IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 38, NO. 12, DECEMBER 2003 2131
Integrated Transversal Equalizers in High-Speed
Fiber-Optic Systems
Hui Wu, Student Member, IEEE, Jose A. Tierno, Petar Pepeljugoski, Senior Member, IEEE,
Jeremy Schaub, Member, IEEE, Sudhir Gowda, Member, IEEE, Jeffrey A. Kash, Senior Member, IEEE, and
Ali Hajimiri, Member, IEEE
Abstract—Intersymbol interference (ISI) caused by intermodal
dispersion in multimode fibers is the major limiting factor in the
achievable data rate or transmission distance in high-speed multi-
mode fiber-optic links for local area networks applications. Com-
pared with optical-domain and other electrical-domain dispersion
compensation methods, equalization with transversal filters based
on distributed circuit techniques presents a cost-effective and low-
power solution. The design of integrated distributed transversal
equalizers is described in detail with focus on delay lines and gain
stages. This seven-tap distributed transversal equalizer prototype
has been implemented in a commercial 0.18-
m SiGe BiCMOS
process for 10-Gb/s multimode fiber-optic links. A seven-tap dis-
tributed transversal equalizer reduces the ISI of a 10-Gb/s signal
after 800 m of 50-
m multimode fiber from 5 to 1.38 dB, and im-
proves the bit-error rate from about 10
5
to less than 10
12
.
Index Terms—Dispersion, distributed circuit, equalization,
fiber-optic communications, transversal filter.
I. INTRODUCTION
I
NTERSYMBOL interference (ISI) is a fundamental
problem in digital communications in bandwidth-limited
links. One such example are multimode fibers, which are the
dominant fiber type in LAN links (Gigabit Ethernet [1], Fiber
Channel [2]). In these links, the ISI is the dominant power
penalty in the link power budget and effectively sets the limits
for the achievable data rate or transmission distance.
The main source of ISI in a fiber-optic system is signal pulse
broadening due to fiber dispersion. There are three types of dis-
persion ina fiber-opticsystem: modal dispersion, chromatic dis-
persion, and polarization mode dispersion [3]. In a multimode
fiber, different mode groups have different velocities, which
is called modal dispersion. Chromatic dispersion is due to the
fact that different wavelengths of light have different velocities.
The polarization-mode dispersion, which comes from different
velocities of different polarizations, can be neglected in multi-
mode fibers.
Manuscript received April 22, 2003; revised July 7, 2003. This work was sup-
ported by NIST/ATP throughthe Photonics CAD Consortium, National Science
Foundation, under Contracts ECS-0083220 and ECS-0239343, and by the Lee
Center for Advanced Networking.
H. Wu was withthe Department of Electrical Engineering, California Institute
of Technology, Pasadena, CA 91125, USA. He is now with the Department of
Electrical and Computer Engineering, University of Rochester, Rochester, NY
14627 USA (e-mail: hwu@ece.rochester.edu).
J. A. Tierno, P. Pepeljugoski, J. Schaub, S. Gowda, and J. A. Kash are with the
IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598 USA.
A. Hajimiri is with the Department of Electrical Engineering, California In-
stitute of Technology, Pasadena, CA 91125, USA.
Digital Object Identifier 10.1109/JSSC.2003.819084
In multimode fiber-optic links, for a given data rate, the ISI
effectively sets the limit on the achievable link distance, due to
the fact that it increases exponentiallywith the distance and thus,
dominates the other penalties in the link power budget. For ex-
ample, Table I shows the effective bandwidth and achievable
link distance in 10 GBASE-S base links in the IEEE 802.3ae
standard, running at 10.3125 Gb/s. It is evident that neither the
common FDDI-grade 62.5-
m multi-mode fiber (MMF) nor
50-
m MMF is capable of achieving practical distances. Even
though the latest laser-optimized 50-
m next-generation MMF
(NGMMF) can achieve the same distance as in the previous gen-
eration networks (300 m), any further increase in the data rate
would imply shorter distances. Furthermore, there is a need to
utilize the huge installed base of multimode fibers.
In order to reduce the dispersion effect, different methods
have been proposed and implemented in all three parts of a re-
generator span (transmitter, fiber, and receiver), and in both op-
tical and electrical domains [4]–[6]. The main criteria for a good
dispersion reduction method are small power penalty (low loss),
good integration with current networks, low cost, and adapt-
ability. The latter is important because: 1) dispersion is usually
time varying due to environmental change such as temperature
variation and 2) dispersion is also related to fiber length, and
thus, an adaptable solution would be faster, easier, and cheaper
to implement and maintain.
