Digital Signal Processing Reference
In-Depth Information
CHAPTER 9
Understanding Trace-to-Trace Coupling
9.1 Introduction
This chapter discusses how coupling caused by parasitic capacitance and induc-
tance linking traces changes their impedance and propagation time. We will use this
understanding in the following chapters, especially when discussing crosstalk, serial
signaling, and transmission line terminations and reflections.
9.2
Understanding Mutual Capacitance and Inductance
Chapter 7 showed how capacitance is created between a trace and the ground plane
(the return path). In fact, as shown in Figure 9.1(a), besides this self-capacitance
(and implied but not shown, self-inductance), parasitic coupling capacitance and
inductance are also present between traces.
We know from Chapter 7 that a transmission line can be thought of as a chain
of very small, identical distributed circuit elements. It is apparent from Figure
9.1(b) that this is also true for the parasitic circuit elements between traces (the mu-
tual terms). The line itself is made from an infinite number of these tiny segments,
each with their own identical self and mutual elements. This means that similar to
the self terms, the mutuals can be described per unit length (PUL), introduced in
Chapter 6).
9.2.1 What Are the Capacitance and Inductance Matrices?
It is convenient (and mathematically desirable) to record all of the self and mutual
elements as matrices.
As shown in (9.1a) and (9.1b), and in Figure 9.1, a two-digit numbering scheme
is used to identify the terms.
LLL
LL L L
LLL
11
12
13
(9.1a)
=
21
22
23
31
32
33
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