Large-Signal Network Analysis Going beyond S-parameters Dr. Jan Verspecht URL: http://www.janverspecht.com This presentation contains several slides which are used with the permission of Agilent Technologies, Inc. 1
Part I Introduction Instrumentation and Calibration Break Coffee and Cookies Part II Outline Applications Conclusions 2
Part I - Outline Introduction Signal Representations Instrumentation Hardware Calibration Aspects 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 4
Part I - Outline Introduction Signal Representations Instrumentation Hardware Calibration Aspects 5
Signal Representations I ( t 1 ) V 1 ( t) I ( t 2 ) V ( t 2 ) TUNER Set of Physical Quantities Traveling Waves (A, B) Voltage/Current (V, I) A 1 ( f B 1 ( f ) ) D.U.T. A 2 ( f B 2 ( f ) ) TUNER Representation Domain Frequency (f) Time (t) Envelope (f,t) LSNA is capable of periodic and periodically modulated signals 6
Traveling Waves versus Current/Voltage DUT A B DUT I V A = V + 2 Z c I V = A + B Typically = 50 Ω Z c B = V 2 Z c I I = A Z c B 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 1 2 3 4 Freq. (GHz) Spectral components X h = complex Fourier Series coefficients of the waveforms 8
CW: Time and Frequency Domain x( t ) H = Re h= 0 X h e j 2π hf t 1 f X = 2f x( t) e j 2π hf t dt h 0 f = 1/ period = fundamental frequency 9
Time Domain V/I Representation Time (ns) Time (ns) 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 1 2 3 10 khz Freq. (GHz) 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 f f C M = = 1 T T T x( t) e carrier frequency modulation frequency j 2π ( hfc + mfm ) t dt 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 13
Modulation: Time and Envelope Domain B 2 (Volt) Fundamental envelope 3rd harmonic envelope Time (normalized) 14
Modulation: Frequency Domain Incident signal (a1) dbm Fund @ 1.9 GHz 2nd @ 3.8 GHz 3rd @ 5.7 GHz Transmitted signal (b2) dbm Reflected signal (b1) dbm IF freq (MHz) IF freq (MHz) IF freq (MHz) 15
Modulation: 2D Time Domain B 2 (Volt) t S (normalized) t F (normalized) x2d( tf, ts ) Re x( t) = x2 ( f t, f t) D c = M H + M h= 0 m= M X hm e j 2π ( ht F + m t S ) 16
Part I - Outline Introduction Signal Representations Instrumentation Hardware Calibration Aspects 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 MTA s 1996 Verspecht & al.: NNMS, 4 couplers, 4 channel converter, 4 ADC s 1998 Nebus & al.: VNA test set + receiver with loadpull and pulsed capability 2003 Maury Microwave, Inc.: commercial introduction (LSNA) 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... 19
RF-IF converter: Simplified Schematic 1 LP 1 2 RF (50 GHz) LP 2 IF (4 MHz) 3 LP 3 4 LP 4 f LO (20 MHz) 20
Harmonic Sampling - Signal Class: CW RF f LO =19.98 MHz = (1GHz-1MHz)/50 50 f LO 100 f LO 150 f LO 1 2 3 Freq. (GHz) IF 1 2 3 Freq. (MHz) 21
Part I - Outline Introduction Signal Representations Instrumentation Hardware Calibration Aspects 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 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) 23
Raw Quantities versus DUT Quantities Computer 10MHz A-to-D RF-IF converter Attenuators Raw quantities R 1 R 1 R 2 a hm b hm a hm TUNER R 2 b hm D1 a hm D1 b hm DUT quantities D2 a hm D2 b hm... 24
25 The Error Model = 2 4 2 3 1 2 1 1 2 2 1 1 0 0 0 0 0 0 0 0 1 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
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) 26
Coaxial Amplitude and Phase Calibration Amplitude Harmonic Phase 27
On Wafer Amplitude & Phase Calibration Coaxial LOS LRRM 28
Calibration Traceability Relative Cal Power Cal Harmonic Phase Nose-to-Nose Standard Precision Airline Calorimetry National Standards (NIST) Electro-Optical Sampler 29