In the electrical domain, fiber dispersion can be compensated
at the transmitter by pre-emphasis [7] or coding [8]. However,
both approaches lack adaptability. Instead, equalization at the
receiver is preferred, which is expected to be integrated with
the receiver circuit. Therefore, there is a strong demand for an
integrated equalizer solution in high-speed fiber-optic commu-
nications, especially in cost-sensitive short-haul systems.
This paper is organized as follows. Section II presents the
distributed transversal equalizer, with comparison to other
transversal equalizer implementations. Section III describes
the design of delay elements and gain stages. Measurement
results of prototypes are presented in Section IV. Conclusions
are drawn in Section V.
II. D
ISTRIBUTED TRANSVERSAL EQUALIZER
A. Transversal Equalizer
In a communication system, equalization is the process
of correcting channel induced distortion. In a multimode
fiber-optic channel, modal dispersion is the main source of
this distortion [9]. An equalizer is a filter that can be adjusted
0018-9200/03$17.00 © 2003 IEEE
2132 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 38, NO. 12, DECEMBER 2003
TABLE I
A
CHIEVABLE DISTANCES IN 10-Gb/s ETHERNET LINKS USING VARIOUS
TYPES OF MULTIMODE FIBERS
(a)
(b)
Fig. 1. Transversal equalizer. (a) Transversal filter. (b) Adaptive transversal
equalizer.
to compensate for the distortion of the channel. Equalizers
have been widely used in telephone networks and magnetic
recording systems [10]. Transversal filter equalizers are of
particular interest. They have relatively simple structures, can
compensate many types of linear distortion, and can be made
adaptive with simple algorithms. They can also be used as
building blocks for more advanced equalizer architectures,
such as a decision-feedback equalizer [11], [12] and maximum
likelihood detection [13].
In a transversal equalizer [Fig. 1(a)], the input signal
propagates along a delay line. The signal and its delayed
versions
(where , the signal period, and
) are tapped along the delay line, multiplied by equal-
ization coefficients (weights), and then summed to generate the
equalized output
. Thus, this architecture is sometimes re-
ferred to as a tapped-delay-line structure. A fractionally spaced
equalizer (FSE), in which each tap has a delay of
, can
reduce the aliasing problem in a
-spaced transversal equalizer
and improve the equalizer performance [14].
One implementation of an adaptive transversal equalizer
is shown in Fig. 1(b). In the initial training period, a known
training sequence is transmitted and compared with its local
copy in the receiver to find the channel characteristics and cal-
culate the initial values for the equalization coefficients. Then
the coefficients can be adjusted based on the decision results
using an adaptive algorithm such as least mean square (LMS)
[15] or zero-forcing algorithm [16]. Other implementations
(blind equalization) exist, in which no training sequence is
used.
At low speed, transversal equalizers can be implemented as
digital finite-impulse response (FIR) filters: the input signal is
Fig. 2. Schematic of prototype equalizers.
firstsampled and digitized, and the delay line can be constructed
using a shift register [17] or memory [18]. The maximum data
rate of digital FIR filters is limited by the speed of the dig-
itizer and the power consumption and circuit complexity re-
quired for the high-speed implementation. In addition, clock
generation poses another problem if fractionally spaced equal-
ization is required.
Continuous-time transversal equalizers have been explored
for high-speed applications, using charge-coupled devices
(CCDs) [19] and surface accoustic wave (SAW) filters [20], as
well as switch capacitors [21] and
- ladder filters [22],
[23]. Besides speed, such analog equalization has an additional
advantage: Since sampling is done after equalization, signal
delay in the equalizer does not affect the performance and
stability of the clock-and-data-recovery (CDR) timing loop
[24]. However, as signal speed further increases beyond 1 Gb/s,
even these analog equalizers become inadequate to achieve the
high-speed operation. We try to address this problem by using
RF/microwave techniques.
B. Distributed Architecture
Distributed circuits are a good candidate for high-speed inte-
grated circuits because of their unique wideband characteristic,
which was originated from traveling-wave amplifiers [25], [26].
Fig. 2 shows an integrated transversal filter with a distributed
architecture. The similarity with a traveling-wave amplifier is
immediately evident. In fact, it can be viewed as a distributed
amplifier operating in the reverse-gain mode. The input signal
travels along the input transmission lines, and is tapped by each
gain stage in sequence (from left to right in Fig. 2). Thus, the
loaded transmission lines act as delay elements. The tapped
signal is amplified by each gain stage by a gain proportional
to the corresponding equalization coefficient (weight), and the
output signals from all stages are added on the output transmis-
sion lines. It should be noted that the delay between adjacent
WU et al.: INTEGRATED TRANSVERSAL EQUALIZERS IN HIGH-SPEED FIBER-OPTIC SYSTEMS 2133
stages consists of that from both the input and output transmis-
sion lines.
