1. Copyright 2003 Jan Verspecht bvba 1 Large-Signal Network Analysis “Going beyond S-parameters” Dr. Jan Verspecht “Jan Verspecht bvba” URL: http://www.janverspecht.com This presentation contains several slides which are used with the permission of Agilent Technologies, Inc.

2. Copyright 2003 Jan Verspecht bvba 2 Part I –Introduction –Instrumentation and Calibration Break –Coffee and Cookies Part II –Applications –Conclusions Outline

3. Copyright 2003 Jan Verspecht bvba 3 Introduction Signal Representations Instrumentation Hardware Calibration Aspects Part I - Outline

4. Copyright 2003 Jan Verspecht bvba 4 Large-Signal Network Analysis? Put a D.U.T. (“network”) in realistic large- signal operating conditions Completely and accurately characterize the D.U.T. behavior Analyze the D.U.T. behavior using the measured data Copyright 1998 Agilent Technologies, Inc. – Used with Permission

5. Copyright 2003 Jan Verspecht bvba 5 Introduction Signal Representations Instrumentation Hardware Calibration Aspects Part I - Outline

6. Copyright 2003 Jan Verspecht bvba 6 Signal Representations D.U.T. TUNER Representation Domain –Frequency (f) –Time (t) –Envelope (f,t) Set of Physical Quantities –Traveling Waves (A, B) –Voltage/Current (V, I) LSNA is capable of periodic and periodically modulated signals Copyright 1998 Agilent Technologies, Inc. – Used with Permission

7. Copyright 2003 Jan Verspecht bvba 7 Traveling Waves versus Current/Voltage Typically Copyright 1998 Agilent Technologies, Inc. – Used with Permission A B V I DUT

8. Copyright 2003 Jan Verspecht bvba 8 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 Spectral components X h = complex Fourier Series coefficients of the waveforms Signal Class: CW Signals Freq. (GHz)123 4 DC Copyright 1998 Agilent Technologies, Inc. – Used with Permission

9. Copyright 2003 Jan Verspecht bvba 9 CW: Time and Frequency Domain Copyright 1998 Agilent Technologies, Inc. – Used with Permission

10. Copyright 2003 Jan Verspecht bvba 10 Time Domain V/I Representation Time (ns) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

11. Copyright 2003 Jan Verspecht bvba 11 Periodically modulated version of the previous case e.g. transistor excited by a modulated 1 GHz tone (modulation period = 10 kHz) Spectral components X hm Signal Class: Modulated Signals Freq. (GHz) 12 3 DC 10 kHz Copyright 1998 Agilent Technologies, Inc. – Used with Permission

12. Copyright 2003 Jan Verspecht bvba 12 Modulation: Time and Frequency Domain Copyright 1998 Agilent Technologies, Inc. – Used with Permission

13. Copyright 2003 Jan Verspecht bvba 13 Modulation: Envelope Domain Copyright 1998 Agilent Technologies, Inc. – Used with Permission

14. Copyright 2003 Jan Verspecht bvba 14 Modulation: Time and Envelope Domain Time (normalized) B 2 (Volt) Fundamental envelope 3rd harmonic envelope Copyright 1998 Agilent Technologies, Inc. – Used with Permission

15. Copyright 2003 Jan Verspecht bvba 15 Modulation: Frequency Domain Fund @ 1.9 GHz2nd @ 3.8 GHz3rd @ 5.7 GHz Incident signal (a1) Transmitted signal (b2) Reflected signal (b1) IF freq (MHz) dBm Copyright 1998 Agilent Technologies, Inc. – Used with Permission

16. Copyright 2003 Jan Verspecht bvba 16 Modulation: 2D Time Domain t S (normalized) t F (normalized) B 2 (Volt) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

17. Copyright 2003 Jan Verspecht bvba 17 Introduction Signal Representations Instrumentation Hardware Calibration Aspects Part I - Outline

