Analytical Extraction of Via Near-Field Coupling Using a Multiple Scattering Approach

Transcription

1 Analytical Extraction of Via Near-Field Coupling Using a Multiple Scattering Approach 17 th IEEE Workshop on Signal and Power Integrity May 12-15, 213 Paris, France Sebastian Müller 1, Andreas Hardock 1, Renato Rimolo-Donadio 2, Heinz-D. Brüns 1, Christian Schuster 1 1 Institut für, Technische Universität Hamburg-Harburg, Hamburg, Germany 2 IBM T. J. Watson Research Center, Yorktown Heights, New York, USA Technische Universität Hamburg-Harburg

2 Motivation Basic target: simulation of (multilayer) printed circuit boards (see e.g. [1]) Input: geometry data of the printed circuit board (PCB) Output: network parameters of the PCB as seen from the ports Port 1 Socket Socket Port 2 2

3 Motivation Approach: segmented equivalent circuit model (External) Port 1 Cavity 1 (eq. circuit) (External) Port 2 Cavity 2 (eq. circuit) Cavity 3 (eq. circuit) Internal ports Advantages: short simulation times simulation of large structures Cavity N (eq. circuit) (External) Port 3 (External) Port 4 3

4 Study in [4]: Motivation What are the limiting cases for the accuracy of current equivalent circuits? Experiment: modeling of very closely spaced vias 1) Via separation d = 12.2 mil 2) Via separation d = 4 mil Vias (PEC, r v = 5 mil) Antipads (r a = 6 mil) Port 1 Port 2 ε r = 3.8 tan δ =.2 h = 12 mil d = 4 mil Reference planes (PEC, t = 1 mil) d=12.2mil Port 3 Port 4 4

5 S 31 [db] S 11 [db] Motivation Transmission and reflection for closely spaced vias d=12.2mil Transmission Full wave 2 Equivalent circuit Frequency [GHz] Reflection d=12.2mil Frequency [GHz] 1 HFSS 2 Physics-based model [1] with Williamson near-field model [8] 5

6 S 21 [db] S 41 [db] Introduction Near- and far-end crosstalk for closely spaced vias Near-end crosstalk d=12.2mil d=4mil -1-2 Far-end crosstalk d=12.2mil 3 4 d=4mil -3 Full wave Equivalent circuit Frequency [GHz] -3 Full wave Equivalent circuit Frequency [GHz] 6

7 Contents Introduction Physical Behavior of Coupled Vias Analysis of Near-Field Coupling Relevance of Near-Field Coupling Conclusions 7

8 H (2) (kl ) Radial Waveguide Modes in the PCB Cavity Physics-based equivalent circuit model of a single PCB cavity: Electric field inside the cavity (d = 4 mil) 1 Port 1 Port 2 Local field model (e.g. C c ) Propagating field model (Z pp or Y pp ) Local field model (e.g. C c ) Local via field Propagating field Local via field Port 3 Port 4 Field models are calculated based on TM z ln modes: l n Local field model L max Propagating field model Mode numbers considered 1 Screenshot from CST Microwave Studio Distance [mil] 8 l = l = 1 l = 2 Attenuation of TM z ln modes (ρ = distance to via surface; f = 5 GHz)

9 C [ff] Coupling for Closely Spaced Vias Change of the coupling behavior for very closely spaced vias: Electric field inside the cavity (d = 12.2 mil) 1 Static via-to-via capacitance: 15 2 C via-to-via C two-wire line 1 5 C = 28 ff for d = 12.2 mil Field distribution changed due to presence of the nearby second via Coupling provided by higher order modes ( near-field coupling ) Via separation d [mil] 1 Screenshot from CST Microwave Studio 2 Capacitance extracted using Q3D 9

10 Contents Introduction Physical Behavior of Coupled Vias Analysis of Near-Field Coupling Relevance of Near-Field Coupling Conclusions 1

11 Approach Used: Multiple Scattering Source: MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 31, No. 3, November

12 S 21 [db] S 41 [db] S 31 [db] S 11 [db] Multiple Scattering: Results Comparison between full wave solution 1 and results from multiple scattering approach 2 (L max = 15, N max = ) Transmission Frequency [GHz] Near-end crosstalk -1-2 Reflection -3 Full wave Multiple scattering Frequency [GHz] Far-end crosstalk Frequency [GHz] Frequency [GHz] 1 HFSS 2 [6] (Tsang et al) 12

13 Analysis of Higher Order Modes Decomposition of multiple scattering results into contributions Y Y by the fundamental mode (l = ) and higher order modes (l > ): l Y l l1 Y-matrix due to higher order modes (1 st column) for A) Typical via separations: l1 Y ( Y Y ) Y T l i,1 c p p B) Very small via separations: l1 ( Y Y Y Y ) Y Y Y T Y l c 12 p p 14 i,1 ~ ~ ~

