Modeling I/O Links With X Parameters

Transcription

1 Modeling I/O Links With X Parameters José E. Schutt Ainé and Pavle Milosevic Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign Urbana, IL Wendemagegnehu T. Beyene Research & Technology Development Rambus Inc. Los Altos, CA

2 Outline Motivation S Parameters PHD Framework and X Parameters a. Definitions b. Properties c. Matrix Formulation d. Time Domain Simulation Application to CMOS Inverter High-Speed Link Simulations Conclusions 2

3 Scattering Parameters V1 a1 b1 I b1 S11a1 S12a2 a a2 b 1 b1 2 b2 S21a1 S22a I 2 2 Z Z o o B SA For a two-port For a general N-port N B B i SA Sij A Ak 0 i ij j j1 most successful behavioral models V a b j k j k1,..., N 3

4 Challenges in HS Links High speed Serial channels are pushing the current limits of simulation. Models/Simulator need to handle current challenges Need to accurately handle very high data rates Simulate large number of bits to achieve low BER Non linear blocks with time variant systems Model TX/RX equalization All types of jitter: (random, deterministic, etc.) Crosstalk, loss, dispersion, attenuation, etc Handle and manage vendor specific device settings Clock data recovery (CDR) circuits These cannot be accurately modeled with S parameters 4

5 X Parameters for SI Objective Adopt X parameters as the framework for highspeed channel design modeling and simulation. Advantages - Mathematically robust framework - Can handle nonlinearities - Instrument exists (NVNA) - Blackbox format vendor IP protection - Matrix format easy incorporation in CAD tools - X Parameters are a superset of S parameters See Refs [1] & [2] by Verspecht and Root 5

6 Cascading X Parameters GOAL: Simulate complete channel by combining X- parameter blocks from different sources into a single composite X matrix. Vendor A Foundry In-House Vendor B In-House Vendor C Foundry X X-parameters of individual devices can be accurately cascaded within a harmonic balance simulator environment. 6

7 Nonlinear Vector Network Analyzer (NVNA) NVNA instruments will gradually replace all VNAs 7

8 PHD Modeling Polyharmonic distortion (PHD) modeling is a frequency-domain modeling technique PHD model defines X parameters which form a superset of S parameters To construct PHD model, DUT is stimulated by a set of harmonically related discrete tones In stimulus, fundamental tone is dominant and higher-order harmonics are smaller 8

9 PHD Framework Signal is represented by a fundamental with harmonics Signals are periodic or narrowband modulated versions of a fundamental with harmonics Harmonic index: 0 for dc contribution, 1 for fundamental and 2 for second harmonic Power level, fundamental frequency can be varied to generate complete data for DUT 9

10 Excitation Design Excitation 1 Excitation 2 Excitation 3 Excitation 4 Each excitation will generate response with fundamental and all harmonics 10

11 PHD Framework 11

12 Harmonic Superposition In many situations, there is only one dominant largesignal input component present. The harmonic frequency components are relatively small harmonic components can be superposed Harmonic superposition principle is key to PHD model 12

13 X-Parameter Data File TOP: FILE DESCRIPTION! Created Fri Jul 30 07:44: ! Version = 2.0! HB_MaxOrder = 25! XParamMaxOrder = 12! NumExtractedPorts = 3! IDC_1=0 NumPts=1! IDC_2=0 NumPts=1! VDC_3=12 NumPts=1! ZM_2_1=50 NumPts=1! ZP_2_1=0 NumPts=1! AN_1_1=100e-03( dBm) NumPts=1! fund_1=[100 Hz->1 GHz] NumPts=4 13