Characterization of the Harmonic Phase Reference Generator Harmonic Phase Reference generator Sampling oscilloscope 30
Sampling Oscilloscope Characterization: Nose-to-Nose Calibration Procedure 31
Nose-to-Nose Measurement 32
3 Oscilloscopes are Needed 1 2 1 3 2 3 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. 34
Part I Introduction Instrumentation and Calibration Break Coffee and Cookies Part II Outline Applications Conclusions 35
Part I Introduction Instrumentation and Calibration Break Coffee and Cookies Part II Outline Applications Conclusions 36
Part II - Outline Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions 37
Breakdown Current Time (ns) (transistor provided by David Root, Agilent Technologies - MWTC) 38
Forward Gate Current Time (ns) 39
Resistive Mixer Schematic HEMT transistor (no drain bias applied) (transistor provided by Dominique Schreurs, IMEC & KUL-TELEMIC) 40
Resistive Mixer: Time Domain Waveforms 41
High-Speed Digital Signal Integrity Calibrated Eye Measurement On Wafer (@10GB/sec) Oscilloscope Data (courtesy of Jonathan Scott, Agilent Technologies) Copyright 2002 42
Loadpull and Waveform Engineering MesFET Class F LSNA HARMONIC TUNER PAE 50% Data courtesy of IRCOM / Limoges (France) Z(f 0 )=130+j73 Ω Z(2f 0 )=1-j2.8 Ω Z(3f 0 )=20-j97 Ω PAE=84% 43
Part II - Outline Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions 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, 45
Physical Model Improvement (courtesy of Dr. Dominique Schreurs, IMEC & KUL-TELEMIC) Chalmers model to optimize GaAs pseudomorphic HEMT gate l=0.2 um w=100 um Parameter Boundaries generators apply waveforms measured by an LSNA Swept power measurements under mismatched conditions 46
Using the Built-in Optimizer Before OPTIMIZATION Voltage - Current State Space voltage current gate drain Time domain waveforms gate drain Frequency domain 47
Verification of the Optimized Model After OPTIMIZATION Voltage - Current State Space voltage current gate drain Time domain waveforms gate drain Frequency domain 48
Part II - Outline Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions 49
State Space Function Model I I 1 2 = F = F 1 ( V 2 1 ( V, V 1 2, V dv, dt 2 1 dv, dt 1 dv, dt 2 dv, dt 2 di, dt 1 di, dt 1...)...) Fit with e.g. artificial neural network or spline (David Root, John Wood, Dominique Schreurs) 50
Experiment Design: Crucial to Explore Component Behavior I 1 I 2 V 1 V 2 4.2 GHz 4.8 GHz 51
State Space Coverage through Proper Experiment Design 52
Part II - Outline Waveform Measurements Physical Models State-Space Models Scattering Functions Conclusions 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 circuit When the component has distributed characteristics 54
Theoretical Concepts Scattering Functions for Nonlinear Behavioral Modeling in the Frequency Domain Quantities are Waves Functional Relationship Input and Output are Discrete Tone Signals 55
Quantities are Traveling Voltage Waves V I ( ) V + ZI A Z 2 = ( ) V ZI B Z 2 Default value of Z = 50 Ohm (classic S-parameters) 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 57
Notation - Graphical Illustration A 1k A 2k B 1k B 2k B B = k F1 k ( A11, A12,..., A21, 22,...) F A, A,..., A,,...) 1 A = 2 k 2 k ( 11 12 21 A22 58
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) 59
Phase Normalization: Mathematics We define a reference phasor: P = e jϕ ( A 11 ) We define phase normalized quantities: A N mk = A mk P k B N mk = B mk P k Special case: A N = A 11 11 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) 61
Harmonic Superposition: Illustration A 1 B 2 62
Basic Mathematical Equation B N mk = S ( A N ) A N + S ( A N mknh 11 nh mknh 11 nh nh ) A N nh * 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 63
