Packages
At microwave frequencies, packages cannot be ignored. Nor is it likely to be adequate to model a package pin as a simple inductor or even a capacitor and inductor. The length and crosstalk of the trace in the package coupled, with the tolerance of the termination presumably on the chip, will result in a frequency-dependent impedance at the pins of the connector.

An optimized board interconnect has to, absolutely must, include these factors. It would not be as bad if the termination could be relied on as being purely resistive, but the pin capacitance at the silicon will typically, at the very least, be significant, and sometimes even the dominant impedance at the high-frequency end of the spectrum. Also, crosstalk in the package will sometimes be a significant factor.

Even though signal characteristics may well be specified at the pin at the point where the package meets the board, it is not adequate to specify impedance as a single number at that point. Optimized board design will require that the impedance either be explicitly defined as a function of frequency, or be implied by specifying a transmission line model for the package.

Significant problems can occur when generating a model of a package. You might rely solely on simulations, but the real physical entity might not really hit the mark chosen for the simulation. Simulations are great tools, but measured values make a better basis for a working model.

Note that there is not exactly universal agreement on that last statement, but authors get to state their opinion. The design of the package will have made good use of simulations, but the final characterization of the physical part should be based on measurement.

Two measurements are available: time domain (TDR) and frequency domain (NA). In either case, SPICE models will usually be the translation of these into some form of transmission line model. This can be done by something such as the application of the peeling algorithm. If you are using such a model, you have the easy job. If you are the one who must generate this model, you probably already know that you have the hard job.

The special mechanical requirements of packages make the use of field solvers unavoidable in many cases. Often the physical size requirements force the use of very thin conductors and result in the accompanying high loss. Mechanical requirements placed on the reference planes often result in geometries that cannot be accommodated by the 2D field solvers found in many signal integrity tools.

Recall that as shown earlier in this series, a lumped element transmission line model, and a single section was deemed adequate because the section was physically short. In the case of packages, the transmission lines are often not short enough to model with a single section.

If you try to model a transmission line that is too long as a single lumped section, you'll get substantial errors at high frequencies. This can easily be seen by SPICE frequency sweeping the model with a single and with multiple sections.

To model a line with n sections, simply calculate the inductance and capacitance values for a single section, then divide those values by n; repeat the section n times. Recall that knowledge of the dielectric constant and impedance of a line is adequate to calculate the inductance and capacitance per unit length. Scale those values to the actual length of the segment that is to be modeled.

I modeled an inch-long segment of transmission line with one, two, and three segments. The frequency response, shown in Figure 7.19 below , of each look good up to about a gigahertz. By the time you get to two gigahertz, the one-segment model begins looking inadequate.

By the time you get to five, only the three-segment case looks usable. This illustrates the impact of using too few segments to model a section of transmission line for a particular range of frequency.

Figure 7.19. Three L-C models

Reference was previously made to a rule sometimes called the tenth-wavelength rule. It says something like, "Always keep segment size in your models at most a tenth wavelength of the highest frequency you are concerned about." Examination of Figure 7.19 can show just how much error would result from relaxing this rule in this case.

Let me climb onto my soap box: It is no worse to violate a rule of thumb than it is to use it without understanding what it does for you. Rules of thumb save us a lot of time. If used intelligently, they can even promote good engineering.