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Large-Signal Network Analysis Going beyond S-parameters Dr. Jan Verspecht Jan Verspecht bvba URL: http://www.janverspecht.com Copyright 2003 Jan Verspecht bvba This presentation contains several slides which are used with the permission of Agilent Technologies, Inc. 1 Outline Part I Introduction Instrumentation and Calibration Break Coffee and Cookies

Part II Applications Conclusions Copyright 2003 Jan Verspecht bvba 2 Part I - Outline Introduction Signal Representations Instrumentation Hardware Calibration Aspects Copyright 2003 Jan Verspecht bvba 3 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 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 4 Part I - Outline Introduction Signal Representations Instrumentation Hardware Calibration Aspects Copyright 2003 Jan Verspecht bvba

5 Signal Representations I1 (t ) Set of Physical Quantities I 2 (t ) V1 (t ) V2 (t ) TUNER Traveling Waves (A, B) Voltage/Current (V, I) D.U.T. A1 ( f )

Representation Domain A2 ( f ) TUNER B1 ( f ) B2 ( f ) Frequency (f) Time (t) Envelope (f,t) LSNA is capable of periodic and periodically modulated signals Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 6

Traveling Waves versus Current/Voltage DUT A I DUT V B V Zc I A 2 V A B V Zc I B 2

A B I Zc Copyright 2003 Jan Verspecht bvba Typically Z c 50 Copyright 1998 Agilent Technologies, Inc. Used with Permission 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

4 Freq. (GHz) DC 1 2 3 Spectral components Xh = complex Fourier Series coefficients of the waveforms Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 8 CW: Time and Frequency Domain H j 2 h f t

x (t ) Re X h e h 0 f 1 X h 2 f x(t )e j 2 h f t dt 0 f 1/ period fundamenta l frequency Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 9

Time Domain V/I Representation Time (ns) Time (ns) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 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) Spectral components Xhm DC

1 10 kHz Copyright 2003 Jan Verspecht bvba 2 3 Copyright 1998 Agilent Technologies, Inc. Used with Permission Freq. (GHz) 11 Modulation: Time and Frequency Domain H M j 2 ( h fC m fM ) t

x (t ) Re X hm e h 0 m M T X hm 1 j 2 ( h fC m fM ) t lim x(t )e dt TT T fC carrier frequency fM modulation frequency Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission

12 Modulation: Envelope Domain H j 2 h fc t x(t ) Re X h (t ) e h 0 X h (t ) M X hm e j 2 m fM t m M Copyright 2003 Jan Verspecht bvba

Copyright 1998 Agilent Technologies, Inc. Used with Permission 13 Modulation: Time and Envelope Domain Fundamental envelope B2 (Volt) 3rd harmonic envelope Time (normalized) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with

Permission 14 Modulation: Frequency Domain Fund @ 1.9 GHz 2nd @ 3.8 GHz 3rd @ 5.7 GHz dBm Incident signal (a1) dBm Transmitted signal (b2) dBm Reflected signal (b1)

IF freq (MHz) Copyright 2003 Jan Verspecht bvba IF freq (MHz) Copyright 1998 Agilent Technologies, Inc. Used with Permission IF freq (MHz) 15 Modulation: 2D Time Domain B2 (Volt) tS (normalized) tF (normalized)

H M j 2 ( h t F m tS ) x2D (t F , tS ) Re X hm e h 0 m M x (t ) x2D (fc t, fM t ) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 16 Part I - Outline Introduction Signal Representations Instrumentation Hardware Calibration Aspects

Copyright 2003 Jan Verspecht bvba 17 Hardware: Historical Overview 1988 Markku Sipila & al.: 2 channel scope with one coupler at the input (14 GHz) 1989 Kompa & Van Raay: 2 channel scope with VNA test-set + receiver Lott: VNA test set + receiver (26.5 GHz) 1992 Kompa & Van Raay: test-set with MTA (40 GHz) Verspecht & al.: 4 couplers with a 4 channel oscilloscope (20 GHz)

1994 Demmler, Tasker, Leckey, Wei, Tkachenko: test-set with MTA (40 GHz) Verspecht & al.: 4 couplers with 2 synchronized MTAs 1996 Verspecht & al.: NNMS, 4 couplers, 4 channel converter, 4 ADCs 1998 Nebus & al.: VNA test set + receiver with loadpull and pulsed capability 2003 Maury Microwave, Inc.: commercial introduction (LSNA) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 18 Architecture of the LSNA prototype Computer