Applications: Compression and AM-PM conversion Only considering B 21 and A 11 results in N N N B21 = S2111( A11 ) A11 This can be rewritten as 2111 ( A11 ) S = B A 21 11 S 2111 ( A 11 ) represents the compression and AM-PM conversion characteristic 64
Large-Signal Input Match Only considering B 11 and A 11 results in N N N B11 = S1111( A11 ) A11 This can be rewritten as 1111 ( A11 ) S = B A 11 11 S 1111 ( A 11 ) represents the large-signal input reflection coefficient 65
B B N 21 = S 2111 Hot S 22 Considering B 21, A 21 and A 11 results in N N N N N N* ( A11 ) A11 + S2121( A11 ) A21 + S 2121( A11 ) A21 Multiplying both sides with P results in = N 2 ( A ) ( ) ( ) * 11 A11 + S2121 A11 A21 + S 2121 A11 P 21 21 S2111 A The combination of S 2121 and S 2121 are a scientifically sound format for Hot S 22 66
Measurement Example 40 Scattering functions (db) S 2111 20 0 S 2121-20 -40 S 2121-60 -25-20 -15-10 -5 0 5 10 A 11 (dbm) Note that the amplitude of S 2121 becomes arbitrary small for A 11 going to zero 67
Harmonic Distortion Analysis Only considering A 11 and B 2k one can calculate the harmonic distortion as a function of A 11 B 21 = S 2111 ( A 11 ) A 11 B 22 = S 2211 ( A 11 ) A 11 P B 23 = S 2311 ( A 11 ) A 11 P 2 68
Harmonic Loadpull Behavior A 2 h A 11 Γ h B 2 h B A N 2k N 2h N N = S2k 2h( A11 ) A2 h + h h = Γ h B N 2h S 2k 2h ( A N 11 ) A N 2h * Solve the set of equations (linear in the real and imaginary parts of A 2h and B 2h ) 69
SCIR1 due_porte SCIR2 due_porte S[1,1] ca ri ch i S[2,2] ca ri ch i -4.0 New Stability Circles for Multiplier Design DC ω 0 ω 0 DC 2ω 0 2ω 0 0 0.2 0.4 0.2 0.6 0.4 stability_circle 0.8 0.6 0.8 1.0 1.0 2.0 2.0 3.0 4.0 5.0 Swp Max 2GHz 3.0 10.0 4.0 5.0 10.0-10.0-0.2-5.0-0.4-3.0 Research performed by Prof. Giorgio Leuzzi (Universita dell Aquila, Italy) -0.6-0.8-1.0-2.0 Swp Min 2GHz Stability is not ensured 70
N 21 Practical Measurement: Experiment Design Concept Simple example: S 2111, S 2121 and S 2121 B = S 2111 N N N N N N* ( A11 ) A11 + S2121( A11 ) A21 + S 2121( A11 ) A21 Perform 3 independent experiments Input A 21 Output B 21 Im Im Re Re 71
Typical Measurement Setup Large-Signal Network Analyzer Z match TUNER A 11 diplexer A mk A 11 in fundamental harmonics Agilent Technologies, Inc. - Patent Pending 72
Measurement Example Im 0.3 0.2 0.1 0-0.1-0.2-0.3 Input A 21 (V p ) Output B 21 (V p ) 0.8 Im 0.6 0.4 0.2 0-0.3-0.2-0.1 0 0.1 0.2 0.3 Re -0.6-0.4-0.2 0 Re 73
Link to Harmonic Balance Simulators 74
Simulated Model versus Measurements Gate Voltage Power Transistor Waveforms Drain Voltage Gate Current Drain Current 75
Scattering Functions with Modulation 1.9 GHz RFIC (CDMA) (Volt) Incident signal (a1) (Volt) Transmitted signal (b2) Normalized Time Normalized Time 76
Output power (dbm) Dynamic Harmonic Distortion: Transmitted Signal ----- fund ----- 2nd harm ----- 3rd harm Input power (dbm) 77
Output power (dbm) Dynamic Harmonic Distortion: Reflected Signal ----- fund ----- 2nd harm ----- 3rd harm Input power (dbm) 78
Emulate CDMA Statistics using many Periodic Pseudo-Random Sequences Amplitude (dbm) Transmitted Signal Frequency Offset from Carrier (Hz) 79
Apply Fitting Technique For our example we use a piece wise polynomial (3rd order) (V ) I Q 21 21 (V ) a 11 ( V ) a 11 ( V ) 80
Model Verification - Spectral Regrowth Amplitude (dbm) Output signal -----model -----measured Frequency Offset from Carrier (MHz) 81
Part II - Outline Waveform Measurements Physical Models State-Space Models Black-Box Frequency Domain Models Conclusions 82
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 83
Coordinates URL: http://www.janverspecht.com email: info@janverspecht.com fax: 32-52-31.27.85 phone: 32-479-85.59.39 address: Gertrudeveld 15 B-1840 Londerzeel Belgium 84
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