Compared with conventional digital and analog transversal
equalizer architectures, this architecture has the following ad-
vantages.
• It is an RF implementation, which can operate at very high
data rates compatible with all current fiber-optic systems.
• It is an integrated circuit solution, which reduces the
system complexity and cost significantly compared with
conventional optical methods.
• The equalization coefficients can be realized by the gain
from each stage, and thus, it is inherently adaptive.
• It is more power efficient since there is no power-hungry
DSP as in digital implementations.
• Fractionally spaced equalization can be easily imple-
mented without oversampling.
This architecture was first contemplated by Rauscher [27].
In 1989, Schindler developed an MMIC band-pass transversal
filter at 9.8–11.1 GHz using microstrip lines and on-chip ca-
pacitors [28]. Kasper and Mizuhara first suggested the use of
an integrated transversal filter for fiber-optic equalization [4],
followed by others with simulation results [29], [30]. In 1997,
Jamani et al. [31] and Borjak et al. [30] reported the first imple-
mentations using reverse-gain mode and forward-gain mode (in
traveling-wave amplifier terminology), respectively. The latter
group later switched to the reverse-gain mode architecture [32].
In 2000, Lee and Freundorfer introduced the Gilbert cell to gen-
erate both positive and negative weights [33]. These implemen-
tations verified that it is feasible to use distributed amplifica-
tion techniques to achieve integrated transversal equalizer for
high-speed fiber-optic systems.
However, there are important questions to be answered and
problems to be solved.
• Analog weight adjustment is needed. There is no such
mechanism reported in [30] and [32], and only binary
weight control (on/off) in [31] (because of the cascode
gain stage) and [33]. Without analog weight adjustment,
adaptivity cannot be achieved.
• Unlike a traveling-wave amplifier, the gain stages have
to be controlled independently with varying weights to
achieve the adaptive transfer function. This makes it very
difficult to maintain the same loading on the transmission
lines from all stages at all time, i.e., the transfer function
itself tends to disrupt the distributed circuit characteristics.
• Systematic analysis and equalization test data are still
lacking.
III. D
ESIGN
It is the goal of this work to answer the questions above in the
context of a practical fiber-optic system [34]. A generic 10-Gb/s
multimode fiber-optic link was chosen, which is fully compat-
ible with the newly adopted 10 Gigabit Ethernet standard (IEEE
802.3ae) [1]. Based on system simulations using data from dif-
ferent lasers, fibers, and launch conditions, link distance im-
provement and failure rate was evaluated versus complexity,
number of stages, and delay per stage. It was concluded that
a seven-tap transversal equalizer with a 50-ps delay per stage
would be adequate [35].
A. Delay Lines
As in any distributed circuit, the design of transmission
lines is of critical importance [36]. In the case of distributed
transversal equalizers, an additional constraint is the large
time delay per stage. For the prototypes, the delay per stage
is specified as 50 ps, i.e., half of the symbol period. Mi-
crostrip lines or coplanar waveguides would be too long to
effectively implement this delay on chip. For example, for
microstrip lines with metal groundplane, the phase velocity of
a transverse electromagnetic (TEM) wave can be estimated as
, and then the microstrip line length
per stage would be
ps mm.
Even if the loading effect is taken into account, the required
length is still impractical. The total length of delay lines is a
function of the number of bits of ISI that the filter is intended to
cancel. Therefore, the physical size limitation still exists even
when using smaller
for each stage, which results in a larger
number of stages. Considering these practical constraints, the
delay elements were implemented using artificial transmission
lines constructed with LC ladders of spiral inductors and MIM
capacitors. For a given chip area, this approach can generate a
larger time delay.
The inset in Fig. 2 shows a section of the transmission line
structure. Since the spiral inductors are densely packed, the elec-
tromagnetic coupling between them has to be properly modeled.
A six-port electromagnetic simulation [37] is used to simulate
the whole transmission line section, and generate frequency-
swept S-parameters for circuit simulation.
Another important design consideration is the ac ground path.
Since the physical size of the equalizer is comparable to the
wavelength of the signal, it is critical to have a well-defined
return path for the ac current. This is a difficult problem for a
wideband circuit like the equalizer, particularly because of the
lossy and poorly modeled silicon substrate. In our design, this is
addressed by adopting a differential architecture for the equal-
izer, i.e., using differential delay line structures and differential
gain stages. This ensures a local virtual ground within each gain
stage and each section of delay line structures, since the fun-
damental frequency components of the differential ac currents
cancel each other. The differential architecture also reduces the
return-path loss significantly.
