Calculated and measured impedance in woven glass reinforced laminates
Application Note AP139
Variations between calculated and measured impedance in woven glass reinforced laminates

Background

In this note we discuss how measured impedance may vary from field solver calculations when using woven glass reinforced laminates. Field solvers are in widespread use for calculation and analyzing controlled impedance structures. However when designing differential structures, especially those using fine geometries, it is necessary to have a good understanding of the base laminate and pre-preg structure in order to achieve good yields.

Design Considerations

FR4 (and other woven glass laminates) are composed of a curing resin system and a woven glass reinforcement. The picture below illustrates a micro-section of an FR4 pcb showing clearly the planes, single ended and differential signal traces and the bundles of glass fibers in a woven structure. The remaining space is filled with resin.

Micro section of single ended and differential traces in FR4
(Note that glass position will also vary from board to board and lot to lot)

The structure above, therefore, is a mix of two differing dielectrics. Glass has a dielectric constant of approximately 6, and the resin in FR4 has a dielectric constant of approximately 3.

Why do results differ from theory?

First consider the dielectric constant Er. Typically a value of around 4.2 is used for FR4; however, this is the nominal dielectric for bulk material. With glass having an Er of 6 and resin and Er of 3 (lower in some high performance materials) it is unlikely that the electric field will experience the nominal dielectric constant of bulk material.

Look at the differential pairs on the picture; when they are close to each other and relatively distant from the adjacent ground planes, the field is strong between the two traces. When differential traces are close to each other you need to take into account that the electric field "sees" a resin rich area and use a lower Er to compensate for this. The field surrounding the pairs in the picture above will experience an Er closer to that of resin than that of glass/resin mix.

If you are a fabricator, then you can achieve better yields on differential by taking into account that the effective Er will not only depend on material but also on structure and geometry. Looking at a micro-section can help you see why your results on differential traces may be higher than your design.

What if my differential impedance requirements are very tight?

Using a laminate where the reinforcement's Er is similar to that of the resin is one way of achieving this; some suppliers have introduced high performance laminates whose reinforcement has an Er similar to the resin filler (e.g. low Er glass fabric) which reduces the fibre weave effect and helps overcome the problem. You should discuss this with your supplier as you will need to balance the increase in yield against the increase in material costs.

Ensure your measurements are valid

Whatever TDR you use to measure impedance, you should ensure that it is calibrated to a traceable impedance standard. TDR measurements need to be made with the same DC conditions at the end of the trace as those on the TDR head during verification. As most coupons are unterminated it is good practice to use reference air lines or precision semi rigid coax which is measured against a traceable standard. Calibrating a TDR with a precision load resistance can introduce measurement errors of up to 3 or 4 ohms at 50 Ohms.

Possible variations

Look at the graph below. This shows you the range of impedance for a differential pair taking into account different Er; these are the types of errors you may introduce when not taking the above effects into consideration.

Note that because of these effects, which are real and a result of the physical properties of the materials you are working with, when designing or tailoring your process you may need to use one value of Er for single ended traces, and another for differential configurations. You may even need a third value for coplanar structures. This may be determined experimentally by building some sample coupons and running through your process. An economic way of doing this may be to add additional coupons to boards you are already running through production.

How can I make a closer prediction?

Manufacturers should rely on experience as well as material specifications when choosing the Er value with which to calculate. Allow for the absence of glass between differential tracks by using a lower Er than the dielectric material manufacturer quotes for the bulk of the laminate material. Experience shows that for today's typical differential track dimensions of 5 mils with 5 - 7 mil spacing between tracks and >8 mils laminate thickness, an Er in the range of 3.6 - 3.9 for FR4 (10 ~ 15% reduction in Er) will achieve predictions close to actual. (See the highlighted area in graph below.)

Modern laminates incorporate glass cloth woven so as minimise the variation across the weave; for example, some manufacturers have moved from twisted fibre bundles to untwisted yarn, which tends to lie flat and spread out more easily; the result is a more even distribution of the glass fibres, lower stresses with the laminate material and a significantly reduced percentage of the laminate where glass is absent. The uniformity of the glass weave combined with the appropriate resin technologies results in a more homogeneous reinforcement layer and hence a more uniform Er.

PCB fabricators and PCB designers should discuss the benefits of increased yield compared with increased material costs.

Modifying designs

It is important to maintain a good dialog between the original designer of impedance controlled boards and the fabricator.  To assist in this process the Polar Si8000m Field Solving Impedance Design System can goal seek new values and graph sensitivity to changes in build parameters.