Learn some of the basic building blocks that make digital
systems work. This chapter starts with a discussion of a basic digital
communications link, covers the most commonly used clocking architectures,
discusses line-coding methods, and concludes with special techniques for
high-speed serial transmission systems.
During the last ten years, most major communications and broadcast systems
and many other systems were converted from analog to digital. Examples of
digital systems that we use every day include mobile phones, television, radio,
and of course the Internet. CDs and MP3s are replacing records and tapes, and
the number of digital cameras sold this year exceeded the number of analog
cameras by a factor of three. In this chapter, you will see some of the basic
building blocks that make all of these digital systems work.
The material in this chapter is intended to provide a background that will
be useful when studying digital communications test and measurement techniques
described in later chapters. We start with a discussion of a basic digital
communications link, cover the most commonly used clocking architectures,
discuss line-coding methods, and conclude with special techniques for
high-speed serial transmission systems.
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1.1 Introduction
The most important aspect of any digital communications system is the
required transmission speed. Just how much data needs to be transmitted, and
how fast? The variability is huge, even within a single system: The keyboard
interface of a typical PC, for example, runs at several kilobits per second,
which is still significantly faster than anyone can type. However, the fastest
interface available for graphics adapters is not nearly fast enough for the
newest games, even at 40 Gbit/s (which is the accumulated bandwidth of a PCIe
x16 link, the current standard for graphics adapters).
The second, equally important aspect is the link distance. How far apart
are sender and receiver? Again, there is huge variability: The main processor
of a computer communicates with its main memory over a distance that's usually
less than 10 cm. But when you type a URL into a Web browser, you communicate
with a server that's potentially on a different continent.
Generally, digital transmission becomes harder when the transmission speed
and link distance increase. A measure for the effort required to make a digital
communications link work is the bandwidth-distance product. An old telegraph,
for example, transmitted about 100 bit/s, over a maximum distance of 20 km. The
radio downlink from the Voyager spacecraft transmits data
slightly faster, at 160 bit/s, but over an incredible distance of 14.821
billion km. The much larger bandwidth-distance product of the spacecraft link
can be achieved only with incredible effort.
Every digital link consists of three components: a sender, a transport
medium, and a receiver. Usually, the medium is defined first, depending on the
required link bandwidth, the distance between transmitter and receiver, and
economic considerations. Electrical links are still the most common type; they
come in a great variety, ranging from bond wires within an integrated circuit
package to printed circuit board traces on a motherboard to Ethernet cables
connecting office computers. Fiber-optic cables are used for very high bandwidth
connections in network and storage environments, but it seems as if "fiber
to the home" might be replaced by wireless links in the near future.
1.2 Line Coding of Digital Signals
When binary data is sent through a link, it is represented by a physical
quantity in the transport medium. In electrical links, that's usually a voltage
or current; optical systems use the intensity of light; and wireless radio
links often use the phase and frequency of a signal carrier. Line coding
determines how the binary data is represented on the link.
Numerous coding schemes are available, and which one is best for any given
application depends on many factors. Coding can influence the frequency
spectrum, the direct current content, and the transition density of the
resulting data stream. Coding efficiency determines the required link
bandwidth, and the cost of implementation depends on the complexity of the code.
1.2.1 Properties of Binary Data
1.2.1.1 Mark Density
The mark density (MD) of a binary data pattern is defined as the number of
one bits in the pattern, divided by the length of the pattern:
where NOne is the number of ones in the pattern, and NZero is
the number of zeros. The mark density ranges from 0.0 to 1.0, where the
extremes are marked by all-zeros (NOne equals 0) and all-ones
data (NZero equals 0). Random data is exactly at the middle of
the range: It contains as many one bits as zero bits, and its long-term mark
density is therefore 0.5. If we look only at a subsection of the random data
pattern, however, its mark density can be very different.
If we represent a zero bit by 0.0 and a one bit by 1.0, the mark density
is equal to the time average over the pattern. It is therefore a direct measure
for the DC content of the signal. A pattern with a mark density of 0.5 is
therefore also called a DC-balanced pattern. DC balance is an important
property in some applications; if it is required to maintain a DC level in the
link, then amplifiers and other system components need to be DC coupled, often
leading to a more complicated and problematic design.
1.2.1.2 Transition Density
The transition density (TD) of a data pattern is defined as the number of
transitions in the pattern, divided by the length of the pattern:
where NT is the number of transitions in the pattern, NOne is
the number of ones, and NZero is the number of zeros. The
transition density ranges from 0.0 to 1.0, where the extremes are marked by
static patterns (all-zeros or all-ones) and toggle patterns. Random data is
again exactly at the middle of the range: Because the probability that two
consecutive bits are identical is 0.5, the transition density is 0.5, too.
1.2.1.3 Run Length Distribution
The run length distribution of a data pattern gives the relative
probabilities for runs of identical consecutive bits. Longer runs create stress
in many applications, because of either excessive intersymbol interference
(ISI) or baseline wander due to local disparity.
1.2.2 Binary Line Codes
1.2.2.1 Non-Return-to-Zero Code
The non-return-to-zero (NRZ) format is the prototypical representation of
binary data: A logical zero state is transmitted as one signal level, and a
logical one state as another level. Levels change at bit boundaries only if the
bit value changes and remain stable for the entire duration of the bit period.
