 4 couplers with a 4 channel oscilloscope (20 GHz) Demmler, Tasker, Leckey, Wei, Tkachenko: test-set with MTA (40 GHz) Verspecht & al.: 4 couplers with 2 synchronized MTA s Verspecht & al.: NNMS, 4 couplers, 4 channel converter, 4 ADC s Nebus & al.: VNA test set + receiver with loadpull and pulsed capability Page 17

18 Architecture of the NNMS Modulatus Computer 10MHz A-to-D RF-IF converter Attenuators RF bandwidth: 600MHz - 20GHz max RF power: 10 Watt IF bandwidth: 8 MHz Needs periodic modulation (4 khz typical) TUNER... Page 18

19 RF-IF converter: Simplified Schematic 1 LP 1 2 RF (20 GHz) LP 2 IF (4 MHz) 3 LP 3 4 LP 4 f LO (20 MHz) Page 19

20 Harmonic Sampling - Signal Class: CW LP RF f LO =19.98 MHz = (1GHz-1MHz)/50 50 f LO 100 f LO 150 f LO Freq. (GHz) IF Freq. (MHz) Page 20

21 Part 3 What is Large-Signal Network Analysis? Instrument Hardware Calibration Aspects Application Examples Conclusion Page 21

22 Calibration: Historical Overview 1988 VNA-like characterization of the test-set power calibration with power meter assumption of ideal-phase receiver 1989 phase calibration by golden diode approach (Urs Lott) 1994 harmonic phase calibration with characterized SRD, traceable to a nose-to-nose calibrated sampling oscilloscope (Verspecht) 2000 IF calibration (Verspecht) 2000 NIST investigates reference generator approach (DeGroot) Page 22

23 Raw Quantities versus DUT Quantities Computer 10MHz A-to-D RF-IF converter Attenuators Raw quantities R1 a hm R1 b hm R2 a hm R2 b hm TUNER D1 a hm D1 b hm DUT quantities D2 a hm D2 b hm... Page 23

24 Page 24 The Error Model = R hm R hm R hm R hm h h h h h h h j h D hm D hm D hm D hm b C a C b C a C e K b a b a h η γ φ ε δ χ β ϕ RF amplitude error RF phase error RF relative error IF error Raw quantities DUT quantities

25 RF Calibration Coaxial SOLT calibration OR On wafer LRRM calibration Combined with HF amplitude calibration with power meter HF harmonic phase calibration with a SRD diode (characterized by a nose-to-nose calibrated scope) Page 25

26 Coaxial Amplitude and Phase Calibration Page 26

27 On Wafer Amplitude & Phase Calibration Coaxial LOS Page 27

28 Measurement Traceability Relative Cal Phase Cal Power Cal Agilent Nose-to-Nose Standard National Standards (NIST) Page 28

29 Phase Reference Generator Characterization Reference generator Sampling oscilloscope Page 29

30 Sampling Oscilloscope Characterization: Nose-to-Nose Calibration Procedure Page 30

31 Nose-to-Nose Measurement Page 31

32 3 Oscilloscopes are Needed Page 32

33 Part 4 What is Large-Signal Network Analysis? Instrument Hardware Calibration Aspects Application Examples Conclusion Page 33

34 Breakdown Current Time (ns) (transistor provided by David Root, - MWTC) Page 34

35 Forward Gate Conductance Time (ns) Page 35

36 Resistive Mixer Schematic HEMT transistor (no drain bias applied) (transistor provided by Dominique Schreurs, IMEC & KUL-TELEMIC) Page 36

37 Resistive Mixer: Time Domain Waveforms Page 37

38 Modeling based on Large-Signal Measurements Classic large-signal models are derived from DC and small-signal S-parameters Recent approach is to improve and derive the large-signal models directly from large-signal measurements Page 38

39 Model Classes Empirical models: electrical circuit schematics with non-linear components defined by analytical functions State-space models: describe voltage and current relationship by means of a state-space approach Black-box frequency domain models: describe the relationships between incident and scattered phasors by means of describing functions Page 39

