Digital Signal Processing Reference
In-Depth Information
When holding the width (
w
) and thickness (
t
) fixed, the impedance gradually
goes down when the distance to the ground plane (
b
or
h
) is made smaller.
•
The impedance goes up as the dielectric constant (
ε
r_eff
for
microstrip) goes down, and it does so as the square root of the change.
ε
r
for stripline, or
•
For instance, doubling the trace width from 5 mils to 10 mils but keeping the
spacing
b
constant at 13.5 mils causes the stripline impedance to fall by less than
half from 50
on FR4. In a similar way, reducing the dielectric constant in
half from 4.2 to 2.1 causes the stripline impedance to increase from 50 to nearly
71
Ω
to 31
Ω
(rather than doubling).
Because the units cancel, either inch-based or metric units may be used with
these equations to obtain the impedance. For impedances of 40
Ω
or higher, (7.3) is
accurate for striplines to better than 5%. Equation (7.4a) is accurate to within 10%
for microstrips without solder mask across that same impedance range when used
with (7.4b) to calculate
Ω
ε
r_eff
. Chapter 17 shows how to calculate the impedance of
solder mask-covered microstrip.
This chapter's Problems further illustrate uses for these equations, but they are
plotted for FR4 (
4.2) in Figure 7.8.
For stripline the trace bottom is assumed to be centered between the planes
at the distance shown. For the microstrip traces the distance is from the ground
plane to the trace bottom. The solder mask covers the microstrip by 1 mil and has
a dielectric constant of 4.2.
Figure 7.8 is for illustration only because manufacturing details such as the
actual shape of the trace and the composition of the laminate are not accounted for.
ε
r
=
Trace width (mm)
0.08
0.10
0.13
0.15
0.18
0.20
0.23
0.25
34
0.85
70
Ω
32
60
Ω
0.80
30
0.75
28
0.70
26
0.65
24
0.60
50
Ω
22
0.55
20
0.50
18
0.45
40
Ω
16
0.40
14
0.35
12
0.30
70
Ω
10
0.25
60
Ω
8
0.20
6
50
Ω
0.15
4
40
Ω
0.10
2
0.05
0
0.00
3
4
5
6
7
8
9
10
Trace width (mils)
Figure 7.8
The distance (
b
or
h
) and trace width (
w
) necessary to obtain various impedances for
stripline (solid curve) and solder mask-covered microstrip (dotted curve). Data from the Polar Si9000
2D fi eld solver.
