Sensitivity to Physical Parameters
Sensitivity to Physical Parameters
Most even slightly experienced engineers know that the Er of FR-4 is wildly variable not only between vendors but with frequency. This is true, but how does this variability stack up against the other obvious variable – like board thickness? Figure 3 compares all these variations.
Figure 3: The sensitivity to Er and board thickness are compared on FR-4 over a range of values. First the sensitivity to trace impedance with varying Er was tabulated over the commonly thought of values for Er (4.3 to 4.9). Then the sensitivity to trace impedance with varying the board thickness was calculated. The line length to get a 45 degree phase shift at 6 GHz was likewise recorded for each parameter.
As can be seen, the result is that while Er does indeed affect trace impedance, its sensitivity is proportional to the square root of Er. So for a huge Er change of 4.3 to 4.9, the total trace impedance changes only 2.7 ohms peak to peak. It should be noted that on my 2-inch test board that I have been building for years, I have not seen this level of variation which suggests that the lot-to-lot variation of a single FR-4 supplier is quite good and way better than the worst-case numbers commonly quoted.
What is more interesting however is the impedance variation due to board thickness. Figure 3 also shows this for a 5% thickness variation in a nominally 59-mil thick PCB. The trace impedance changes 3.5 ohms peak to peak.
So the board thickness variation causes the calculated trace impedance to vary more than the wildly variable Er values that are commonly quoted.
Another interesting fact about Figure 3: I tabulated what length an electrical 45 degree line would need to be for each case at 6 GHz. The electrical length changes with changing Er, but not with changing board thickness. If your circuit design incorporates distributed elements made from transmission lines to build circuits like filters or matching networks, then you are calculating line lengths to make certain electrical lengths to synthesize the equivalent capacitive or inductive elements. These lumped elements will change value with changing Er, but not so much with PCB thickness changes.
The Er of FR-4 also varies with frequency as shown in figure 4.
Figure 4: It is well known that the Er of plain old FR-4 varies with frequency. This composite data from various sources suggests that the variation is from about 4.7 at low frequencies to less than 4.4 at high frequencies.
Now that we have analyzed some of the performance parameters and trade-offs of plain old FR-4 we have found that the loss isn't all that bad under 6 GHz, and the many times unspecified and wildly varying Er is sometimes troublesome - especially if you are trying to use distributed circuit elements in your designs - but otherwise FR-4 can work in even high-performance RF circuits.
Incrementally Improving on Plain Old FR-4
The first thing that can be done to improve on the generic FR-4 is to use a FR-4-like material that has a specified and controlled Er range. This material won't be called FR-4 but will be made out of the same type of "Glass Epoxy" technology. PCB shops typically like these materials because they process with the same FR-4 manufacturing flow. There are many manufacturers that supply materials like this  and you should also make sure that the completed board uses material that can survive the high-temperature lead-free assembly processing temperatures, if you have this requirement also.
The Er of these materials is usually also much more stable with frequency than FR-4, so if the Er was plotted as shown in figure 4, the Er line would be very much flatter. Most of these materials have an Er of around 4.4 to 3.9 or so.
Your PCB shop can then probably design the required single or multilayer stack-up and supply the effective or Design Value for Er that should be used in your design, or they can generate this data for you if you tell the target trace width and reference plane spacing, etc.
Some of these improved Glass Epoxy board materials also have better losses than the generic FR-4 so that can be a plus also.
The thermal conductivity of these improved FR-4 materials is usually about the same as plain old FR-4. The thermal conductivity of your finished PCB will be more influenced if you use multiple layers and flood copper ground planes on all layers.
The big advantage of these improved RF-specified Glass Epoxy materials is that they are only incrementally more expensive than plain old FR-4 and many of them are rated for lead-free soldering temperatures, something that plain old FR-4 usually can't do.