1. A Fast Evaluation of Power Delivery System Input Impedance of Printed Circuit Boards with Decoupling Capacitors Jin Zhao (jzhao@sigrity.com) Sigrity Inc. Santa Clara, CA 95051 Om P. Mandhana (Om.Mandhana@freescale.com) Freescale Semiconductor, Austin, TX 78729 October 2004 EPEP 2004, Portland Oregon

2. October 2004EPEP 2004, Portland Oregon2 Content Introduction Applied Methodology Application Examples Conclusion

3. October 2004EPEP 2004, Portland Oregon3 Introduction A noise-free, stable power delivery system is required for high speed system Hundreds of decoupling capacitors are placed on PCB to satisfy the requirement Efficiently selecting and placing decoupling capacitors on board is a critical task for power integrity analysis and design

4. October 2004EPEP 2004, Portland Oregon4 Traditional Approach IC CKTs VRM on PCB Printed Circuit Board Package or Substrate On-die Interconnection On-board Decaps On-package Decaps On-die Decaps Whole system has been represented as multi-stage lumped circuits As frequency increases, the wave propagation effects within the board structure must be considered in the analysis and design of a PDS

5. October 2004EPEP 2004, Portland Oregon5 Applied Methodology IC CKTs VRM on PCB Printed Circuit Board Package or Substrate On-die Interconnection On-board Decaps On-package Decaps On-die Decaps Lumped Circuit model Multiple port network Representing Printed Circuit Board Traditional approach New approach

6. October 2004EPEP 2004, Portland Oregon6 Applied Methodology (cont) Multiple port network Representing Printed Circuit Board Commercial Field Solver Real physical board with pre-selected locations of VRM, decoupling capacitors, and interested IC chip locations Multiple ports corresponding to VRM, decoupling capacitors and interested IC chip locations

7. October 2004EPEP 2004, Portland Oregon7 Applied Methodology (cont) Multiple port network Representing Printed Circuit Board Multiple ports corresponding to VRM, decoupling capacitors and interested IC chip locations These multiple ports can be divided into two groups: Ports with no termination (open), and Ports terminated with loads An impedance matrix can be used to represent the network

8. October 2004EPEP 2004, Portland Oregon8 Applied Methodology (cont) For those ports terminated with a loading, one has The resultant input impedance matrix (at the IC locations) can be calculated as Impedance matrix can be expressed as

9. October 2004EPEP 2004, Portland Oregon9 Applied Methodology (cont) Challenges: Involves large matrix inverse with several large matrix multiplications at every frequency point Very time consuming as the number of decoupling capacitors placed on board increases As the impedance of a decoupling capacitor, which depends on the capacitance (C), equivalent series resistance (ESR) and equivalent series inductance (ESL), is included in the matrix operations, ITERATIVELY selecting a decoupling capacitor of appropriate C, ESR and ESL to optimize the power delivery system performance becomes a time consuming process.

10. October 2004EPEP 2004, Portland Oregon10 Admittance Matrix Approach The power ground admittance matrix with some decoupling capacitors mounted on board can be easily calculated by adding the admittance of the decoupling capacitor to the corresponding diagonal entry in the original power ground admittance matrix without any decoupling capacitors mounted on board If no decoupling capacitor mounted at a port, the corresponding entry in the second matrix is 0. Applied Methodology (cont)

11. October 2004EPEP 2004, Portland Oregon11 Application Example A six layer printed circuit board U17 Edge Connector For board power supply There are 0.22uF x 8 decoupling capacitors mounted on the upper side There are 0.01uF x 20 and 0.1uF x 8 decaps mounted on the lower side

12. October 2004EPEP 2004, Portland Oregon12 Application Example (cont) Upper side of the board, U17 is the interested location of power and ground. C21~C28 are eight 0.22 uF decoupling capacitors mounted on board.

13. October 2004EPEP 2004, Portland Oregon13 Application Example (cont) Lower side of the board, C1~C20 are twenty 0.01 uF decoupling capacitors, C29~C36 are eight 1.0 uF decoupling capacitors mounted on board.

14. October 2004EPEP 2004, Portland Oregon14 Application Example (cont) Input impedance with and without decoupling capacitors mounted on board

15. October 2004EPEP 2004, Portland Oregon15 Application Example (cont) Input impedance obtained from commercial software and admittance approach

16. October 2004EPEP 2004, Portland Oregon16 Conclusion A fast power ground input impedance evaluation methodology for the printed circuit board with decoupling capacitor placement study is presented. The admittance approach can accurately estimate the power and ground input impedance up to gigahertz frequency range, which is typically high enough for board level power delivery system analysis and design with targeting of decoupling capacitor placement study.