14 C [ff] C [ff] Effective Coupling capacitances The via coupling by higher order modes can be described by effective coupling capacitances: Y 12 = jωc 12 and Y 14 = jωc A) Frequency dependency: B) Dependency on via separation: 8 Extracted C (12.2 mil) 12 Extracted C (12.2 mil) C (1 MHz) 12 C (1 MHz) Frequency [GHz] Via separation d [mil] 14

15 Contents Introduction Physical Behavior of Coupled Vias Analysis of Near-Field Coupling Relevance of Near-Field Coupling Conclusions 15

16 d min [mil] Relevance of Near-Field Coupling Criterion: ratio between effective coupling capacitance and via barrel-to-plane capacitance Target: C 12 / C c 1% ~ 1 db deviation in S-parameter results 3 Empirical formula for minimum via separation (least squares fit, h = 12 mil = const.): d' min d min.2( r r v 2r a v r v d ) d 2.4( r r v a r v ) rv = 4 mil rv = 5 mil rv = 6 mil (ra-rv) [mil] Black / red / blue: results of original evaluation; green: results of fitted empirical formula. 16

17 Contents Introduction Physical Behavior of Coupled Vias Analysis of Near-Field Coupling Relevance of Near-Field Coupling Conclusions 17

18 Conclusions Near-field coupling between vias (due to higher order modes) impacts the crosstalk between very closely spaced vias can be described by effective coupling capacitances changes the via barrel-to-plane capacitance Necessary separation between vias to neglect near-field coupling has been described by empirical formula 3 mil separation is sufficient for typical geometries near-field coupling can be neglected for most designs 18

19 References (1) [1] R. Rimolo-Donadio, X. Gu, Y. H. Kwark, M. B. Ritter, B. Archambeault, F. De Paulis, Y. Zhang, J. Fan, H.-D. Brüns, and C. Schuster, Physics-based via and trace models for efficient link simulation on multilayer structures up to 4 GHz, IEEE Trans. Microw. Theory Tech., vol. 57, no. 8, pp , Aug. 29. [2] Y.-J. Zhang and J. Fan, An intrinsic circuit model for multiple vias in an irregular plate pair through rigorous electromagnetic analysis, IEEE Trans. Microw. Theory Tech., vol. 58, no. 8, Aug 21. [3] S. Müller, F. Happ, X. Duan, R. Rimolo-Donadio, H.-D. Brüns, and C. Schuster, Complete modeling of large via constellations in multilayer printed circuit boards, IEEE Trans. Compon. Packag. Manuf. Technol., to be published. [4] S. Müller, X. Duan, M. Kotzev, Y.-J. Zhang, J. Fan, X. Gu, Y. Kwark, R. Rimolo-Donadio, H.-D. Brüns, and C. Schuster, Accuracy of physics-based via models for simulation of dense via arrays, IEEE Trans. Electromagn. Compat., vol. 54, no. 5, pp , Oct [5] Ansys Corporation. (21). HFSS, Ver. 13, Canonsburg, PA [Online]. Available: [6] L. Tsang, H. Chen, C.-C. Huang, and V. Jandhyala, Modeling of multiple scattering among vias in planar waveguides using Foldy-Lax equations, Microwave and Optical Technology Letters, vol. 31, no. 3, pp , Nov

20 References (2) [7] L. Tsang, and X. Chang, Modeling of vias sharing the same antipad in planar waveguide with boundary integral equation and group T-matrix method, IEEE Trans. Compon. Packag. Manuf. Technol., to be published. [8] A. G. Williamson, Radial-line/coaxial-line junctions: analysis and equivalent circuits, Int. J. Electronics, vol. 58, no. 1, pp , [9] C. A. Balanis, Advanced Engineering Electromagnetics, chapter 9.4. John Wiley & Sons, New York, [1] Ansys Corporation. (211). Q3D, Ver. 11, Canonsburg, PA [Online]. Available: [11] S. Müller, X. Duan, R. Rimolo-Donadio, H.-D. Brüns, and C. Schuster, Non-uniform currents on vias and their effects in a parallel-plate environment, 21 IEEE Electrical Design of Advanced Package & Systems Symposium (EDAPS), Singapore, December 7-9, 21. [12] Y. Zhang, J. Fan, G. Selli, M. Cocchini, and F. de Paulis, Analytical evaluation of via-plate capacitance for multilayer printed circuit boards and packages, IEEE Trans. Microw. Theory Tech., vol. 56, no. 9, Sept