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

Schematic 1 LP 1 2 RF (50 GHz) LP 2 3 LP 3 4 LP

4 IF (4 MHz) fLO (20 MHz) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 20 Harmonic Sampling - Signal Class: CW fLO=19.98 MHz = (1GHz-1MHz)/50 RF 50 fLO

100 fLO 1 150 fLO 2 3 Freq. (GHz) IF 1 Copyright 2003 Jan Verspecht bvba 2 3 Freq. (MHz)

Copyright 1998 Agilent Technologies, Inc. Used with Permission 21 Part I - Outline Introduction Signal Representations Instrumentation Hardware Calibration Aspects Copyright 2003 Jan Verspecht bvba 22 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 (DeGroot) NIST investigates phase reference generator approach 2001 calibrated electro-optical sampling (D.F. Williams, P. Hale @ NIST) (provides better harmonic phase accuracy than nose-to-nose) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with

Permission 23 Raw Quantities versus DUT Quantities Computer 10MHz A-to-D Raw quantities R1 R1 R2 R2 ahm bhm ahm bhm RF-IF converter Attenuators TUNER

D1 ahm D1 bhm D2 ahm D2 bhm DUT quantities Copyright 2003 Jan Verspecht bvba ... Copyright 1998 Agilent Technologies, Inc. Used with Permission 24 The Error Model

IF error RF amplitude error D1 ahm 1 D1 b hm K e j h h h D2 ahm 0 D2 bhm 0 DUT quantities R1

h 0 0 C1 ahm R1 h 0 0 C2 bhm R2 0 h h C3 ahm R2 0 h h C4 bhm RF relative error RF phase error Copyright 2003 Jan Verspecht bvba Raw quantities Copyright 1998 Agilent Technologies, Inc. Used with Permission

25 RF Calibration 1. Coaxial SOLT calibration OR On wafer LRRM calibration Combined with 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) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 26

Coaxial Amplitude and Phase Calibration Amplitude Harmonic Phase Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 27 On Wafer Amplitude & Phase Calibration Coaxial LOS LRRM Copyright 2003

Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 28 Calibration Traceability Relative Cal Power Cal Harmonic Phase Nose-to-Nose Standard Electro-Optical Sampler Precision Airline Calorimetry National Standards (NIST) Copyright 2003 Jan Verspecht bvba

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

Nose-to-Nose Calibration Procedure Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 31 Nose-to-Nose Measurement Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 32 3 Oscilloscopes are Needed

1 2 1 3 2 3 Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 33 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. Copyright 2003 Jan Verspecht bvba 34 Outline Part I Introduction Instrumentation and Calibration Break Coffee and Cookies Part II Applications

Conclusions Copyright 2003 Jan Verspecht bvba 35 Outline Part I Introduction Instrumentation and Calibration Break Coffee and Cookies Part II Applications Conclusions Copyright 2003 Jan Verspecht bvba 36 Part II - Outline

Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions Copyright 2003 Jan Verspecht bvba 37 Breakdown Current Time (ns) (transistor provided by David Root, Agilent Technologies - MWTC) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 38

Forward Gate Current Time (ns) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 39 Resistive Mixer Schematic HEMT transistor (no drain bias applied) (transistor provided by Dominique Schreurs, IMEC & KUL-TELEMIC) Copyright 2003 Jan Verspecht bvba Copyright 1998

Agilent Technologies, Inc. Used with Permission 40 Resistive Mixer: Time Domain Waveforms Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 41 High-Speed Digital Signal Integrity Calibrated Eye Measurement On Wafer (@10GB/sec) Oscilloscope Data (courtesy of Jonathan Scott, Agilent Technologies)

Copyright 2003 Jan Verspecht bvba Copyright 2002 Agilent Technologies, Inc. Used with Permission 42 Loadpull and Waveform Engineering MesFET Class F LSNA HARMONIC TUNER PAE50% Data courtesy of IRCOM / Limoges (France) Copyright 2003 Jan Verspecht bvba Z(f0)=130+j73

Z(2f0)=1-j2.8 Z(3f0)=20-j97 PAE=84% 43 Part II - Outline Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions Copyright 2003 Jan Verspecht bvba 44 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, Copyright 2003 Jan Verspecht bvba 45 Physical Model Improvement (courtesy of Dr. Dominique Schreurs, IMEC & KUL-TELEMIC) Parameter Boundaries Chalmers model to optimize GaAs pseudomorphic HEMT gate l=0.2 um w=100 um generators apply waveforms measured by an LSNA Swept power measurements under mismatched conditions Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with

