IEEE Solid-State Circuits Magazine - Fall 2015 - 20

Here, C 0 is the transmission line's
capacitance per unit length at low
frequencies, while i and f0 are
parameters that provide for linearly
increasing (20 dB/decade) losses at
very high frequencies.
Since dielectric losses impose
such strict bandwidth limitations on
chip-to-chip communication, there
is strong motivation to consider
low-loss materials such as Teflon as

characteristic impedance that cause
signal reflection evident as "echoes"
in the channel pulse response. In
extreme cases, the discontinuities
can establish standing waves on the
link that completely attenuate portions of the signal spectrum while
leaving others almost untouched.
Over longer links, the impact of
discontinuities may become less
significant because the resulting

Digital coding methods can be applied to make
long strings of CIDs impossible or improbable.
reflections must traverse a longer
length of PCB trace before appearing
at the receiver and so are attenuated
by skin effect and dielectric losses.
Frequency-dependent
channel
loss or, equivalently, ISI is commonly addressed using an equalizer
intended to restore lost components
of the signal spectrum. Equalizer
design is a primary consideration
in modern I/O transceivers and so
is the specific subject of another
article in this issue (see John

0.35

-5

0.3
Normalized Pulse Response

Magnitude Response (dB)

a PCB substrate. However, the epoxy
laminate FR4 remains popular in
spite of its relatively high loss due
to its mechanical robustness and
low cost.
Discontinuities in digital I/O
links between chips are another
major source of ISI. Specifically,
the integrated circuit packaging,
sockets, and connections to ac-coupling capacitors, PCB vias, routing
anomalies or connectors all introduce discontinuities in the link's

-10
-15
-20
-25
-30
Skin Effect Loss
Dielectric Loss
Notch Loss

-35
-40

0.2

0.4

Bulzacchelli's "Equalization for Electrical Links").
It is common among specialists
in the field to quantify the loss of
a digital I/O channel, as well as the
performance of the corresponding
equalizer, by reporting its attenuation (in dB) at a frequency of onehalf the bit rate, fbit /2. However, this
is insufficient to capture the subtleties of the link's bandwidth limitations. Shown in Figure 12 are three
examples of channel responses: one
dominated by skin-effect loss, one
by dielectric loss, and another by
a discontinuity. When used for a
10-Gb/s link, all three channels are
said to exhibit 25-dB loss at fbit /2.
Practical channels generally combine properties of all three, of course,
but it is instructive to note that the
skin-effect-dominated channel has
a pulse response that decays slowly,
with ISI persisting over dozens of UIs,
whereas the channel dominated by
dielectric loss has a pulse response
that decays more quickly. Finally, the
discontinuity-limited channel has an
echo that peaks at the third post-cursor ISI. Yet these widely differing channel characteristics are all commonly

Skin Effect Loss
Dielectric Loss
Notch Loss

0.25
0.2
0.15
0.1
0.05
0

0.6

0.8

-0.05

Normalized Frequency (fbit)

Time (UI)

(a)

(b)

Figure 12: Three channel responses having the same 25-dB loss at 5 GHz: one dominated by skin effect, one by dielectric loss, and one by a
discontinuity in the link. Shown are (a) the magnitude responses and (b) the pulse responses.

fa l l 2 0 15

IEEE SOLID-STATE CIRCUITS MAGAZINE

Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Fall 2015