Think Small

If you read my last missive, you know I have been working recently to understand crosstalk in BGA packages (../news/8_03.htm). This work led me to some new experiments involving a—guess what—gigantic scale model of a BGA package. The model incorporates 100 balls, spaced on a pitch of 2-1/4 inches (scale factor 57:1). Crosstalk measurements taken from this model correspond perfectly to the crosstalk actually accrued in the spaces between the BGA balls underneath a realistic BGA package.

The most excellent part of this model is that you can easily change the assignment of ground balls in the model package. This lets you instantly try out various ground pin assignments, to study the relationship of crosstalk to BGA ground ball assignment.

I published the results of my measurements in the form of tech online webcast, open to all viewers, in 2005, but the link to that techonline presentation has gone dead. Here is a copy of my notes from the presentation: BGA Ground Ball Placement

This month's article, Think Small, addresses in a general way the topic of physically scaling a BGA package.

Think Small

If you want to go fast, think small.

The three-dimensional rule for physical scaling of electrical connections immutably controls the performance of connectors, packages, component bodies, vias, and many other common structures on a printed circuit board. Technically, it applies to any lossless physical structure, meaning any structure that does not lose power due to resistive losses, dielectric losses, or radiation losses in any appreciable way.

For example, a BGA ball, while it may create a signal reflection or create some crosstalk, does not lose any power. The power you put into the structure propagates through the circuit (S21), reflects back to the source (S11), or goes into an adjacent circuit (crosstalk). There may be a miniscule resistive loss, but if the ball is used as a signal via that loss is small enough to simply ignore. Such a structure qualifies as perfectly lossless for the purpose of applying the 3-D rule of scaling.

Quoting from my book, High-Speed Signal Propagation,

"When you change the physical dimensions of a distributed circuit, modifying all geometrical dimensions x, y and z by a common factor k, without changing either the electric permittivity or the magnetic permeability, you find that all inductances change by a factor of k and all capacitances change by the same factor.

"If the circuit is passive and lossless (that is, composed only of inductive and capacitive effects, with no resistances) it will have been scaled in time, whereby the new circuit should behave the same as the old circuit, only its step response stretched (or compressed) in time by the factor k. A network-analyzer plot of the new system will show the same frequency response as the old, only shifted in frequency by a factor of one-over-k. A resonance at frequency f in the original circuit appears at frequency fdivided by k in the new circuit. As a consequence, physically enlarging a system of physical conductors lowers its resonant frequencies, while shrinking the system physically raises them.

"The rule of physical scaling applies well to low-loss conducting structures like metal plates, conducting wires, connector pins, and semiconductor packages. This rule is valid over any range of physical scales for which useful conducting objects may be constructed. It breaks down for certain structures near the atomic level, for which the conducting surfaces cannot be scaled due to the inherent quantization of atomic matter. As far physicists know, this law applies to structures of galactic dimensions, although such structures have not been tested to verify conformance with the rule."

In the simplest terms, large objects have low resonant frequencies, and small objects have higher ones. This simple rule of scaling explains why a flip-chip package is better than a surface mounted package, why a surface-mount package is better than a DIP, and (going even further back in time) a DIP package is better than a miniature 9-pin tube socket. Tiny dimensions push the parasitic resonances up to frequencies above the bandwidth of your signal, resulting in a perfectly flat frequency response across the band that matters. When you want to go fast, small is good.

OK, now let's apply this rule to something like a BGA package. A package with 0.8 mm ball pitch has a smaller form factor than a 1-mm pitch, and so should work better at higher frequencies, right? Well, at this point I must remind you that all three physical dimensions, x, y, and z are involved in the scaling process. Shrinking x and y is good, but not if it comes at the expense of increasing the overall height z. Yet, that is what often happens with reduced form-factor BGA arrays. If you can, for example, accomplish double-track routing with the larger form-factor ball layout but only single-track routing with the smaller form factor, it may actually take more layers to completely route your design, thus adding to z. Since most crosstalk and reflection problems scale in proportion to z (total sum of BGA height plus board thickness), things that make the board thicker are generally bad ideas.

Best Regards,
Dr. Howard Johnson