Permission 46 Using the Built-in Optimizer Before OPTIMIZATION Voltage - Current State Space voltage current gate drain Time domain waveforms Copyright 2003 Jan Verspecht bvba gate

drain Frequency domain Copyright 1998 Agilent Technologies, Inc. Used with Permission 47 Verification of the Optimized Model After OPTIMIZATION Voltage - Current State Space voltage current gate drain

Time domain waveforms Copyright 2003 Jan Verspecht bvba gate drain Frequency domain Copyright 1998 Agilent Technologies, Inc. Used with Permission 48 Part II - Outline Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions

Copyright 2003 Jan Verspecht bvba 49 State Space Function Model dV1 dV2 dI1 I 1 F1(V1,V 2, , , ...) dt dt dt dV1 dV2 dI1 I 2 F 2 (V1,V 2, , , ...) dt dt dt Fit with e.g. artificial neural network or spline (David Root, John Wood, Dominique Schreurs) Copyright 2003 Jan Verspecht bvba 50

Experiment Design: Crucial to Explore Component Behavior I1 4.2 GHz Copyright 2003 Jan Verspecht bvba V1 I2 V2 Copyright 1998 Agilent Technologies, Inc. Used with Permission 4.8 GHz 51

State Space Coverage through Proper Experiment Design Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 52 Part II - Outline Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions Copyright 2003 Jan Verspecht bvba

53 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 Copyright 2003 circuit Jan Verspecht bvba 54 Theoretical Concepts Scattering Functions for Nonlinear Behavioral Modeling

in the Frequency Domain Copyright 2003 Jan Verspecht bvba Quantities are Waves Functional Relationshi p Input and Output are Discrete Tone Signals 55 Quantities are Traveling Voltage Waves V V A

I B Z V Z ZI 2 ZI 2 Default value of Z = 50 Ohm (classic S-parameters) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission

56 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 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 57 Notation - Graphical Illustration

A1k B1k A2 k B2 k B1k F1k ( A11 , A12 ,..., A21 , A22 ,...) B2 k F2 k ( A11 , A12 ,..., A21 , A22 ,...) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 58 Phase Normalization Phase normalized quantities are used Defines unambiguous phase for harmonics Large-signal A11 is the phase reference (most useful for many applications)

Copyright 2003 Jan Verspecht bvba 59 Phase Normalization: Mathematics P e We define a reference phasor: j ( A11 ) We define phase normalized quantities: N k N k Amk Amk P mk mk B

Special case: Copyright 2003 Jan Verspecht bvba B P N 11 A A11 60 Harmonic Superposition Principle In general superposition cannot be used to describe the functional relationship between the spectral components F A A F ( A) F ( A) The superposition principle can be used for relatively small components (e.g. harmonics)

Copyright 2003 Jan Verspecht bvba 61 Harmonic Superposition: Illustration A1 B2 Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 62 Basic Mathematical Equation N mk B

N 11 N nh N 11 (A ) A S mknh (A ) A S mknh nh * N nh nh A11 assumed to be the only large-signal component

Superposition assumed to be valid for other Anh The notation A* means the complex conjugate of A S and S are called the scattering functions Note 2003 that Smk11 = 0 Copyright Jan Verspecht bvba 63 Applications: Compression and AM-PM conversion Only considering B21 and A11 results in B21N S 2111 ( A11N ) A11N This can be rewritten as B21 S 2111 ( A11 ) A11 S2111(|A11|) represents the compression and AM-PM conversion characteristic

Copyright 2003 Jan Verspecht bvba 64 Large-Signal Input Match Only considering B11 and A11 results in B11N S1111 ( A11N ) A11N This can be rewritten as B11 S1111 ( A11 ) A11 S1111(|A11|) represents the large-signal input reflection coefficient Copyright 2003 Jan Verspecht bvba 65 Hot S22 Considering B21, A21 and A11 results in

N 21 N 11 N 11 N 11 N 21 N 11 * N 21

(A )A B S 2111 ( A ) A S 2121 ( A ) A S 2121 Multiplying both sides with P results in N 2 * B21 S 2111 ( A11 ) A11 S 2121 ( A11 ) A21 S 2121 ( A11 ) P A21 The combination of S2121 and S2121 are a scientifically sound format for Hot S22 Copyright 2003 Jan Verspecht bvba 66 Scattering functions (dB) Measurement Example 40 S2111 20

0 S2121 -20 S2121 -40 -60 -25 -20 -15 -10 -5 0

5 10 |A11| (dBm) Note that the amplitude of S2121 becomes arbitrary small for |A11| going to zero Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 67 Harmonic Distortion Analysis Only considering A11 and B2k one can calculate the harmonic distortion as a function of |A11| B21 S 2111 ( A11 ) A11

