EMC’14/Tokyo
13A-B7
Signal Integrity: Influence of Non-linear Driver,
Different Bit Rates, and Estimation by Different
Algorithms
Sheng-Yun Hsu, Chiu-Chih Chou, and Tzong-Lin Wu
Graduate Institute of Communication Engineering
National Taiwan University
Taipei, Taiwan
tlwu@ntu.edu.tw
Abstract— Signal integrity issue has become more and more
important in recent years. In order to have a good signal quality,
many aspects in a digital channel must be carefully considered.
In this paper we compare the effects of non-ideal output driver
and different power distribution networks (PDNs) on the signal
integrity. The channel performance variation under different
driving bit rates is also analyzed. In addition, to reduce
simulation time, various algorithms for fast and accurate signal
integrity estimation have been proposed [1, 4] as alternatives to
the conventional time-consuming PRBS simulation. The next
part of this paper compares the performances of these algorithms
for a circuit with nonideal PDN. From these results, we could get
a qualitative understanding of these algorithms.
Keywords—bit rate; eye diagrm; power distribution network;
non-linear driver; signal integrity
I.
INTRODUCTION
In a modern high-speed digital channel, various effects
may influence the signal integrity (SI). For example,
transmission line discontinuities such as bent or mismatch
might cause multiple reflections of the data signal, thus
producing the intersymbol interference (ISI) and degrading the
signal quality greatly. Also, the output waveforms of a digital
driver might be distorted by a nonideal power distribution
network (PDN) [2-3]. Fig. 1 shows a general picture of a
digital channel. In addition, as the data rate increases, the
allowed charge (discharge) time for the pull up (pull down)
circuitry in the output driver becomes shorter. If the driver
cannot follow such high-speed transitions, the output signal
would be distorted and thus increasing the bit error rate (BER).
The increasing data rate will also cause severer voltage
ripples on the PDN because of the PDN’s parasitic inductors
and capacitors. To put it briefly, everything gets worse as the
data rate goes higher.
Input
Signal
Output
Driver
Fig. 1. A general digital channel.
Copyright 2014 IEICE
Receiver
Signal
Channel
Receiver
Conventionally the digital channel is evaluated by running
PRBS simulation. However, for more complex systems, this
takes more time. Therefore, several algorithms were proposed
[1,4] to predict the channel performance without running
PRBS. These algorithms can be categorized into two parts.
First, peak distortion algorithm [1] can predict the worstcase inner/outer boundary of the eye diagram based on
superposition principle. Since there are many non-linear
effects in the channel, the multiple edge response (MER)
method [4] was proposed to approximately estimate the
performance of a non-linear channel. Second, statistical
analysis [5] can provide BER. It is a more general
methodology for SI evaluation since the worst-case eye
boundary obtained in the previous part might be meaningless
if the eye diagram is closed. Both methods, however, rely on
the superposition of one or more basis waveforms. As a result,
when the nonlinear effects such as the interaction between
driver and PDN are included, these algorithms may have
errors.
In this paper, the above issues are examined. Section II
compares the SI degradation of four different of circuits,
including ideal/nonideal driver, two different PDNs, and
different bit rates. Section III briefly introduces the algorithms
and discusses the accuracy issue comparing with PRBS.
II.
NONIDEAL DRIVER, PDN, AND DIFFERENT BIT RATE
In this section, part A shows the circuits that we used to
conduct the simulation. Part B shows the simulation results
including the eye height, jitter, and bathtub curves of different
circuits. The effect of different bit rates is also analyzed. In the
end of this section, a short conclusion is given.
A. Circuit Setting
Fig. 2 shows the basic topology of the circuit used for
simulation. Ideal input signal Vin is transmitted through a
driver (ideal or CMOS) with or without PDN connected to it,
followed by two ideal transmission lines with a series inductor
L1 and a shunt capacitor C2 between them representing
nonideal effects in the channel. The transmission line is then
terminated with a resistor R2. The CMOS driver is a 2-stage
inverter as in Fig. 3(a), which is commonly used in practical
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A
13A-B7
Jitter (ps)
Eye Height (V)
1.8V
B
PDN
1
60
0.9
50
0.8
C1
Driver
Vin
R1
40
0.7
L1
Ideal TL
Vout
Ideal TL
C2
Circuit 1
R2
30
Circuit 2
0.6
Circuit 3
20
Circuit 4
0.5
10
0.4
A
PDN
0.3
B
0
2
Fig. 2. The circuit setting for simulation.
