Progress In Electromagnetics Research
,
PIER 20, 179–211, 1998
SYSTEM MOEDELING OF HIGH-SPEED DIGITAL
PRINTED CIRCUIT BOARD USING SPICE
F. W. L. Kung and H. T. Chuah
Faculty of Engineering
Universiti Telekom
Jalan Ayer Keroh Lama
75450 Melaka, Malaysia
1.
2.
Introduction
Modeling Procedures in the Proposed Structural
Approach
3. Derivation of Equivalent Circuit Model Using
Electromagnetic Field Solution
3.1 Modeling Sockets and Connectors
3.2 Modeling Transmission Line
3.2 Transmission Line Discontinuities
4. Derivation of Equivalent Circuit Model Through
Measurement
4.1 TDR Measurement Method
4.2 Impedance Profile Method
4.3 Frequency Domain Measurement Method
4.4 Modeling I.C. Buffer
5. Modeling Power Planes
6. Simulation Examples
7. Conclusions
Acknowledgment
References
1. INTRODUCTION
Implementation of digital systems is usually carried out in the form of
printed circuit board (PCB) populated with active components such
180
Kung and Chuah
as integrated circuits and passive components such as surface mount
resistors, capacitors, sockets, connectors, cables, etc. These compo-
nents together with the PCB traces and metal planes form the net-
work which manifests as a digital PCB assembly. With the increase
in operating frequency of devices in access of 100MHz and switching
speed of digital devices within sub-nanoseconds, electromagnetic inter-
ference, stray parameters of components and unintentional radiation
have become a major concern, affecting the integrity of a system. To
cope with the issues of system performance, analog and digital cir-
cuit simulation tools are used to verify system performance in terms of
signal integrity, noise margin and bandwidth under various signal pat-
terns (vectors) and biasing during CAD layout process to ensure first-
time-working prototypes. This article illustrates a structural modeling
approach in which the digital PCB is considered as an assembly of
parts which are modeled as electrical networks with input and output
ports. The networks are linked together to form a complete system of
equivalent circuit in SPICE format. Various methods have been de-
veloped by many authors [1–19] for modeling a certain aspect of the
digital PCB system. Based on their work, the authors consolidate the
methods and propose a structural approach to derive a system level
equivalent circuit model for a digital PCB system. Section 2 outlines
the modeling procedures using the structural approach. Section 3 gives
the EM Field Method for deriving equivalent circuit models of sockets,
connectors, interconnecting traces and discontinuities in PCB. Section
4 contains circuit models of discontinuities and IC buffers using mea-
surement techniques. In Section 5, the power planes are modeled using
a planar circuit approach [20]. A simple digital PCB system modeling
example is presented in Section 6 to illustrate the proposed approach.
Detailed system simulation is carried out using SPICE Version 6.1 on
an IBM compatible PC. Both time and frequency domain simulations
are performed. Areas of large current concentration in the power plane
at any instance can be located. This allows one to determine the op-
timum location to install decoupling capacitors and filters to suppress
EMI. An IC in the system is then replaced with a power validator. The
power validator is a programmable load having the same footprint as
the IC. It simulates the IC, drawing varying amount of current from
the power distribution systems. An equivalent circuit is derived and
SPICE simulation is performed to study the noise introduced by the
die within the IC.
System modeling of high-speed circuit board
181
2. MODELING PROCEDURES IN THE PROPOSED
STRUCTURAL APPROACH
A direct approach to derive an equivalent circuit network for the PCB
assembly is through application of numerical methods which include
differential method such as Finite Element Method (FEM) [2] and in-
tegral method such as Method of Moments (MoM) [3]. The conducting
traces on the PCB and its surrounding are discretized into triangular
elements and the integro-differential equations are transformed into a
system of linear equations. An admittance matrix
Y
(ω) linking the
equivalent voltage and current on the conducting elements is defined.
Under quasi-static approximation equivalent circuit using passive ele-
ments such as R, L, C, and G can be assigned to the elements
y
ij
(ω)
of the admittance matrix and an approximate circuit representing the
system is constructed [4,5].
