TOPICS IN HIGH-SPEED CHANNEL MODELING - Advanced Signal Integrity for High-Speed Digital Design - page 414

10.1 CREATING A PHYSICAL TRANSMISSION-LINE MODEL
Digital design is typically performed using circuit simulators. Fortunately, most
commercially available tools have transmission-line models that can be inte-
grated with the digital circuitry to perform system-level bus simulations. Problems
arise, however, when the assumptions built into the models break down or
are simply not known by the engineer. For example, many simulators employ
transmission-line models with frequency-invariant dielectric permittivity and loss
tangents. Although these models are perfectly adequate for very short bus lengths
or data rates below about 1 Gbit/s the incorrect relationship between ε r and
tan δ induces causality errors (such as the model in Example 8-4) that can
render the simulations almost useless. Additionally, few commercial simulators
account properly for such things as surface roughness or internal inductance.
Consequently, it is usually desirable for the digital designer to create custom
transmission-line models that use the methodologies presented in Chapters 3
through 6 to ensure accurate results.
10.1.1 Tabular Approach
A convenient method of implementing user-defined transmission-line models
is to use a tabular approach, which is simply a lookup table that defines the
transmission-line equivalent-circuit parameters at each frequency. Fortunately,
user-definable tabular models are available in many commercial simulators. A
tabular methodology allows calculation of the system transfer function in the
frequency domain. An inverse Fourier transform can then be used to get a
time-domain impulse response, which can be convolved with an arbitrary input
waveform to evaluate signal integrity.
A practical and efficient approach to incorporate surface roughness, internal
inductance, and wideband frequency-dependent dielectric properties into printed
circuit board (PCB) transmission-line models is defined here as a two-step proce-
dure. In the first step, quasistatic RLGC matrices in the transmission line model
are generated at a single reference frequency ( ω ref ), using a 2D transmission-line
calculator or analytically with the methods outlined in Chapters 3 through 6. In
this step it is important that the value of ε r and tan δ be known at the reference
frequency. This model will reflect the single-valued frequency response of the
transmission-line geometry and configuration but will not yet account for the
frequency dependence of surface roughness losses, internal inductance, and
dielectric properties. The matrices calculated during this step will be known
as the reference values R ( ω ref ), L ( ω ref ), C ( ω ref ), and G ( ω ref ). In the second
step, the reference values are modified to account for frequency-dependent
material properties, internal inductance, and surface roughness [Liang et al.,
2006].