Digital Signal Processing Reference
In-Depth Information
For instance, the capacitance of a 5-mil (0.13-mm)-wide, 60
Ω
microstrip is
about 2.6 pF/inch, but it increases to about 4 pF/inch for a 40
Ω
microstrip of the
same width. A 40
stripline of any width has a capacitance of about 4.3 pF/inch,
which is about 10% higher than the microstrip capacitance.
Ω
7.3.3 How Does Frequency Alter the Loss Tangent?
In general, the loss tangent (introduced in Chapter 1) will have its highest value at
low frequencies, and the value of the loss tangent falls as frequency increases. This
trend is evident for three FR4 laminate systems in Table 7.1. For instance, the loss
tangent of the first laminate is 0.025 at 1 MHz, but falls to 0.014 for higher fre-
quencies. As in this case, once reaching a high enough frequency, the loss tangent
will often remain nearly constant and in some cases it may begin to climb again.
Moisture uptake (described in Chapter 8) can cause the loss tangent to increase in
high-humidity environments.
7.3.4 What Is Conductance and How Is It Determined?
Conductance is used in many SPICE lossy transmission line models to account for
stripline and microstrip dielectric losses, and this chapter's Problems show how
to create SPICE lossy transmission line models. In Chapter 8 we will see how to
directly determine loss from the loss tangent without using the conductance. How-
ever, because conductance is so widely used in simulators, it is worthwhile to un-
derstand how its value is determined.
From Chapter 6 we recall that the conductance (
G
, units of Siemens/length)
is modeled as a resistor in parallel with the trace capacitance. Higher values of
conductance represent higher dielectric losses. As shown in (7.1), the conductance
value is determined by the trace capacitance (
C
), the frequency (
f
), and the value
of the loss tangent (
LT
).
G
=
6.28
×
C
×
f
×
LT
(7.1)
Evidently traces with larger capacitance and loss tangent values have corre-
spondingly larger values for
G
(and so, higher dielectric losses). This means that
dielectric loss is highest for low impedance traces (because these have larger capaci-
tance), and the loss increases with higher loss tangent values.
As we just saw, for a given impedance the capacitance of a stripline is the same
for all trace widths, but it changes for microstrip widths. This means that for a
given impedance, the dielectric loss is the same for striplines regardless of its width,
but the dielectric loss will be different for various widths of microstrip. This as-
sumes the loss tangent has the same value everywhere on the circuit board.
The effects with microstrips are small, especially if the microstrip is covered
with solder mask, and although not evident from the equation, because the loss
tangent for air is lower than that of the laminate, for any given impedance
G
is
lower for microstrip than for stripline.
For instance, on FR4 (
,
half-ounce stripline of any width at 1 GHz. At that same frequency it is slightly
more than 15m S/m for a 5-mil-wide microstrip that is covered by 1 mil of solder
ε
r
=
4.2,
LT
=
0.02),
G
is just over 17m S/m for a 50
Ω