However the application of numerical method becomes extremely
computer intensive when applied to practical PCB with hundreds of
conducting elements scattered in different layers. An alternative ap-
proach, termed a structural approach by the authors, is to consider the
PCB assembly to be divided into many distinct regions. Each region
encloses certain elements of the system, for instance a group of traces,
a via, a pad etc. The structural approach considers a digital PCB
assembly to be integration of the following components:
(a) Transmission line interconnections such as PCB traces.
(b) Integrated circuit sockets, edge connectors, PCB headers, coaxial
to PCB adapter etc.
(c) Discontinuities in interconnection such as vias, bends, crossing,
T-junction etc as shown in Figure 1.
(d) Power distribution system consisting of power and ground planes.
(e) Discrete components such as surface-mount resistors, capacitors,
integrated circuit sockets and packaging which are approximated
as lumped circuits. The integrated circuit packaging refers to the
physical elements which include the pins, enclosing, interconnec-
tion within the enclosing, but excluding the semiconductor die.
(f) The architecture and logical entity (which is often expressed using
VHDL or Boolean Algebra) of the digital integrated circuit which
is linked to the external environment via input/output buffers,
power pins and packaging.
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Kung and Chuah
Figure 1.
Common discontinuity structures in a PCB assembly
system.
Each of the above components is taken to be a small module with
input and ouput ports. Characteristics of the input and output re-
lationship for a small module are defined through careful theoretical
analysis, numerical method and measurement. Equivalent circuit mod-
els are derived for these modules in terms of linear time invariant circuit
elements using resistor, inductor, capacitor, transmission line and de-
pendent voltage and current. In some instances, such as in modeling
of integrated circuit input-output buffers, no-linear time invariant de-
pendent current and voltage sources may be required. These circuit
elements are compatible with industry standard circuit simulator such
as SPICE [6,7]. All necessary parameters are removed to simplify the
model as much as possible, yet retaining the essence of the model.
These modules are linked to form a large and complex electrical net-
work which is then subjected to computer circuit analysis to determine
System modeling of high-speed circuit board
183
the time and frequency domain response of the system under specific
bias and excitation. In many ways this approach is a simplification
as compared to the direct method. However, it can only be applied
for a loosely coupled system where quasi-static electromagnetic anal-
ysis is valid, and when radiation from the PCB conductors is small.
By a loosely coupled system we mean a system of conductors which
is sufficiently far apart such that the characteristic inductance, capac-
itance, resistance and conductance matrices representing the system
can be approximated by sparse matrices. Upper frequency limit for
quasi-TEM solution is dependent on dielectric thickness of the PCB.
For instance dielectric thickness of 1.0mm between conducting layers
has upper frequency limit of 2–4GHz [21]. From the circuit theory
point of view, a distributed component can be considered as a lumped
circuit if:
1
≤
1
λ
10
(1)
(2)
1
λ
=
√
f ε
r
ε
o
µ
r
µ
o
where
l
is the electrical length and
λ
is the shortest electromagnetic
wavelength in the system. At 2GHz, using
ε
r
= 4.3 for typical epoxy
resin dielectric,
λ
= 72.3 mm. In a typical PCB, most feature size,
such as trace discontinuity and gap in power plane, ranges from 1 -
10 mm. Thus a conservative estimate for suitable frequency band-
width using structural approach in PCB of average component density
is between 0 to 1GHz. As radiation intensity from PCB conductors in-
creases, equivalent network representing radiation coupling has to be
incorporated. This would mean each conductor is strongly coupled to
every other conductors in the system. This will invariably lead to a
very complicated equivalent circuit.
It is also assumed here that the electromagnetic field configuration
between the PCB trace and ground/power planes can be approximated
as a two dimensional quasi-TEM field of and infinite length transmis-
sion line. Hence all PCB traces can be modeled as microstrip line and
striplines. Employing the structural approach, a two trace example in
Figure 2 could be modeled as three transmission line segments with
inductors for the bend in AB. We can compare this with direct dis-
cretization approach where a mesh of RLCG elements are generated.
Discretization is necessary in both approaches as it is required to esti-
mate the quasi-TEM fields through numerical method. From Figure 2,
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