Digital Signal Processing Reference
In-Depth Information
Low-impedance traces are seen to have lower inductance than high impedance
traces. For example, the 40
stripline inductance is about 7 nH/inch for any width
versus about 10.5 nH/inch for the 60
Ω
stripline.
Also evident is that for a given impedance and width, the stripline has a higher
inductance than microstrip. For instance, a 5-mil-wide 50
Ω
Ω
stripline has an induc-
tance of 8.7 nH/inch, while the microstrip is 8 nH/inch.
7.5
How Does the Skin Effect Change the Trace's Resistance?
At low frequencies the signal current flows through the entire cross-section of a
trace. However, at high frequencies the skin effect causes current to only flow near
the trace surface in a region defined by the skin depth. The skin depth (or the depth
of penetration) is large for low frequencies, which is why the current flows through
the entire trace cross section at DC.
However, at a high frequency the resistance of the trace and the return path (the
loop resistance,
R
ac
) increases as the square root of the frequency. This is shown in:
f
R
=
R
2
(7.2)
ac
_2
f
ac
_1
f
f
1
For instance, increasing the frequency by a factor of 4 from 500 MHz to 2 GHz
causes the resistance to increase by 2.
The skin effect becomes apparent in 1-ounce traces at roughly 14 MHz; it is
evident at about 65 MHz for half-ounce traces [7].
The loop resistance at 350 MHz (corresponding to the 3-dB bandwidth of a
1-ns pulse) is plotted for various widths of striplines and solder mask covered mi-
crostrips in Figure 7.6. For the laminate and the solder mask, the dielectric constant
is 4.2, and the loss tangent is 0.02. The solder mask is 1-mil thick.
The loop resistance for frequencies other than 350 MHz can be found by using
(7.2). For instance, Figure 7.6 shows the loop resistance of a 4-mil (0.11-mm)-wide
50 stripline to be about 0.8
/inch. Increasing the frequency to 1.4 GHz causes the
resistance to increase by a factor of 2 (
f
1
Ω
=
350 MHz,
f
2
=
1.4 GHz,
R
ac_f
1
=
0.8
Ω
),
to 1.6
Ω
/inch.
7.5.1 What Is the Proximity Effect?
One property of the skin effect (the proximity effect) is that as frequency increases,
current in the return path gradually collects underneath the trace, rather than
spreading out and using the entire ground plane as it does at lower frequencies
[9-12]. For a given trace width, the spreading is greatest for traces further away
from the ground plane, which is why higher-impedance traces (which as we will see
in Section 7.7 are further away from the return plane) use more of the return path
metal than lower-impedance ones. This is shown in Figure 7.7.
