Differential Receivers
Just as SPICE doesn't inherently recognize differential drivers, neither does it recognize differential receivers. Again, you are typically going to have to build the model. It is fairly easy to do because primitives such as the voltage-controlled voltage source already embody most of the characteristics needed in an ideal differential receiver.

All the model needs is appropriate parasitics, termination impedances, capacitance, and so on, and you can use it as your receiver. At this time, non-linearities and dynamic range will not be covered because the target of this book is the interconnect circuitry rather than what goes on inside the silicon.

Figure 7.8. A SPICE Ideal Component to Monitor Differential Voltage

Signal level and phase arriving at the receiver are usually critical parameters in any high-speed link. Viewing the differential signal is easily achieved through use of an ideal voltage-controlled voltage source, as in Figure 7.8 above.

In the case of using such a device to monitor a differential signal, all parasitics are left off so that the source produces infinite impedance at the point of measurement, and the gain is usually set to one. As such, it is possible to make measurements in SPICE that cannot be made in the real world.

Alternately, many versions of SPICE have the capability to do math on signals, so the differential voltage can simply be defined as an equation. Placement of a physical probe on a line always adds parasytics.

At microwave frequencies, the added parasytics, indicated in Figure 7.9 below, are usually far too large to ignore. That makes it difficult to measure waveforms that exist on the line when the test probe is not present.

Figure 7.9. Parasitics Added for a Voltage Probe

Two solutions are possible. One is to get or generate a good model of the test probe, and run a simulation with the probe model in place to correlate what is measured with what is there when the probe is not present. An alternate is to use a receiver designed to measure the signal quality at its inputs. A third alternative that actually works well in the frequency domain is to electrically characterize the parts, packages, and so on and calculate the result.

Differential Transmission Lines
Almost everything can be modeled. Recall the "T" line that came with the original SPICE implementations. This was an ideal transmission line. It had no loss.

When it was used, you did not have to calculate an inductance-capacitance ratio that would yield the desired impedance and velocity; the "T" model made that unnecessary. It simply asked for the desired impedance and delay. That level of support for differential transmission lines does not yet exist in most SPICE tools.

Among the parameters that you might like to see in your modeling tool is the ability to accept a transmission line definition in terms of differential and common-mode impedance, loss per unit of distance, and delay. The fact that such facilities as these are not there does not stop you from performing simulations; it merely adds a bit more work to include them by hand.

Of course, eventually all of this work might be bypassed by the enabling of S-parameter models in SPICE. Again, in an ideal world you would work entirely in the frequency domain. Components would be characterized by their S-parameters, and the response of the entire circuit response would be calculated by applying chaining to the various elements of the interconnect.

In this ideal world, circuit simulation would not even be needed. The response would be mathematically generated from measured or simulated frequency domain models  - S-parameters - and no iterative procedures would be required. Rather than simulation, there would be an extremely fast mathematical procedure.

Unfortunately, that ideal is not the world as it is. The problem is linearity. You cannot presume that the voltage and current sources are linear. They are not. The interconnect circuitry might be reasonably linear, but the silicon at the ends is nonlinear, at least to some degree.

That nonlinearity makes it inadequate to examine the response one frequency at a time. The actual response will have interactions between harmonics, and the response will be dependent on the amplitude and phase relationships between the harmonics. It becomes a modulation problem.

But the interconnect, the packages and circuit board traces, are likely to be linear in voltage response. The sort of thing that would make these parts nonlinear would be the presence of magnetic material. Without magnetic material, the parts are linear.

That linearity makes it practical to solve the response of the interconnect in the frequency domain using very fast analytic procedures and then add the impact of nonlinear drivers in an iterative, time domain, analysis. The capability of using blocks defined with S-parameters in time-domain simulations is just beginning to show up in SPICE tools.

One reason for interest in the frequency domain is this: Time domain simulations often rely on iterative methods and so are relatively slow. Frequency domain solutions can often be achieved through analytic methods and can be extremely fast and not iterative.

You can even see this in SPICE. Compare the time it takes SPICE to calculate the time domain response of a moderately complex L-C circuit with the time it takes to do a frequency sweep of the same circuit.