14 X-Parameter Data File MIDDLE: FORMAT DESCRIPTION BEGIN XParamData % fund_1(real) FV_1(real) FV_2(real) FI_3(real) FB_1_1(complex) % FB_1_2(complex) FB_1_3(complex) FB_1_4(complex) % FB_1_7(complex) FB_1_8(complex) FB_1_9(complex) % FB_1_12(complex) FB_2_1(complex) FB_2_2(complex) % FB_2_5(complex) FB_2_6(complex) FB_2_7(complex) % FB_2_10(complex) FB_2_11(complex) FB_2_12(complex) % T_1_1_1_1(complex) S_1_2_1_1(complex) T_1_2_1_1(complex) % S_1_4_1_1(complex) T_1_4_1_1(complex) S_1_5_1_1(complex) % T_1_6_1_1(complex) S_1_7_1_1(complex) T_1_7_1_1(complex) % S_1_9_1_1(complex) T_1_9_1_1(complex) S_1_10_1_1(complex)) % T_1_11_1_1(complex) S_1_12_1_1(complex) T_1_12_1_1(complex) % T_2_1_1_1(complex) S_2_2_1_1(complex) T_2_2_1_1(complex) % S_2_4_1_1(complex) T_2_4_1_1(complex) S_2_5_1_1(complex % T_2_6_1_1(complex) S_2_7_1_1(complex) T_2_7_1_1(complex) % S_2_9_1_1(complex) T_2_9_1_1(complex) S_2_10_1_1(complex) 14

15 X-Parameter Data File BOTTOM: DATA LISTING e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e-14 Remarks Data is measured or generated from a harmonic balance simulator Data file can be very large 15

16 X-Parameter Relationship k kl kl * 11, 11, 11 b D a P S a P a T a P a ik ik ik jl jl ik jl jl ( jl, ) (1,1) P : Phase of a 11 D : B type X parameter ik Sik, jl : S type X parameter Tik, jl : T type X parameter 16

17 Index Convention S ik,jl T ik,jl out port in port harmonic out harmonic in out port in port harmonic out harmonic in a ik b ik port harmonic port harmonic 17

18 X Parameters of CMOS -1 x S11,11 - Amplitude (db) GHz 1 GHz T11,11 - Amplitude (db) GHz 1 GHz A11 (dbm) A11 (dbm) S21,11 - Amplitude (db) GHz 1 GHz T21,11 - Amplitude (db) GHz 1 GHz A11 (dbm) A11 (dbm) 18

19 X Parameters of CMOS S12,11 - Amplitude (db) GHz 1 GHz T12,11 - Amplitude (db) GHz 1 GHz A11 (dbm) A11 (dbm) S22,11 - Amplitude (db) GHz 1 GHz T22,11 - Amplitude (db) GHz 1 GHz A11 (dbm) A11 (dbm) 19

20 Special Terms T-Type X Parameter Spectral mapping is non-analytical Real and imaginary parts in FD are treated differently Even and odd parts in TD are treated differently T involves non-causal component of signal Phase Term P P is phase of large-signal excitation (a 11 ) Contributions to B waves will depend on P In measurements, system must be calibrated for phase 20

21 Handling Phase Term k kl kl * 11, 11, 11 b D a P S a P a T a P a ik ik ik jl jl ik jl jl ( jl, ) (1,1) Multiply through by P k * 11, 11, 11 bp D a S a P a T a P a k l l ik ik ik jl jl ik jl jl ( jl, ) (1,1) P where is the phase of a j 11 e we can always express the relationship in terms of modified power wave variables * 11, 11, 11 b D a S a a T a a ik ik ik jl jl ik jl jl ( jl, ) (1,1) where k b b P and a a P ik ik ik ik k 21

22 Handling R&I Components Because of non-analytical nature of spectral mapping, real and imaginary component interactions must be accounted for separately. we have b X X a r rr ri r b X X a i ir ii i where, X S T X S T rr r r ri i i, X S T X S T ir i i ii r r 22

23 Handling Phase Term Phase term can be accounted for by applying following transformations br Xrr Xriar b X X a i ir ii i ' cosb sinb b cos sin r Xrr Xri a a ' sinb cos b b Xir X ii sina cos i a ' a r ' ai in which ' br cosb sinbb r ' b i sinb cos b bi ' ar cosa sina a r ' a i sina cos a ai 23