18. Copyright 2003 Jan Verspecht bvba 18 Hardware: Historical Overview 1988Markku Sipila & al.: 2 channel scope with one coupler at the input (14 GHz) 1989Kompa & Van Raay: 2 channel scope with VNA test-set + receiver Lott: VNA test set + receiver (26.5 GHz) 1992Kompa & Van Raay: test-set with MTA (40 GHz) Verspecht & al.: 4 couplers with a 4 channel oscilloscope (20 GHz) 1994Demmler, Tasker, Leckey, Wei, Tkachenko: test-set with MTA (40 GHz) Verspecht & al.: 4 couplers with 2 synchronized MTA’s 1996Verspecht & al.: NNMS, 4 couplers, 4 channel converter, 4 ADC’s 1998Nebus & al.: VNA test set + receiver with loadpull and pulsed capability 2003Maury Microwave, Inc.: commercial introduction (LSNA) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

19. Copyright 2003 Jan Verspecht bvba 19 Architecture of the LSNA prototype TUNER Attenuators... 10MHz A-to-D Computer RF-IF converter RF bandwidth: 600MHz - 50GHz max RF power: 10 Watt IF bandwidth: 8 MHz Needs periodic modulation (4 kHz typical) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

20. Copyright 2003 Jan Verspecht bvba 20 RF-IF converter: Simplified Schematic LP 1 2 3 4 1 2 3 4 RF (50 GHz) IF (4 MHz) f LO (20 MHz) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

21. Copyright 2003 Jan Verspecht bvba 21 Harmonic Sampling - Signal Class: CW Freq. (GHz) 1 2 3 50 f LO 100 f LO 150 f LO Freq. (MHz) 1 2 3 RF IF f LO =19.98 MHz = (1GHz-1MHz)/50 Copyright 1998 Agilent Technologies, Inc. – Used with Permission

22. Copyright 2003 Jan Verspecht bvba 22 Introduction Signal Representations Instrumentation Hardware Calibration Aspects Part I - Outline

23. Copyright 2003 Jan Verspecht bvba 23 Calibration: Historical Overview 1988 VNA-like characterization of the test-set power calibration with a power meter assumption of an ideal-phase receiver 1989 phase calibration by the “golden diode” approach (Urs Lott) 1994 harmonic phase calibration with a characterized SRD, traceable to a nose-to-nose calibrated sampling oscilloscope (Verspecht) 2000 IF calibration (Verspecht) 2000 NIST investigates “phase reference generator” approach (DeGroot) 2001 calibrated electro-optical sampling (D.F. Williams, P. Hale @ NIST) (provides better harmonic phase accuracy than nose-to-nose) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

24. Copyright 2003 Jan Verspecht bvba 24 Raw Quantities versus DUT Quantities TUNER Attenuators... 10MHz A-to-D RF-IF converter DUT quantities Raw quantities Computer Copyright 1998 Agilent Technologies, Inc. – Used with Permission

25. Copyright 2003 Jan Verspecht bvba 25 The Error Model RF amplitude error RF phase error RF relative error IF error Raw quantities DUT quantities Copyright 1998 Agilent Technologies, Inc. – Used with Permission

26. Copyright 2003 Jan Verspecht bvba 26 RF Calibration 1.Coaxial SOLT calibration On wafer LRRM calibration 2.HF amplitude calibration with power meter 3.HF harmonic phase calibration with a SRD diode (characterized by a nose-to-nose calibrated sampling oscilloscope) OR Combined with Copyright 1998 Agilent Technologies, Inc. – Used with Permission

27. Copyright 2003 Jan Verspecht bvba 27 Coaxial Amplitude and Phase Calibration Amplitude Harmonic Phase Copyright 1998 Agilent Technologies, Inc. – Used with Permission

28. Copyright 2003 Jan Verspecht bvba 28 On Wafer Amplitude & Phase Calibration Coaxial LOS LRRM Copyright 1998 Agilent Technologies, Inc. – Used with Permission

29. Copyright 2003 Jan Verspecht bvba 29 Calibration Traceability Relative Cal Power Cal National Standards (NIST) Precision AirlineCalorimetry Harmonic Phase Nose-to-Nose Standard Electro-Optical Sampler

30. Copyright 2003 Jan Verspecht bvba 30 Characterization of the Harmonic Phase Reference Generator Sampling oscilloscope Harmonic Phase Reference generator Copyright 1998 Agilent Technologies, Inc. – Used with Permission