B. Gain Stage
The function of the gain stage in a transversal filter is to
implement the equalization coefficient (weight). The gain
stage should have a flat and linearly controllable amplitude
response. It should also be able to change the phase of its
gain by 180
in order to generate negative coefficients. A
flat group-delay response across the equalizer bandwidth is
required to prevent phase distortion in the equalization process.
This is critical, since such phase distortion cannot be easily
compensated by equalization itself. Therefore, the gain stage
can be considered an analog multiplier with a high-speed data
input and a low-speed control signal. In addition, the gain stage
should present a constant load to both the input and output
2134 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 38, NO. 12, DECEMBER 2003
Fig. 3. Gain stage.
transmission lines when changing the weights, in order to
maintain a constant delay between adjacent stages.
Fig. 3 shows the simplified schematic of the gain stage. The
core of the circuit is a Gilbert cell (
– ). The absolute value
of the weight is implemented using the tail current source
.In
this manner,the linearity of the weighting function, i.e., between
and the output voltage, is better than a cascode structure as
in [31]. The sign of the weight is implemented using two dif-
ferential pairs (
, , , ) to steer the differential current
from
and to the output transmission lines. The control
signals of these transistors (
and ) are analog voltages (
and ) selected by a single digital bit , which represents the
sign of the corresponding weight. Because the output nodes are
always connected to the collector of an
ON transistor and that of
an
OFF transistor,there is no variationin the loading of the output
transmission lines when the sign of the coefficient is switched.
The differential input signals are buffered using emitter fol-
lowers (
, , , ). Buffering reduces the loading and
thus, improves the linearity of the phase response on the input
transmission lines. Further, the buffers are biased with constant
currents, and thus, the parasitic capacitances of
and
do not change with the applied weight . Hence, there is no
variation in the loading of the input transmission lines.
The gain stage satisfies the strong impedance mismatching
condition [38] between succeeding stages (the input delay lines,
emitter-follower buffers, core differential amplifier, switch
pairs, and output delay lines), and therefore, can achieve the
stringent requirements for bandwidth and group delay.
C. Prototypes
A seven-tap prototype of distributed transversal equalizers
was designed and fabricated [34] using a 0.18-
m SiGe
BiCMOS process with
of 120 GHz [39]. Fig. 2 shows its
top-level schematic. The filter was simulated using ADS [40]
with frequency-swept S-parameters of the delay lines that were
obtained from EM simulations.
Fig. 4 shows the chip micrograph of the prototype transversal
equalizer. It occupies an area of 3 mm
1.5mm, including pads.
The pads on the top are inputs of sign bits of weights, and the
bottom ones are inputs of absolute values of weights (reference
voltage for the current mirror). The pads on the right are for
ON/OFF voltages and dc bias. The pads on the left are for differ-
ential input and output, and are tilted 45
for RF probing. Note
that the terminations are implemented with multiple resistors in
Fig. 4. Seven-tap prototype transversal equalizer.
Fig. 5. Tap-delay uniformity measurement using 2.5-Gb/s square signal. We
observe uniform tap delays, with typical values of approximately 45 ps.
parallel, which can be laser trimmed to fine tune the matching
properties of the transmission lines.
IV. M
EASUREMENT RESULTS
Fig. 5 shows the step response of the equalizer to a 2.5-GHz
square-wave input with each tap weighted independently. The
delay per stage is approximately 50 ps. The earlier taps demon-
strate more peaking and less attenuation than the later stages.
Fig. 6 shows the frequency response of four stages of the
equalizer with each tap weighted independently. Consistent
with the time domain measurement, the earlier taps show more
peaking and less attenuation. In particular, tap 5 demonstrated
a smooth response that peaked in the 3–6-GHz band. Not
surprisingly, tap 5 had the highest weighting factor in the
most successful data transmission measurements described
below. The amplitude fluctuation is larger than the simulation,
possibly due to the following reasons: 1) the measurement was
single-ended instead of differential, i.e., only one input and
one output were used; 2) the termination was not fine tuned to
achieve the best matching for both transmission lines; and 3)
the wideband modeling of transistors and spiral inductors was
not accurate.
The ability of the circuit to equalize highly dispersed data sig-
nals was tested using the setup in Fig. 7, which is similar to its
application environment. A pattern generator was used to drive
an 850-nm vertical cavity surface emitting laser (VCSEL) using
WU et al.: INTEGRATED TRANSVERSAL EQUALIZERS IN HIGH-SPEED FIBER-OPTIC SYSTEMS 2135
Fig. 6. Measured
S
data for taps 1, 3, 5, and 7.