B22 S 2211 ( A11 ) A11 P B23 S 2311 ( A11 ) A11 P Copyright 2003 Jan Verspecht bvba 2 68 Harmonic Loadpull Behavior A2 h A11 h B2 h * B2Nk S 2 k 2 h (A11N ) A2Nh S 2k 2 h (A11N ) A2Nh h h A2Nh h B2Nh

Solve the set of equations (linear in the real and imaginary parts of A2h and B2h) Copyright 2003 Jan Verspecht bvba 69 New Stability Circles for Multiplier Design S[1,1 ] ca ri chi SC IR2 S[2,2 ] due_po rte ca ri chi stability_circle Swp Max

2GHz 1.0 SC IR1 due_po rte 2. 0 0. 6 0 .8 DC DC 0.

4 0 3. 0 0 4. 0 5. 0 0.2 10.0 5.0 4.0

3.0 2.0 1.0 0.8 0.6 20 -10 .0 2 0 .0 .0 Copyright 2003 Jan Verspecht bvba

-1.0 -0 .8 Research performed by Prof. Giorgio Leuzzi (Universita dellAquila, Italy) -0 .6 -2 .0 .4 -3 -0

-4 -0 . -5 . 20 0.4 0 0.2 10. 0 Swp Min 2GHz Stability is not ensured 70

Practical Measurement: Experiment Design Concept Simple example: S2111, S2121 and S2121 ( A11N ) A21N * B21N S 2111 ( A11N ) A11N S 2121 ( A11N ) A21N S 2121 Perform 3 independent experiments Input A21 Im Output B21 Im Re Re Copyright 2003 Jan Verspecht bvba 71 Typical Measurement Setup Large-Signal Network Analyzer

Z match TUNER A11 diplexer fundamental Amk A11 in harmonics Agilent Technologies, Inc. - Patent Pending Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 72 Measurement Example

Input A21 (Vp) Im 0.3 0.8 Output B21 (Vp) Im 0.2 0.6 0.1 0.4 0 - 0.1 0.2

- 0.2 0 - 0.3 - 0.3 - 0.2 - 0.1 0 0.1 0.2 0.3 - 0.6 - 0.4 Re Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission - 0.2 0

Re 73 Link to Harmonic Balance Simulators Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 74 Simulated Model versus Measurements Power Transistor Waveforms Gate Voltage Drain

Voltage Gate Current Drain Current Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 75 Scattering Functions with Modulation 1.9 GHz RFIC (CDMA) Incident signal (a1) (Volt)

Normalized Time Transmitted signal (b2) (Volt) Normalized Time Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 76 Dynamic Harmonic Distortion: Transmitted Signal Output power (dBm) ----- fund ----- 2nd harm

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

Copyright 1998 Agilent Technologies, Inc. Used with Permission 78 Emulate CDMA Statistics using many Periodic Pseudo-Random Sequences Amplitude (dBm) Transmitted Signal Frequency Offset from Carrier (Hz) Copyright 2003 Jan Verspecht bvba Copyright 1998 Agilent Technologies, Inc. Used with Permission 79

Apply Fitting Technique For our example we use a piece wise polynomial (3rd order) Q21 I 21 (V ) (V ) a11 Copyright 2003 Jan Verspecht bvba (V ) Copyright 1998 Agilent Technologies, Inc. Used with Permission a11

(V ) 80 Model Verification - Spectral Regrowth Output signal Amplitude (dBm) -----model -----measured Copyright 2003 Jan Verspecht bvba Frequency Offset from Carrier (MHz) Copyright 1998 Agilent Technologies, Inc. Used with Permission 81

Part II - Outline Waveform Measurements Physical Models State-Space Models Black-Box Frequency Domain Models Conclusions Copyright 2003 Jan Verspecht bvba 82 Conclusions The dream of accurate and complete largesignal 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 2003 Jan Verspecht bvba Copyright 1998

Agilent Technologies, Inc. Used with Permission 83 Jan Verspecht bvba Coordinates URL: http://www.janverspecht.com email: [email protected] fax: 32-52-31.27.85 phone: 32-479-85.59.39 address: Jan Verspecht bvba Gertrudeveld 15 B-1840 Londerzeel Belgium Copyright 2003 Jan Verspecht bvba 84 Copyright 2003 Jan Verspecht bvba

85 Copyright 2003 Jan Verspecht bvba 86

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