Calculating Trace and Plane Electrical Values - Understanding Signal Integrity - page 228

λ

Time

Figure 17.4 Wavelength of a sine wave is the distance between identical successive points.

1. Equation (17.14) is used to fi nd that the effective dielectric constant of the
exposed microstrip

4).
2. The impedance of the exposed microstrip is found from (17.26) to be Z o
=

ε r_eff = 3.067 ( h = 3, w = 5, ε r =

.
3. The effective dielectric constant of the solder mask-covered microstrip is
found from (17.28) to be

56.4 Ω

3.067, and
tsm is the total thickness of the solder mask, which is the thickness of the
trace plus the coating thickness, or 1.65 mils in this case).
4. The impedance is then found from (17.27) to be:

ε r_eff_sm = 3.689 (from step 1 ε r_eff =

ZZ ε
ε

3.067

r f _

= = 56.4 Ω = 51.4 Ω

osm _ o

3.689

r f sm __

This is about 2.5% higher than the actual value of 50.2 Ω .

17.15 Wavelength

As shown in Figure 17.4, the distance separating identical points on a sine wave
(such as points of maximum amplitude) is called the sine waves wavelength.
Because the sine wave's frequency determines how frequently the wave repeats,
the wavelength (

) is shorter for high frequencies. The dielectric constant of the
media through which the wave is passing also alters the sine wave's wavelength. It
is longest when traveling through free space and becomes shorter when traveling
through a dielectric such as FR4. For instance, a 300-MHz sine wave has a “free
space wavelength” of 1 meter, but it is less than half that when it travels through
FR4.
Wavelength in meters is calculated with (17.29) when the frequency f is in
megahertz.

λ

300

λ =

(17.29)

f × ε

r

For stripline the dielectric constant of the laminate is used for ε r , but ε r_eff can

be used for microstrip. For example, ε r is 4.2 for a 5-mil-wide half-ounce 65 Ω

stripline on FR4, but ε r_eff is only 3.6 for microstrip. At 300 MHz this makes the