40 Empirical Model Improvement (by Dominique Schreurs, IMEC & KUL-TELEMIC) Parameter Boundaries GaAs pseudomorphic HEMT gate l=0.2 um w=100 um MODEL TO BE OPTIMIZED Chalmers Model generators apply NNMS measured waveforms Power swept measurements under mismatched conditions Page 40

41 Using the Built-in Optimizer During OPTIMIZATION Voltage - Current State Space voltage current gate drain gate drain Time domain waveforms Frequency domain Page 41

42 Verification of the Optimized Model AFTER OPTIMIZATION Voltage - Current State Space voltage current gate drain gate drain Time domain waveforms Frequency domain Page 42

43 Page 43 State Space Function Model (David Root, Dominique Schreurs) ), ( ), ( ), ( ), ( V V L dt d V V K I V V L dt d V V K I + = + = Current Function Charge Function Fit with e.g. artificial neural network or spline

44 Experiment Design: Crucial to Explore Component Behavior I 1 I 2 V 1 V GHz 4.8 GHz Page 44

45 State Space Coverage through Proper Experiment Design Page 45

46 When to use Frequency Domain Models? With new less understood technology When there is a difficult de-embedding problem When there are multiple transistors in the circuit When the component has distributed characteristics These models, directly derived from large-signal measurements, can directly be used by designers (the models are application specific). Page 46

47 Black-Box Models? A 1 A 2 B 1 B 2 B = F ij ij ( A kl ) Describing Function fit by ANN or polynomials Page 47

48 Time Delay Invariance Constraint Describing Function F(A) is fitted by G(A, α, β,...) parameters G(A, α, β,...) has a very important constraint: delaying A has to result in same delay for B Mathematically expressed: for every τ jωτ,...) G A e jωτ G ( Ae = ( ) Page 48

49 Simplify Behavioral Models by using Superposition for Harmonic Inputs A 1 B 2 Page 49

50 Model Parameter Estimation NNMS Measurements Set of Experiments A A... B B... Approximate F(A) by G(A, α, β,...) 3. Find α, β, by minimizing experimental F( A) G( A, α, β,...) A 2 da Page 50

51 Artificial Neural Net Curve Fitting F ( V ) 21 ANN = smooth multidimensional fitters I base 2 A 11 ( V ) (ma) 0 V collector = 4. 5V Si BJT 1.8 GHz Page 51

52 Time Domain: Model and Measurement 1.8 GHz Silicon BJT Power Transistor Page 52

53 Black-Box Models Describe: Compression characteristic AM-PM PAE Harmonic Distortion Fundamental loadpull behavior Harmonic loadpull behavior Time domain voltage & current Influence of bias can be included Page 53

54 Behavioral Model under Modulation: 1.9 GHz RFIC (CDMA) (Volt) Incident signal (a1) (Volt) Transmitted signal (b2) Normalized Time Normalized Time Page 54

55 Dynamic Harmonic Distortion: Transmitted Signal Output power (dbm) fund nd harm rd harm Input power (dbm) Page 55

56 Dynamic Harmonic Distortion: Reflected Signal Output power (dbm) fund nd harm rd harm Input power (dbm) Page 56

57 Emulate CDMA Statistics using many Periodic Pseudo-Random Sequences Amplitude (dbm) Transmitted Signal Frequency Offset from Carrier (Hz) Page 57

58 Apply Fitting Technique to DBF For our example we use a piece wise polynomial (3rd order) (V ) I Q (V ) a 11 ( V ) a 11 ( V ) Page 58

59 Model Verification - Spectral Regrowth Amplitude (dbm) Output signal -----model -----measured Frequency Offset from Carrier (MHz) Page 59

60 Part 5 What is Large-Signal Network Analysis? Instrument Hardware Calibration Aspects Application Examples Conclusion Page 60

61 Conclusions The dream of accurate and complete large-signal characterization of components under realistic operating conditions is made real The only limit to the scope of applications is the imagination of the R&D people who have access to this measurement capability Page 61

62 Coordinates URL: fax: phone: address: Belgium S.A./N.V. Network Measurement & Description Group Van Kerckhovenstraat 110 B-2880 Bornem Belgium Page 62