31. Copyright 2003 Jan Verspecht bvba 31 Sampling Oscilloscope Characterization: Nose-to-Nose Calibration Procedure Copyright 1998 Agilent Technologies, Inc. – Used with Permission

32. Copyright 2003 Jan Verspecht bvba 32 Nose-to-Nose Measurement Copyright 1998 Agilent Technologies, Inc. – Used with Permission

33. Copyright 2003 Jan Verspecht bvba 33 3 Oscilloscopes are Needed 1 2 1 3 3 2 Copyright 1998 Agilent Technologies, Inc. – Used with Permission

34. Copyright 2003 Jan Verspecht bvba 34 Electro-Optic Sampling* (D. Williams et al., NIST) * The schematic that is shown is “U.S. Government work not subject to copyright.” D.F. Williams, P.D. Hale, T.S. Clement, and J.M. Morgan, "Calibrating electro-optic sampling systems,“ Int. Microwave Symposium Digest, Phoenix, AZ, pp. 1527-1530, May 20-25, 2001.

35. Copyright 2003 Jan Verspecht bvba 35 Part I –Introduction –Instrumentation and Calibration Break –Coffee and Cookies Part II –Applications –Conclusions Outline

36. Copyright 2003 Jan Verspecht bvba 36 Part I –Introduction –Instrumentation and Calibration Break –Coffee and Cookies Part II –Applications –Conclusions Outline

37. Copyright 2003 Jan Verspecht bvba 37 Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions Part II - Outline

38. Copyright 2003 Jan Verspecht bvba 38 Breakdown Current Time (ns) (transistor provided by David Root, Agilent Technologies - MWTC) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

39. Copyright 2003 Jan Verspecht bvba 39 Forward Gate Current Time (ns) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

40. Copyright 2003 Jan Verspecht bvba 40 Resistive Mixer Schematic HEMT transistor (no drain bias applied) (transistor provided by Dominique Schreurs, IMEC & KUL-TELEMIC) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

41. Copyright 2003 Jan Verspecht bvba 41 Resistive Mixer: Time Domain Waveforms Copyright 1998 Agilent Technologies, Inc. – Used with Permission

42. Copyright 2003 Jan Verspecht bvba 42 High-Speed Digital Signal Integrity Calibrated Eye Measurement On Wafer (@10GB/sec) Oscilloscope Data Copyright 2002 Agilent Technologies, Inc. – Used with Permission (courtesy of Jonathan Scott, Agilent Technologies)

43. Copyright 2003 Jan Verspecht bvba 43 Loadpull and Waveform Engineering MesFET Class F Z(f 0 )=130+j73  Z(2f 0 )=1-j2.8  Z(3f 0 )=20-j97  PAE=84% PAE  50% Data courtesy of IRCOM / Limoges (France) HARMONIC TUNER LSNA

44. Copyright 2003 Jan Verspecht bvba 44 Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions Part II - Outline

45. Copyright 2003 Jan Verspecht bvba 45 Physical Models Represent transistor behavior Use electrical circuit schematics Contain linear and nonlinear elements such as current sources, capacitors, resistors E.g. BSIM3, Chalmers, Materka, Curtice,…

46. Copyright 2003 Jan Verspecht bvba 46 Physical Model Improvement generators apply waveforms measured by an LSNA “Swept power measurements under mismatched conditions” Chalmers model to optimize GaAs pseudomorphic HEMT gate l=0.2 um w=100 um Parameter Boundaries (courtesy of Dr. Dominique Schreurs, IMEC & KUL-TELEMIC) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

47. Copyright 2003 Jan Verspecht bvba 47 Before OPTIMIZATION Time domain waveformsFrequency domain gatedrain voltage current gatedrain Voltage - Current State Space Using the Built-in Optimizer Copyright 1998 Agilent Technologies, Inc. – Used with Permission

48. Copyright 2003 Jan Verspecht bvba 48 After OPTIMIZATION Time domain waveformsFrequency domain gatedrain voltage current gatedrain Voltage - Current State Space Verification of the Optimized Model Copyright 1998 Agilent Technologies, Inc. – Used with Permission