4
6
Bit Rate(Gb/s)
8
10
Fig. 4. Eye height and jitter of four kinds of circuits in different bit rates.
B
log10(BER)
0
L2
OUT
IN
-1
A
Circuit 1
Circuit 2
-2
R3
Circuit 3
Circuit 4
-3
(a)
-4
(b)
0
Fig. 3. (a)The output driver consists of two stages of CMOS inverter.
(b)The PDN consists of series inductor and resistor.
circuits to amplify the input signal. The PDN is built up with
L2 and R3 in Fig. 3(b), and node A in Fig. 3(b) is connected to
C1 in Fig. 2.
In Fig. 2 and 3, R1=50Ω, L1=1nH, C2=1pF, R2=50Ω,
transmission line Z0=50Ω, time delay=100ps. Four different
kinds of circuits are defined as follows:
Circuit1: ideal driver, no PDN.
Circuit2: CMOS driver, no PDN.
Circuit3: CMOS driver, PDN L2=1nH, C1=1nF, R3=0.2Ω.
Circuit4: CMOS driver, PDN L2=5nH, C1=200pF, R3=0.2Ω.
We compare the effect of CMOS driver on the eye diagram
through Circuit 1 and Circuit 2. Adding PDN effects in Circuit
2 then becomes Circuit 3, from which we can evaluate the
effect of PDN on SI by observing the changes of the eye
diagrams. In Circuit 4 the PDN is making worse by increasing
L2 and decreasing C1. After analyzing these four circuits, we
can easily tell which is the major issue that degrades the signal
integrity.
B. Simulation Results
To simulate these 4 circuits, five different bit rates are used: (2,
4, 5, 8, 10) Gbps. After running PRBS, the eye height and
jitter of each circuit are recorded in Fig. 4, where the
horizontal axis is bit rate, and the left and right axis are eye
height and jitter respectively. As can be seen, generally the
Copyright 2014 IEICE
0.2
0.4
0.6
0.8
1
1.2
1.4
Time (UI, 1UI=100ps)
1.6
1.8
2
Fig. 5. Bathtub curve of four kinds of circuits.
eye heights become smaller as the bit rate goes higher, no
matter which circuit it is. Specifically, circuit 1 and circuit 2
show only minor difference as the bit rate increases, although
circuit 2 uses a non-ideal CMOS driver. For circuit 3, where a
nonideal PDN is presented, the eye height decreases
dramatically as bit rate soars, which means that the voltage
ripples in the PDN caused by the parasitic resistors and
inductors affect the output signal of the driver significantly,
and this phenomenon becomes even worse as bit rate climbs
up. Increasing the effect of PDN in circuit 4 by decreasing C1
to 200pF and increasing L2 to 5nH, we see that the eye height
becomes even smaller for high bit rates, which indicates that a
poor designed PDN will result in a considerable SI
degradation. Similar results can be found for the jitter in Fig. 4.
Fig. 5 shows the bathtub curve of the 4 circuits. The bit
rate is 10 Gbps with rise/fall time both 10ps. As can be seen,
the results in Fig. 5 are in accordance with Fig. 4, where
circuit 3 and 4 show clear difference between Circuit 1 and 2,
and circuit 4 possess the smallest eye width.
To sum up, the main cause that degrades the signal
integrity in this circuit is the PDN, rather than the non-ideal
driver. It is clear in Fig. 4 and Fig. 5 that, especially at high bit
rates, a poor PDN will result in a poor signal quality. Although
limited to this specific circuit setting, this result may be
considered a general fact. The PDN design is as much
important as the output driver in modern high speed circuits.
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III.
13A-B7
ALGORITHM FOR FAST SIGNAL INTEGRITY ESTIMATION
In this section, the very fundamental core of the SI
estimation algorithms mentioned in the Introduction section
will be introduced. Part A covers the basic equations of the
algorithms and explains its meaning, followed by a brief
description of the estimation method. Simulation results will
be given and discussed in part B, including the estimated
worst-case eye boundary and the bathtub curve.
the approximate received signal, the eye diagram and bathtub
curve can be directly calculated.
