Macromodels of Packages Via Scattering Data and Complex Frequency Hopping

Size: px

Start display at page:

Download "Macromodels of Packages Via Scattering Data and Complex Frequency Hopping"

Stephanie Parsons
10 years ago
Views:

1 F. G. Canavero ½, I. A. Maio ½, P. Thoma ¾ Macromodels of Packages Via Scattering Data and Complex Frequency Hopping ½ Dept. Electronics, Politecnico di Torino, Italy ¾ CST, Darmstadt, Germany

2 Introduction Development of equivalent circuits of linear junctions (connectors, vias, packages,...) from measured/simulated responses Ð Ò Ö ÙÒØ ÓÒ responses Ú modeling algorithm eq. circuit allows to include complex or poorly documented devices in circuit simulators 1

..) from measured/simulated responses Ð Ò Ö ÙÒØ ÓÒ responses Ú

3 Introduction measured/ simulated responses eq. circuit linear parametric identification problem many applications several identification methods Linear Subspace Methods / Pencil of Functions [many] Global Rational Approximation [J.L. Prince] Block Complex Frequency Hopping [M.S. Nakhla]

several identification methods Linear Subspace Methods / Pencil of

4 Objective Experiment with Block Complex Frequency Hopping (BCFH) applied directly to quasi-matched scattering data measured/ simulated scattering responses BCFH eq. circuit simpler smooth shapes easier to model preliminary results of a case study poles far from imaginary axis difficult to estimate 3

5 Case Study: IC Package Structure Port Definition 4

6 Case Study: IC Package Simulated transient wave variables Board side a1 b.1.5 b b b Time ns Time ns 5

6 1.. 1.15.8 a1 b.1.5 b3.6.4.5 b6..1.15 b1.

7 Case Study: IC Package Computed (FFT) scattering functions 1 S1 magnitude, linear.1 S31 magnitude, linear frequency GHz 4 S1 phase, rads frequency GHz 4 S31 phase, rads frequency GHz frequency GHz 6

.7 4 6 8 frequency GHz 4 S1 phase, rads 4 6 8 frequency GHz 4 S31

8 Æ µ Ò BCFH technique: key elements 1. Build the actual set of dominant Ô poles Æ ½ Ò of the multiport element by applying the pole convergence property of Padé approximants to available network functions. Represent every network function by a partial fraction expansion and compute its residues by least square fitting in the f-domain Ë µ Ë µ Ò ½ Ô Ò 7

$Represent every network function by a partial fraction expansion and compute its$

9 expansion point «Ë µ ¼ ½ «µ ¾ «µ ¾ BCFH technique: key elements Pole convergence property Let Ë Ä Å È Ä µ É Å µ be the Padé approximant generated from the moments Ë µ of at the For Ä ½ the poles of Ë Ä Å converge to the M actual poles Ë µ of closest «to 8

approximant generated from the moments Ë µ of at the For Ä ½

10 Ò ½ Ò ½ Øµ Ò Øµ ÜÔ «Øµ Ø Moment evaluation Integrals of transient responses ¼ normalised time and frequency scales moment scaling Õ Õ Õ ½ Ä Å µ ¼ Ä Å 9

11 Search Ë ½ for poles 6 4 expansion point last iteration poles converged poles validated poles accuracy ranges

12 Validation issues Qualitative agreement with the pole distribution of weakly coupled multiland interconnects (but for real poles) Poles estimated from Ë ½½, Ë ¾½, Ë ½ and Ë ½ indeed coincide Poles estimated from Ë ½ and Ë ½ have up to 5% variations: no high accuracy should be expected Time delay: poles estimated Ë from ¾½ with and 1. 1 without time delay extraction coin-.8 a1 b cide,.6 negligible impact on pole convergence.4. b Time ns 11

have up to 5% variations: no high accuracy should be expected Time delay: poles estimated Ë from ¾½ with and 1.

13 IC Package Pole Set Lands are weakly coupled Scattering elements relating near ports mainly show the same small pole set Such local pole set yield accurate fitting of the parent local scattering elements (example on the paper) Scattering elements relating far ports are very small and useless 1

accurate fitting of the parent local scattering elements (example on the

14 IC Package Pole Set The set of all found poles has a clustered distribution (real poles never detected) The complete set of poles is too large for the generic scattering element local pole sets for local scattering elements equivalent pole set defined by the centers of clusters for every scattering element 13

poles is too large for the generic scattering element local pole sets for local

15 poles ½ ¼ ½ ¾ ¾ ¾ ¼ ¼ Approximation results.7 S33 magnitude (linear) 1.5 S43 magnitude (linear) phase (radians) phase (radians)

5 1.4.95.3..1 1 3 1.5 1.5 phase (radians) 1 3.9.85.

16 poles ½ ¼ ½ ¾ ¾ ¾ ¼ ¼ Approximation results.1 S53 magnitude (linear).14 S63 magnitude (linear) phase (radians) phase (radians)

17 poles ½ ¼ ½ ¾ ¾ ¾ ¼ ¼ Approximation results.35 S73 magnitude (linear).5 S83 magnitude (linear) phase (radians) phase (radians)

18 poles ½ ¼ ½ ¾ ¾ ¾ ¼ ¼ Approximation results. S111 magnitude (linear).7 S1111 magnitude (linear) phase (radians) phase (radians)

19 poles ½ ¼ ½ ¾ ¾ ¾ ¼ ¼ Approximation results 1.5 S111 magnitude (linear).14 S1411 magnitude (linear) phase (radians) phase (radians)

1.1.95.8.9.85.8 1 3.5 1 1.5.5 phase (radians) 3 1 3.6.4.

20 Á ½ Î ½ Î Ê Ö Á ¾ Ê Ö ¾ ½ ¾ ¾ Ê Ö Î ¾ Á ¾ Equivalent circuits Synthesis based on controlled sources converting wave variables into ports currents and voltages ¾ Ë ¾ Ë Î Ê Ö Á µ 19

21 ¾ ½ ½ ¾ Equivalent circuits contributions synthesized by RC filters case of simple real poles ½½µ Ë ½ ¾ ½½ Ë ½½ ½ ½½µ ½ ¾ ½ ½ ¾ ½ 1 ½ F ½ F ½ ½ ½½µ ½ ½ ½½µ ½ ¾ Å Å

22 Equivalent circuit validation.7 S11 amplitude. Solid: reference; crosses: SPICE equivalent

23 Conclusion Critical discussion of the estimation of poles from sampled quasi-matched scattering responses Quasi-matched scattering functions are little sensitive to pole position estimated poles can be accurate enough reduced set of approximate poles can be used to model large weakly coupled multiconductor interconnects Open questions (validation, noise sensitivity, passivity (see paper)...) Improvments are possible (input signal, time window, moment calculation...)

Laboratory 4: Feedback and Compensation

Laboratory 4: Feedback and Compensation To be performed during Week 9 (Oct. 20-24) and Week 10 (Oct. 27-31) Due Week 11 (Nov. 3-7) 1 Pre-Lab This Pre-Lab should be completed before attending your regular