49. Copyright 2003 Jan Verspecht bvba 49 Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions Part II - Outline

50. Copyright 2003 Jan Verspecht bvba 50 State Space Function Model Fit with e.g. artificial neural network or spline (David Root, John Wood, Dominique Schreurs)

51. Copyright 2003 Jan Verspecht bvba 51 Experiment Design: Crucial to Explore Component Behavior 4.2 GHz 4.8 GHz Copyright 1998 Agilent Technologies, Inc. – Used with Permission

52. Copyright 2003 Jan Verspecht bvba 52 State Space Coverage through Proper Experiment Design Copyright 1998 Agilent Technologies, Inc. – Used with Permission

53. Copyright 2003 Jan Verspecht bvba 53 Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions Part II - Outline

54. Copyright 2003 Jan Verspecht bvba 54 When to use Scattering Functions? Scattering functions are Black-box frequency domain models, Directly derived from large-signal measurements. Scattering functions are used 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

55. Copyright 2003 Jan Verspecht bvba 55 Theoretical Concepts Scattering Functions for Nonlinear Behavioral Modeling in the Frequency Domain Quantities are Waves Functional Relationship Input and Output are Discrete Tone Signals

56. Copyright 2003 Jan Verspecht bvba 56 Quantities are Traveling Voltage Waves Default value of Z = 50 Ohm (classic S-parameters) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

57. Copyright 2003 Jan Verspecht bvba 57 Scattering Functions Describe: Compression characteristic Spectral regrowth AM-PM PAE Harmonic Distortion Fundamental loadpull behavior Harmonic loadpull behavior Time domain voltage & current Influence of bias can be included Copyright 1998 Agilent Technologies, Inc. – Used with Permission

58. Copyright 2003 Jan Verspecht bvba 58 Notation - Graphical Illustration Copyright 1998 Agilent Technologies, Inc. – Used with Permission

59. Copyright 2003 Jan Verspecht bvba 59 Phase Normalization “Phase normalized” quantities are used Defines unambiguous phase for harmonics Large-signal A 11 is the phase reference (most useful for many applications)

60. Copyright 2003 Jan Verspecht bvba 60 Phase Normalization: Mathematics We define a reference phasor: We define phase normalized quantities: Special case:

61. Copyright 2003 Jan Verspecht bvba 61 Harmonic Superposition Principle In general superposition cannot be used to describe the functional relationship between the spectral components The superposition principle can be used for relatively small components (e.g. harmonics)

62. Copyright 2003 Jan Verspecht bvba 62 Harmonic Superposition: Illustration Copyright 1998 Agilent Technologies, Inc. – Used with Permission

63. Copyright 2003 Jan Verspecht bvba 63 Basic Mathematical Equation A 11 assumed to be the only large-signal component Superposition assumed to be valid for other A nh The notation A* means the complex conjugate of A S and S’ are called the scattering functions Note that S’ mk11 = 0

64. Copyright 2003 Jan Verspecht bvba 64 Applications: Compression and AM-PM conversion Only considering B 21 and A 11 results in This can be rewritten as S 2111 (|A 11 |) represents the compression and AM-PM conversion characteristic

65. Copyright 2003 Jan Verspecht bvba 65 Large-Signal Input Match Only considering B 11 and A 11 results in This can be rewritten as S 1111 (|A 11 |) represents the large-signal input reflection coefficient

66. Copyright 2003 Jan Verspecht bvba 66 Hot S 22 Considering B 21, A 21 and A 11 results in Multiplying both sides with P results in The combination of S 2121 and S’ 2121 are a scientifically sound format for “Hot S 22 ”

67. Copyright 2003 Jan Verspecht bvba 67 Measurement Example -60 -40 -20 0 20 40 -25-20-15-10-50510 Scattering functions (dB) |A 11 | (dBm) S 2111 S’ 2121 S 2121 Note that the amplitude of S’ 2121 becomes arbitrary small for |A 11 | going to zero Copyright 1998 Agilent Technologies, Inc. – Used with Permission

