Digital Signal Processing Reference
In-Depth Information
Here we note that a loss of 1.3 dB means that the output is only about 86% of the
input value. This means that about 14% of the signal has been attenuated. About
41% of the signal is lost at 4.7 dB.
Chapter 1 showed that the 3-dB bandwidth is a convenient way to estimate
the highest frequency of interest in a pulse stream. From Table 3.2 we see that fre-
quencies of 2 GHz and higher attenuate the signal by more than 3 dB. Therefore,
the bandwidth for this trace is just under 2 GHz, and signals (including the signal
harmonics) with frequencies higher than this will be severely attenuated.
3.4.3 What Is Refl ection Loss?
The reflection loss (
S
22
and
S
11
) indirectly shows by how much the transmission line
impedance differs from the reference impedance. Chapter 11 shows that a perfect
match results in no reflections, which would make the reflection loss zero. Since on
a decibel scale a large negative number represents a small quantity, a large negative
reflection loss value in decibels shows that the reference impedance and transmis-
sion line impedances are very similar. For instance, a reflection loss of
26 dB rep-
resents a 5% impedance mismatch, which is acceptable in most low and moderate
speed applications. From Table 3.2 we see that at 2 GHz (the 3-dB bandwidth of
this trace) the reflection loss is much smaller than this (
−
−
46 dB). That represents
about a 0.5% mismatch in the impedance.
3.4.4 What Are Touchstone Files?
Those versions of SPICE capable of running S-parameter models nearly universally
use the Touchstone File format [19] to present the S-parameter data, although other
formats also may be supported. Touchstone format model files can come from test
equipment (measurements) or field solvers (simulations).
Often the data is presented in Touchstone files using a magnitude-angle format
with the magnitude in decibels (dB) and the phase angle measured in degrees, but
the specification also defines other formats.
Usually S-parameters are specified at 50
Ω
, but any reference impedance may be
used and its value recorded in the file.
3.5 Field Solvers
Electromagnetic field solvers analyze a physical structure such as a circuit board
trace or the complex geometry of a connector and produce an electrical circuit
model for use in signal integrity simulations.
The most common (and often the easiest to use) field solvers are those that
analyze two-dimensional structures (2D solvers). Three-dimensional structures are
analyzed with 3D simulators.
3.5.1 What Are 2D Field Solvers?
The underlying assumption behind 2D solvers is that the structures shape is uniform
and so can be properly described with only two dimensions. A group of straight