B. Simulation Results
We use circuit C described in section II with bit rate 10
Gbps. Fig. 6 shows the estimated inner boundaries of the eye
diagram as well as the PRBS result for reference. As can be
seen, order 2 is much more accurate than order 1. Another
Voltage(V)
1.3
A. Basic Principles of the Estimation Algorithm
Any input signal x(t) can first be expressed as the linear
superposition of the step function u(t) as
1.2
1.1
∞
x(t ) = ∑ ( s[n] − s[n − 1])u (t − nUI )
1
n =0
∞
= ∑ s[n](u (t − nUI ) − u (t − (n − 1)UI ))
MER order 2
(1)
0.8
n =0
0.6
0.5
0
y (t ) = ∑ | s[n] − s[n − 1] | R s[ n − m ]....s[ n −1] (t − nUI )
(2)
60
80
100
log10(BER)
0
-0.5
-1
MER order 1
-1.5
MER order 2
-2
-2.5
PRBS
-3
-3.5
-4
(3)
0
n=0
0.5
1
1.5
2
Time (UI, 1UI=100ps)
where R(t) is the specific rising or falling response with m
preceding bits being s[n-m] to s[n-1], i.e., the waveform used
for superposition is dynamically selected based on the
preceding bit patterns. Thus, if m is large enough, presumably
all the nonlinear effects in the circuit can be captured in these
R(t)’s, at the cost of 2m many basis waveforms. The m is called
the order of MER. Conceptually, selecting a larger m results in
a more accurate estimation, but also makes the preparation
work more tedious. Practically using order 2~4 would give
reasonably accurate estimation results, and the time required
would still be much less than running PRBS.
The whole process of the MER method is as follows. First,
use SPICE simulator to get the rising and falling responses of
the circuit. For order 1, there are only one rising response
(‘01’) and one falling response (‘10’). For order 2, there will
be two rising responses (‘001’, ‘101’) and two falling
responses (‘110’, ‘010’). Second, randomly build a binary
sequence (say, 1000 or 10000 bits) to represent the PRBS
input. Third, instead of directly running SPICE to get the
PRBS output, use the waveforms obtained in the first step and
equation (3) to construct the output waveform. After obtaining
Copyright 2014 IEICE
40
Time(ps)
where SBR(t) is the single bit response. Once we have SBR,
the channel performance can be estimated using (2) without
running the lengthy PRBS simulation. However, when the
nonlinear effects in the circuit is pronounced, (2) produces
great error. The multiple edge response (MER) method is then
proposed [4] to overcome this problem. In MER method, the
received signal is written as, following the first equality in (1)
and with controllable error,
∞
20
Fig. 6. Inner boundary of the eye diagram estimated by MER algorithm.
∞
n=0
PRBS
0.7
where s[n] is the input binary signal (either 1 or 0) and UI the
unit interval. If n<0, s[n]=0. When the input signal transmits
through output driver, channel, and receiver, the received
signal y(t) can be approximately written as, following the
second equality [1],
y (t ) = ∑ s[n]SBR (t − nUI )
MER order 1
0.9
Fig. 7. Bathtub curve estimated by MER method.
thing worth noting is that, contrary to intuition, order 1 MER
overestimates the inner boundary. This means that although it
is true a larger m gives better accuracy, a smaller m does not
necessarily give an underestimation. Fig. 7 shows the bathtub
curves of the same circuit. Similar results can be seen.
The difference between MER and PRBS may be caused
by the order of the MER. The larger the order is, the smaller
the difference between MER and PRBS will be, but which
also costs more time. In addition, rising or falling waveforms
may have small ripples not due to the circuit itself but the
SPICE convergence error. Such seemingly insignificant tiny
ripples might be added up in the algorithm to produce an
unrealistically poor eye diagram. To some extent this problem
can be solved by choosing an appropriate length of the rising
or falling waveforms. Despite the various causes of error
discussed above, it should be mentioned, however, that the
MER algorithm itself has nothing to do with any particular
kind of circuits. It is a very general method and can be used in
any digital channel, linear or nonlinear.
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As a brief conclusion of this paper, The performance of
PDN in modern high speed systems is becoming increasingly
important because of its significant influence on SI. The MER
method provides an efficient way to quickly estimate SI; but
the accuracy of estimated results must be carefully examined.
[3]
[4]
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