68. Copyright 2003 Jan Verspecht bvba 68 Harmonic Distortion Analysis Only considering A 11 and B 2k one can calculate the harmonic distortion as a function of |A 11 |

69. Copyright 2003 Jan Verspecht bvba 69 Harmonic Loadpull Behavior Solve the set of equations (linear in the real and imaginary parts of A 2h and B 2h )

70. Copyright 2003 Jan Verspecht bvba 70 New Stability Circles for Multiplier Design DC 20202020 DC 0000 0000 20202020 Stability is not ensured Research performed by Prof. Giorgio Leuzzi (Universita dell’Aquila, Italy)

71. Copyright 2003 Jan Verspecht bvba 71 Practical Measurement: Experiment Design Concept Im Re Simple example: S 2111, S 2121 and S’ 2121 Re Im Perform 3 independent experiments Input A 21 Output B 21

72. Copyright 2003 Jan Verspecht bvba 72 Typical Measurement Setup TUNER Large-Signal Network Analyzer diplexer in fundamental harmonics Copyright 1998 Agilent Technologies, Inc. – Used with Permission Agilent Technologies, Inc. - Patent Pending

73. Copyright 2003 Jan Verspecht bvba 73 Measurement Example Input A 21 (V p )Output B 21 (V p ) Im Re Copyright 1998 Agilent Technologies, Inc. – Used with Permission

74. Copyright 2003 Jan Verspecht bvba 74 Link to Harmonic Balance Simulators Copyright 1998 Agilent Technologies, Inc. – Used with Permission

75. Copyright 2003 Jan Verspecht bvba 75 Simulated Model versus Measurements Power Transistor Waveforms Gate Voltage Gate Current Drain Voltage Drain Current Copyright 1998 Agilent Technologies, Inc. – Used with Permission

76. Copyright 2003 Jan Verspecht bvba 76 Scattering Functions with Modulation 1.9 GHz RFIC (CDMA) Incident signal (a1) Transmitted signal (b2) ( Volt ) Normalized Time Copyright 1998 Agilent Technologies, Inc. – Used with Permission

77. Copyright 2003 Jan Verspecht bvba 77 ----- fund ----- 2nd harm ----- 3rd harm Input power (dBm) Output power (dBm) Dynamic Harmonic Distortion: Transmitted Signal Copyright 1998 Agilent Technologies, Inc. – Used with Permission

78. Copyright 2003 Jan Verspecht bvba 78 Dynamic Harmonic Distortion: Reflected Signal Output power (dBm) Input power (dBm) Copyright 1998 Agilent Technologies, Inc. – Used with Permission ----- fund ----- 2nd harm ----- 3rd harm

79. Copyright 2003 Jan Verspecht bvba 79 Emulate CDMA Statistics using many Periodic Pseudo-Random Sequences Frequency Offset from Carrier (Hz) Amplitude (dBm) Transmitted Signal Copyright 1998 Agilent Technologies, Inc. – Used with Permission

80. Copyright 2003 Jan Verspecht bvba 80 Apply Fitting Technique For our example we use a piece wise polynomial (3rd order) Copyright 1998 Agilent Technologies, Inc. – Used with Permission

81. Copyright 2003 Jan Verspecht bvba 81 Model Verification - Spectral Regrowth -----model -----measured Frequency Offset from Carrier (MHz) Amplitude (dBm) Output signal Copyright 1998 Agilent Technologies, Inc. – Used with Permission

82. Copyright 2003 Jan Verspecht bvba 82 Waveform Measurements Physical Models State-Space Models Black-Box Frequency Domain Models Conclusions Part II - Outline

83. Copyright 2003 Jan Verspecht bvba 83 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 Copyright 1998 Agilent Technologies, Inc. – Used with Permission

84. Copyright 2003 Jan Verspecht bvba 84 “Jan Verspecht bvba” Coordinates URL: http://www.janverspecht.com email: info@janverspecht.com fax: 32-52-31.27.85 phone: 32-479-85.59.39 address: Jan Verspecht bvba Gertrudeveld 15 B-1840 Londerzeel Belgium

85. Copyright 2003 Jan Verspecht bvba 85

86. Copyright 2003 Jan Verspecht bvba 86