24 X Matrix Construction Separate real and imaginary components Account for real-imaginary interactions Account for harmonic-to-harmonic contributions Account for harmonic-to-dc contributions Matrix size is 2mn 2mn m: number of harmonics n: number of ports 24

25 Matrix Formulation* size:2mn a1 a 2 a ap an a p a a a a a a (1) pr (1) pi (2) pr (2) pi ( m) pr ( m) pi We wish to use: b=xa b b b b b vector size is 2m m: number of harmonics n: number of ports (real vectors) *DC term not included 1 2 p n b p size:2 mn b b b b b b (1) pr (1) pi (2) pr (2) pi ( m) pr ( m) pi 25

26 X= X X X X 21 X22 Xpq Xn1 X n X pq (real matrix) *DC term not included Matrix Formulation* nn matrix size is 2mn 2mn m: number of harmonics n: number of ports size: 2m 2m X X X X X X X X X X X X X X X X X X (11) (11) (12) (12) (1 m) (1 m) pqrr pqri pqrr pqri pqrr pqri (11) (21) (21) (11) (21) (21) (12) (22) (22) (12) (22) (22) pqir pqrr pqir pqii pqri pqii pqir pqrr pqir pqii pqri pqii X X X X ( m1) ( m1) ( mm) ( mm) pqir pqii pqir pqii 26

27 X Matrix for 2-Port System* (2 harmonics) X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X (11) (11) (12) (12) (11) (11) (12) (12) 11rr 11ri 11rr 11ri 12rr 12ri 12rr 12ri (11) (11) (12) (12) (11) (11) (12) (12) 11ir 11ii 11ir 11ii 12ir 12ii 12ir 12ii (21) (21) (22) (22) (21) (21) (21) (21) 11rr 11ri 11rr 11ri 12rr 12ri X12rr X12ri (21) (21) (22) (22) (21) (21) (22) (22) 11ir 11ii 11ir 11ii 12ir 12ii 12ir 12ii (11) (11) (12) (12) (11) (11) (12) (12) 21rr 21ri 21rr 21ri 22rr 22ri 22rr 22ri (11) (11) (12) (12) (11) (11) (12) (12) 21ir 21ii 21ir 21ii 22ir X22ii X22ir X22ii (21) (21) (22) (22) (21) (21) (22) (22) 21rr 21ri 21rr 21ri 22rr 22ri 22rr 22ri (21) (21) (22) (22) (21) (21) (22) (22) 21ir 21ii 21ir 21ii 22ir 22ii 22ir 22ii (real matrix) For instance, X (12) 21ri is the contribution to the real part of the 1 st harmonic of the wave scattered at port 2 due to the imaginary part of the 2 nd harmonic of the wave incident port in port 1. *DC term not included 27

28 Polyharmonic Impedance Linear Impedance Polyharmonic Impedance Nonlinear Impedance - Time invariant - Linear - Scalar - Time invariant - Linear - Matrix - Time variant - Nonlinear - Function V ZI FD & TD [ V( f)] [ Z( f)][ I( f)] Vt () ZIt ( ()) FD only Model assumes that nonlinear effects are mild and are captured via harmonic superposition. 28

29 Polyharmonic Impedance 4-harmonic system in frequency domain: (1) (11) (12) (13) (14) (1) V Z Z Z Z I (2) (21) (22) (23) (24) (2) V Z Z Z Z I (3) (31) (32) (33) (34) (3) V Z Z Z Z I (4) (41) (42) (43) (44) (4) V Z Z Z Z I in time domain: v t v t v t v t v t (1) (2) (3) (4) () () () () () i t i t i t i t i t (1) (2) (3) (4) () () () () () 29

