Digital Signal Processing Reference
In-Depth Information
7.8
Understanding Stripline and Microstrip Propagation Delay Time
In air, electromagnetic energy requires about 3.3 ns to travel the distance of 1 meter
(about 85 ps per inch), but as shown in (7.5), it takes longer to travel through a di-
electric such as a circuit board laminate. The physics behind this is widely available
(for just one example, see [5]), but we will note here that as shown in Table 7.1,
ε
r
for circuit board laminates is higher than the value for air (which is about 1).
tpd
=
84.7
ε
ps/inch
(7.5a)
r
tpd
=
33.5
ε
ps/cm
(7.5b)
r
In (7.5)
tpd
is the propagation delay time [in picoseconds/inch for (7.5a), and
picoseconds/centimeter for (7.5b)], and
ε
r
is the dielectric constant of the laminate
for stripline or the effective dielectric constant (
ε
r_eff
) for microstrip.
Because only one dielectric is involved with stripline (the dielectric is homoge-
neous), (7.5) shows that the delay is not affected by the trace dimensions or imped-
ance. For example, the delay of a 4-mil-wide, 25
Ω
stripline will be identical to the
delay of a 10-mil-wide, 100
stripline formed on the same layer (where we assume
ε
r
is identical for both traces). In fact, the delay for stripline traces is independent
of the trace geometry.
However, because the two dielectrics (air and the laminate) have such different
dielectric constants, this is not so for microstrips. In this case, the dielectric is not
homogeneous, and the trace width and impedance do influence microstrip delay.
To understand this, we notice from Figure 7.8 that obtaining a given imped-
ance while making
w
larger requires the trace to be further away from the ground
plane. This means that more of the field lines travel in the air as compared to a
trace that is closer to the laminate. Since signals travel faster in air than in a lami-
nate, this results in the delay being smaller. In fact,
Ω
ε
r_eff
becomes closer to 1 as the
trace is moved further away from the ground plane (that is, as
h
in Figure 7.1 is
made larger). From (7.5), lower values of
ε
r_eff
cause
tpd
to be less. Microstrip is
said to be faster than stripline for this reason.
Similarly, as is evident in Figure 7.8, obtaining a particular impedance for a
given trace width requires that
h
change. This means that, unlike stripline, the de-
lay of a 25
Ω
microstrip will not be the same as the delay of a 100
Ω
microstrip. In
fact, the 25
Ω
microstrip will be closer to the laminate than the 100
Ω
microstrip,
making its delay longer.
7.8.1
How Do the Dielectric and Effective Dielectric Constants Affect Delay
Time?
Equations such as (7.4b) do not clearly show how the delay changes with trace
width and impedance. The delay for various trace widths is plotted in Figure 7.9 to
show this relationship.
Signal delay on microstrip is reduced slightly with increases in the trace width
and impedance, and microstrips are faster than stripline. For instance, on FR4
