Reducing Warpage of Printed Circuit Boards by Using Wavy Traces

[+] Author and Article Information
Parsaoran Hutapea, Joachim L. Grenestedt

Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015

J. Electron. Packag 126(3), 282-287 (Oct 06, 2004) (6 pages) doi:10.1115/1.1756591 History: Received February 01, 2003; Revised February 01, 2004; Online October 06, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Ritchey,  L. W., 2000, “PCB Routers and Routing Methods,” Printed Circuit Design, 17(2), pp. 26–29.
Gilleo,  K., Witt,  M., Blumel,  D., and Ongley,  P., 1999, “Towards a Better Understanding of Underfill Encapsulation for Flip Chip Technology: Proposed Developments for the Future,” Microelectronics International, 16(2), pp. 39–43.
Zhang,  S., De Baets,  J., and Van Calster,  A., 1999, “A Two-Layer High Density Printed Circuit Board and Its Reliability,” Microelectron. Reliab., 39, pp. 1337–1341.
Chou,  T.-W., and Takahashi,  K., 1987, “Nonlinear Elastic Behavior of Flexible Fiber Composites,” Composites, 18, pp. 24–34.
Kuo,  C.-M., Takahashi,  K., and Chou,  T.-W., 1988, “Effect of Fiber Waviness on the Nonlinear Elastic Behavior of Flexible Composites,” J. Compos. Mater., 22, pp. 1004–1025.
Highsmith, A. L., Davis, J. J., and Helms, K. L. E., 1992, “The Influence of Fiber Waviness on the Compressive Behavior of Unidirectional Continuous Fiber Composites,” Composites Materials: Testing and Design (Tenth Volume), ASTM STP 1120, Glen C. Grimes, ed., Philadelphia, PA, pp. 20–36.
Hsiao,  H. M., and Daniel,  I. M., 1996, “Elastic Properties of Composites with Fiber Waviness,” Composites, 27, pp. 931–941.
Grenestedt,  J. L., and Hutapea,  P., 2003, “Influence of Electric Artwork on Thermomechanical Properties and Warpage of Printed Circuit Boards,” J. Appl. Phys., 94(1), pp. 686–696.
Hutapea, P., and Grenestedt, J. L., 2004, “Tuning of Electric Artworks of Printed Circuit Boards to Reduce Warpage,” IEEE 9th International Symposium on Advanced Packaging Materials: Processes, Properties and Interfaces, Atlanta, Georgia.
Designing Balanced Printed Circuit Boards, 1997, Merix Corporation, Forest Grove, Oregon.
Krueger, S., Barry, D., and Payne, D., 2001, Breaking the CAM Bottleneck, Atomic29, Los Altos, California.
Zweben, C., 2002, “Advances in Materials for Optoelectronic, Microelectronic and MOEMS/MEMS Packaging,” Proceedings of Eighteen Annual IEEE Semiconductor Thermal Measurement and Management Symposium, San Jose, California, pp. 30–34.
Culbertson, E. C., 1995, “New Laminate Material for High Performance PCBs: Liquid Crystal Polymer Copper Clad Films,” Proceedings of the 1995 45th Electronic Components & Technology Conference, Las Vegas, Nevada, pp. 520–523.
Grenestedt,  J. L., and Hutapea,  P., 2002, “Using Waviness to Reduce Thermal Warpage of Printed Circuit Boards,” Appl. Phys. Lett., 81(21), pp. 4079–4081.
Hutapea,  P., and Grenestedt,  J. L., 2003, “Effect of Temperature on Elastic Properties of Woven Glass Epoxy Composites for Printed Circuit Board Applications,” J. Electron. Mater., 32(4), pp. 221–227.
Taylor, R. E., 1998, Thermal Expansion of Solids, CINDAS Data Series on Material Properties Vol. I-4, Ho, C. Y., ed., ASM International.
Vishay Measurements Group, 1993, Measurement of Thermal Expansion Coefficient Using Strain Gages, www.measurementsgroup.com, TN-513-1.
Sottos,  N. R., Ockers,  J. M., and Swindeman,  M., 1999, “Thermoelastic Properties of Plain Weave Composites for Multilayer Circuit Board Applications,” ASME J. Electron. Packag., 121, pp. 37–43.


Grahic Jump Location
Pins 1 and 2 should be connected, as should Pins 3 and 4. In the X-Y routing figure, solid lines are traces within one layer, dashed within another layer
Grahic Jump Location
Models 1a and 1b have bare traces as the top and bottom layers. Models 2a and 2b have copper traces/FR4 layers as the top and bottom layers. Black is copper and white is FR4
Grahic Jump Location
Thermal warpage of the PCB with in-plane wavy traces. The triangles are FE results, and the fine line is a quadratic curve fit
Grahic Jump Location
A volume sketch of periodic boundary conditions. The vertical boundary surfaces are denoted by letters A, B, C and D
Grahic Jump Location
Photo of the manufactured straight and wavy PCB’s
Grahic Jump Location
Warpage versus temperature obtained from the FE analyses and experiments
Grahic Jump Location
Warpage versus temperature obtained from the FE analyses and experiments
Grahic Jump Location
An artwork of a layer of a real production PCB using wavy electric traces




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In