Dielectric Loss
In dielectrics, the relative dielectric constant is thought to be due
to such things as the physical distortion of molecules, the
reorientation of molecules, the changing of the shape of electron
orbits, etc., as shown in Figure 7.16
below. Each case has a stimulus and a response.
 |
| Figure
7.16. Molecules in an Electric Field |
In such systems, the response always lags the stimulus by some
amount. The lag in response shows up in vector representations of the
dielectric constant as an imaginary part. When calculating the response
of the system to fields through this dielectric, the imaginary part of
the dielectric constant shows up as a loss.
It is typical that the delay in field response is somewhat constant.
That is, the dielectric response to the imposed field lags by a small,
fixed amount of time. In this case, the relationship between the real
and imaginary parts of the dielectric response vector is linearly
dependent on frequency of the imposed field. Thus, dielectric loss is
approximately linearly dependent on frequency.
The dielectric loss is often specified by the angle of the
dielectric vector, illustrated in Figure
7.17 below. The tangent of this angle—that is, the tangent equal
to the imaginary part divided by the real part of the dielectric
constant—is often published as the loss factor for the dielectric.
 |
| Figure
7.17. The Dielectric Constant |
In another feat of scientific innovation, the ratio itself is
designated by the Greek lower-case delta symbol. This is done,
presumably, to maximize the probability of confusing the dielectric
loss with the skin depth.
Of course, there is no relationship between the two, but why miss
such a golden opportunity to generate confusion? The dielectric loss
factor is thus designated tan-delta, which delta is symbolically
identical to the skin depth, but is physically unrelated in any way as
shown below:
At low frequencies and in practical materials, copper loss dominates
and dielectric loss is safely ignored. Depending on geometry, at
moderate frequencies of about one gigahertz in FR4, dielectric loss
catches up and becomes about equal to copper loss. At higher
frequencies, dielectric loss dominates.
The dominance of dielectric loss does not mean that copper loss has
gone away. It is still there. It still is increasing as frequency
increases. You will occasionally encounter the idea that changing the
board material to one of the low-loss materials will reduce signal loss
by an amount equal to the improvement in dielectric loss. This of
course is far from true. To see for yourself, simulate your total link,
silicon to silicon, and vary only the dielectric loss parameter.
When you are looking for a SPICE simulator capable of dealing with
frequency-dependent loss, one choice is the W element available in
HSPICE. This is not intended to be an endorsement of HSPICE, but rather
a simple statement that it is an option, and it appears to work.
Other options also appear to work; not all include the word "SPICE"
in their names. The advantage of tools that include that word in their
names is that they tend to be fairly standard in the code format that
they accept. Other tools have other advantages and, as usual, you need
to choose the tool that fits the job.
Drivers and Receivers
From the perspectives of circuit simulators, all drivers are
essentially the same. Circuitry will vary, but it makes little
difference to the circuit simulator whether that circuit is outputting
microwave signals or lower frequencies.
My own bias is to simplify drivers and receivers through use of
ideal sources surrounded by appropriate parasitics whenever possible.
The advantage of this method is that it typically runs a couple orders
of magnitude faster in SPICE than do transistor-level models. Of
course, some refuse to believe that this method could ever generate
acceptable accuracy.
To them I point out that even the transistors in the
transistor-level models are themselves parametric models. Useful models
are sometimes as simple as the one depicted here in Figure 7.18 below, but often need to
be substantially more complex.
 |
| Figure
7.18. My Favorite Driver Model |
Certainly there are cases where there is no choice available other
than running the transistor-level circuitry. But avoid doing so when
possible. Whether at microwave frequencies or not, these complicated
circuits cause numerous problems in trying to get a simulation running.
Such models are often automatically generated from the layouts of the
driver or receiver circuit.
When so generated, they often are found to include component
arrangements that are physically possible but cannot be handled by
SPICE. Most common is the situation where a node joins three
capacitors, and nothing else. The DC solution at this node is
indeterminate, so SPICE will fail.
It is my recommendation that a vendor should never release a SPICE
model that has not been verified functional in a real simulation, and a
customer should never accept such a model. Getting back to the real
world, if you are stuck with such a model, the only choice may be to go
through it line-by-line and modify it so it will work. Take that
three-capacitor node and add a ten-meg resistor to ground.