In Part 1 and Part 2 I covered a list of items that are not particularly well handled by typical implementations of SPICE. Now, you'll get the other side. Don't get the idea that nothing works in circuit solvers at microwave frequencies. A lot does work.

As pointed out earlier, there are things that cannot be handled without the aid of field solvers, but the idea is to characterize features with the aid of the field solver, translate that characterization into lumped models that SPICE can deal with, and then do the signal integrity work with the SPICE tool.

Any time such a translation is made, there is a frequency range wherein those models are valid. Any time such a model is generated, it should also have the frequency range of applicability specified.

Again, I want to emphasize that there are numerous tools - circuit solvers - which, at heart, are versions of SPICE. The one critical property that such a tool absolutely needs if it is to be useful at microwave frequencies, is the ability to work accurately with transmission lines that have frequency-dependent loss.

Without this capability, it is very difficult to get useful information out of a simulation. That is not to say that without such capability you are not going to be able to work with microwave frequencies; rather, without that capability, reconcile yourself to working with some tool other than SPICE.

Frequency Dependent Loss
Frequency-dependent loss (FDL) is due primarily to two factors: copper loss and dielectric loss. The word "primarily" is used intentionally. Other sources, such as EMI, are important, even very important, from some perspectives. But, for the signal integrity modeling of transmission lines, these two are what will be covered by the description of frequency-dependent loss.

Numerous of the factors impacting the signal available at the receiver are functions of frequency. Examples are radiation reflections and crosstalk, all of which SPICE can be really good at. But these are not included in the meaning assigned here. Here, the words "frequency-dependent loss" mean resistive losses in the copper and dielectric losses.

In fact, signal available at the receiver is often described in terms of eye opening, a concept that will be described later. In that sense, even crosstalk can be a major contributor to signal loss. But all that is yet to come. If you needed something to look forward to, there it is. For now, you need details about copper and dielectric losses.

Copper Loss
Copper has resistive loss as does any conductor. At high frequencies, the internal inductance of conductors pushes the current to the outer surfaces; this effect, shown in Figure 7.15 below, is called skin effect.

Figure 7.15. Skin Effect

This phenomenon decreases the effective area available for current flow and so increases the effective resistance. It is as if there is only a thin layer on the surface of the conductor that is involved in high-frequency current flow, and the thickness of this layer is called the skin depth. As with many physical constants, mathematical operators, and similar scientific things, skin depth is designated by the Greek delta symbol as shown below.

In this equation, pi has its usual meaning, 3.14 and so on, f is the frequency in Hertz, mu is the magnetic constant—usually that of free space, except when not—and sigma is the conductivity of the metal. In this list, the one that is often overlooked is mu.

In copper, gold, silver, and such metals, the relative magnetic constant is unity so that of free space is correct. In metals such as nickel and iron, the relative magnetic constant can be very high. If you want to generate a low-loss conductor for microwave frequencies, magnetic materials are a poor choice. On the other hand, if you really want to have a lot of loss, such as in a chassis, iron might be a really good choice.

The loss due to skin-effect is high at microwave frequencies. Increasing the value of sigma can reduce it. If gold is substituted for copper, this loss will decrease by a couple percent. On the other hand, the loss is inversely proportional to the circumference of the conductor, so increasing the conductor size by a few percent can do the same. Decide for yourself which to do - which makes better economic sense for your design.

The current density decreases exponentially with depth in the conductor. The meaning of skin depth is that it is the equivalent depth if the current were evenly distributed in that skin layer. It is used to calculate the effective resistance of the conductor for a particular frequency.

As an aside, consider what might happen if the skin depth is larger than the thickness of the conductor. Consider this in the context of a reference plane. Fields will be attenuated, but not blocked, by the conductor.

Can this be a problem? Consider one more situation. Your board has a switching regulator mounted on it. That regulator is running at 70 or 80 kilohertz and switching tens of amps. It is a very bad idea, a very bad idea, to run a signal trace under the switching transistor, even though there may be a reference plane between.

Conductor thickness
In printed circuit boards, conductor thickness is usually a constant, so loss in a trace is strongly dependent on trace width. If the impedance is to be maintained, increasing trace width requires greater dielectric thickness. That dependency often means that the total thickness of the board stackup is strongly related to the trace loss, and so can strongly influence the maximum frequency that can be transported a specified distance on a circuit board.

Although dielectric loss increases at a faster rate than does copper loss and at high enough frequencies becomes the dominant material loss, copper loss never becomes negligible. Dielectric loss is sometimes regarded as the only loss that counts. This is a mistake.

In real circuitry, total loss is made up of numerous contributors and, while dielectric loss can become a major contributor at frequencies of one or more gigahertz, it is never the sole contributor. In fact, when package losses, impedance mismatches, connector losses, passives, and copper loss are all accounted for, dielectric loss seldom even contributes the majority of the loss.

Copper loss comes not only from the bulk resistivity of the copper, it also comes from surface roughness and from other materials used at the surface of the copper. Sometimes the copper has a solder plating on it—note that solder has a resistivity about five times higher than copper. Tin plating is often used. Tin has much higher resistivity than copper.

When a fiberglass core is made, often the copper is roughened and coated with copper oxide to increase adhesion. That is unfortunate, but needed. It is always advisable to remove any metal coatings, except perhaps gold, that are not absolutely required for reliable manufacturing of the board. In short, make it as good as you can, but not better.