Fig. 7. Typical equalized link diagram. The equalizer is placed after the
transimpedance amplifier (TIA) and before the postamplifer, and is not present
in Ethernet and Fiber Channel links.
direct modulation, and 800 m of 50- m noncompliant next-gen-
eration MMF fiber was used to generate distortion on the signal.
The fiber was noncompliant because it did not meet any of the
six masks in the specifications [41]. The pattern was a 2
1
pseudorandom bit sequence (PRBS) pattern and the data rate
was 10 Gb/s. This generated a signal with 5 dB of ISI and 62 ps
of deterministic jitter (DJ) at the input of the equalizer.
The response of each tap individually was measured for dif-
ferent values of the tap coefficient, and an optimization routine
was used to fit a linear combination of the individual signals
to an idealized output with a raised cosine output character-
istic. Rigorous linearity measurements were performed to val-
idate this procedure. After each tap coefficient and sign was
determined, the coefficients were fine tuned by hand while mon-
itoring the eyediagram and the bit-error rate (BER) to determine
the optimum set point. As shown in Fig. 8, the equalized signal
has residual ISI of only 1.38 dB and a DJ of only 38 ps. The
overall BER was improved from about 10
to less than 10 .
The total power dissipation, including all biasing circuits, was
30 mW, plus 2 mW per active coefficient (typical dissipation is
40 mW).
The equalization chip was designed to operate on 10-Gb/s
signals. To explore its limits, we tested it at 14 Gb/s (limited by
test equipment). The signal from the pattern generator passed
through the same setup as before, resulting in even larger eye
closure (11 dB). Similar to the previous case at 10 Gb/s, the
equalizer reduced the ISI penalty to 2.2 dB and reduced the de-
terministic jitter from 60 to 21 ps.
V. C
ONCLUSION
Integrated transversal equalizers based on distributed circuit
techniques have been introduced as the solution for dispersion
Fig. 8. Eye diagrams for 800-m 50-
m of multimode fiber before and after
equalization.
compensation in high-speed fiber-optic communications.
The dispersion problem and compensation techniques were
discussed, with the emphasis on adaptive equalization and its
implementations. The design of integrated transversal equal-
izers has been further described with detailed analysis on delay
lines and gain stages, followed by measurement results for a
seven-tap 10-Gb/s prototype. Future work will focus on the
other part of the challenge: How to generate the equalization
coefficients at such high speed and make the equalizer fully
adaptive.
A
CKNOWLEDGMENT
The authors would like to thank M. Oprysko, M. Soyuer,
D. Friedman, H. Ainspan, J. Yang, U. Pfeifer, D. Beisser,
and R. John at IBM Research for their help and support in
this project. They also appreciate discussion with D. Ham,
H. Hashemi, B. Analui, X. Guan, and S. Kee at Caltech.
R
EFERENCES
[1] 10 Gbps Ethernet IEEE Standard 802.3ae, June 2002.
[2] 10 Gigabit Fiber Channel Physical Interface Draft Standard, T11
project 1413-D, rev. 3.5, 2003.
[3] G. Agrawal, Fiber-Optic Communication Systems, 3rd ed. New York:
Wiley, 2002.
[4] J. Winters and R. Gitlin, “Electrical signal processing techniques in
long-haul fiber optics systems,” IEEE Trans. Commun., vol. 38, pp.
1439–53, Sept. 1990.
[5] J. Winters, R. Giltin, and S. Kasturia, “Reducing the effects of transmis-
sion impairments in digital fiber optic systems,” IEEE Commun. Mag.,
vol. 31, pp. 68–76, June 1993.
[6] B. Jopson and A. Gnauck, “Dispersion compensation for optical fiber
systems,” IEEE Commun. Mag., vol. 33, pp. 96–102, June 1995.
[7] T. Koch and R. Alferness, “Dispersion compensation by active predis-
torted synthesis,” J. Lightwave Technol., vol. LT-3, pp. 800–805, Aug.
1985.
[8] N. Swenson and J. Cioffi, “Coding techniques to mitigate dispersion-in-
duced ISI in optical data transmission,” in Proc. IEEE Int. Conf. Com-
munications, 1990, pp. 468–72.
[9] S. Haykin, Communication Systems, 4th ed. New York: Wiley, 2001.
[10] S. Qureshi, “Adaptive equalization,” Proc. IEEE, vol. 73, pp.
1349–1387, Sept. 1985.
[11] J. Winters and S. Kasturia, “Adaptive nonlinear cancellation for high-
speed fiber-optic systems,” J. Lightwave Technol., vol. 10, pp. 971–977,
July 1992.