30 Polyharmonic Impedance Z o : Reference impedance matrix Z V I : Polyharmonic impedance matrix : Voltage vector : Current vector Describes interactions between harmonic Z= 1+X1-X -1 Zo components of voltage and current. V=ZI 30

31 Network Formulation Scattered waves b=xa Termination equations a=dv +Γb g Wave Solution a= 1-ΓX -1 Dvg Voltage Solution v= 1+Xa 31

32 Steady-State Simulations cubic term Time-Domain Response Vin Vout 40 X Parameter Volts time(ns) ADS 32

33 CMOS Driver/Receiver Channel Generate X parameters for composite system Power level: 20 dbm, frequency: 1 GHz Construct X matrix Combine with terminations for simulation 33

34 CMOS Driver/Receiver - Harmonics 8 6 DC+Fundamental Vin Vout Harmonics Vin Vout Volts 0 Volts time(ns) time(ns) Harmonics Vin Vout Harmonics Vin Vout Volts 0 Volts time(ns) time(ns) 34

35 Validation 8 6 Time-Domain Response Vin Vout X Parameter Volts time(ns) ADS Vout, V Vin, V time, nsec 35

36 Equalized Channel ADS model of Tx (non linear) + backplane channel (linear) Rx is passive termination Uses a typical BSIM3 model of a 0.25um 2.5V CMOS process, provided in ADS Note: modified nfet and pfet to remove all parasitic caps, in order to run at higher speed. System Block Diagram: V V Main branch near V far src FIR tap 1 Tx Channel Passive termination 36

37 Channel Analysis Impulse Response, BR=5Gbps, t r =20ps Channel: 40-inch FR4, Z0=50Ohm; terminated with ZL=50 Ohm and Ci=2pF Unequalized impulse response Reveals 1 tap FIR at Tx will cancel most of ISI (m7) Equalized impulse response FIR tap coefficient set to 1/3 (ratio of m6 and m7) DC shift due to equalizer structure 37

38 Transmitter Structure Input signal V src expected: Single ended 2.5V NRZ, 5Gbps, t r =20ps FIR filter: modified single ended push pull Output signal obtained by voltage dividers Resistor sizing sets tap coefficients and DC levels Main branch R 1 V src FIR tap 1 R 2 V near Delay of 1UI = 200ps 38 [1] Heidar et al., Comparison of output drivers for high-speed serial links, ICM 2007.

39 Transmitter Structure 39

40 Transient Response Unequalized Equalized 2 Vin Vout 2 Vin Vout X Parameter Volts Volts Time (ns) Time (ns) ADS 40

41 Far-End Eye Diagrams Unequalized Equalized In-phase Signal In-phase Signal Amplitude (AU) 12 dbm Amplitude (AU) Time (s) In-phase Signal Time (s) In-phase Signal x Amplitude (AU) Amplitude (AU) dbm 0 x Time (s) x Time (s) x 10 41

42 Conclusions X Parameters represent a powerful format for the exchange of nonlinear behavioral models for use in the analysis and design of high-speed links Challenges Ahead Standardization from different levels of approximation Define protocols for X-parameter exchange 42

43 References [1] J Verspecht and D. E. Root, ʺPolyharmonic Distortion Modeling,ʺ IEEE Magazine, June 2006, pp [2] D.E. Root, J. Verspecht, D. Sharrit, J. Wood, and A.Cognata, Broad band poly harmonic distortion (PHD) behavioral models from fast automated simulations and large signal vectorial network measurements, IEEE Trans. Microwave Theory Tech., vol. 53, no. 11, pp , Nov [3] Agilent Nonlinear Vector Network Analyzer (NVNA), Agilent Technologies, Inc., March

44 Acknowledgement The authors thank Agilent Technologies Inc., for encouraging this work and providing the ADS X- parameter generation platform, especially Loren Betts, Steve Fulwider and Bill Wallace for fruitful discussions, insightful comments and helpful suggestions. X parameters is a registered trademark of Agilent Technologies, Inc. 44