If the level representing the zero logical bit state is lower than the level
for the one state, we call this positive logic, and the respective levels are
then called low level and high level. NRZ coding is essentially free because
binary data is already stored in this format in CPUs and other digital devices.
It is therefore the most commonly used coding scheme and the reference for all
other coding schemes in terms of signal properties, efficiency, and
implementation effort.
NRZ signals always have a clock signal associated with them, even if it is
not transmitted along with the data. Figure 1-15 shows the
NRZ representation of a short data sequence, together with a clock signal. Note
how the data signal changes on the falling edge of the clock; the receiver
samples it on the rising edge. There are also systems that work with an
inverted clock. The data then changes on the rising edge, and the receiver
samples at the falling clock edge. The clock signal for NRZ transmission
usually runs at the base frequency of the data: for a 10 Gbit/s signal, the
clock rate is 10 GHz (single data rate, SDR). A variant of NRZ transmission
uses a clock signal at half rate (5 GHz for 10 Gbit/s), and the receiver
samples the data both at the rising and falling edges of the clock. This is
called double data rate (DDR) transmission.
Figure 1-15 NRZ
coding of a short data sequence (PRBS 24-1). Top: single data rate
clock. Bottom: double data rate clock.
The properties of NRZ-formatted data depend entirely on the data itself.
The drawback of NRZ coding is that the DC content, frequency spectrum, and
transition density depend on the data sequence. Long runs of zeros or ones
cause problems in some applications because of effects such as baseline wander
and ISI or because there are not enough transitions for clock data recovery.
Figure 1-16 shows the
power spectral densities of two short NRZ-formatted data sequences. Note how
both spectra have zero power at multiples of the signal base rate (e.g., 1 GHz,
2 GHz, 3 GHz). The PRBS spectrum follows the typical sinc envelope, with nulls
at multiples of the data rate. Because of the very fast rise times that we used
to create the spectrum, there is significant spectral content at very high
frequencies. The spectrum for the toggle pattern equals that of a 500 MHz
square wave. The spectra of all-zeros or all-ones patterns are zero, with the
exception of a DC value.
Figure 1-16 Power
spectral density for NRZ-formatted data at 1 Gbit/s. Left: PRBS 24-1.
Right: Toggle pattern (101010 . . .). Power density is normalized to a maximum
power of 1.0.
1.2.2.2 Return-to-Zero Code
The return-to-zero (RZ) code represents the zero logical state as a static
low level and the one state as a short high-level pulse. The signal always
returns to the level representing a zero state immediately after the high level,
hence the name. RZ signals can be easily created from NRZ signals, by a binary
AND of the NRZ and a clock. The width of the pulses depends on the duty cycle
of the clock. Figure 1-17 shows the
RZ representation of a short data sequence, with 50% and 25% duty cycles.
Figure 1-17 RZ coding
of a short data sequence (PRBS 24-1). Top: 50% duty cycle. Bottom:
25% duty cycle.
RZ coding is used primarily in optical transmission systems because it
minimizes power consumption and the effects of system dispersion on optical
signal distortion. Consecutive one bits carry one transition each, so that
clock data recovery is fairly easy with this coding, provided the signal
doesn't consist of all zeros. The signals also carry significant DC content,
which is not a factor in optics, though.
The signal bandwidth of RZ-coded data is significantly higher than that of
NRZ data, by at least a factor of two (for a 50% duty cycle). The spectral
densities for the RZ-coded signals from Figure 1-17 are shown
in Figure 1-18. The signal
with a 50% duty cycle has significantly less energy at lower frequencies than
the NRZ signal and very distinct spikes at the data rate and its even
harmonics. The 25% duty cycle signal has even less low-frequency content but
distinct spikes at all integer multiples of the data rate.
Figure 1-18 Power
spectral density for a short RZ-formatted data sequence (PRBS 24-1),
at 1 Gbit/s. Left: 50% duty cycle. Right: 25% duty cycle. Power density is
normalized for comparison with NRZ format (dotted line).
1.2.2.3 Return-to-One Code
Return-to-one (R1) code uses a static high level for the logical one state
and a short low-level pulse for a zero. Creating an R1-formatted signal from
NRZ data is a bit more complicated than using the RZ format: It's a binary AND
of the inverted NRZ data with the clock, and the result inverted again. Figure 1-19 shows an
example. The properties of R1-coded data are very similar to those of RZ-coded
data, with the exception of the DC content, which is significantly higher than
for RZ-coded signals.
Figure 1-19 R1 coding
of a short data sequence (PRBS 24-1)
1.2.2.4 Manchester Code
Manchester code is generated from NRZ data by a binary XOR with a clock
signal. Since there are two possible clock phases, there are also two variants
of Manchester code. The coded data has a transition in the middle of every bit,
and the direction of this transition indicates a binary zero or one. The
original Manchester variant uses a falling edge for a one and a rising edge for
a zero; the other variant (which is used in IEEE 802.3 10Base-T Ethernet, for
example) is the exact inverse. Figure 1-20 shows
both variants.
Figure 1-20 Manchester
code representation of a short data sequence (PRBS 24-1). Top:
"10" variant. Bottom: "01" variant.
Manchester code is very attractive for embedded clock applications because
it forces at least one transition per bit, even if the data is a constant zero
or one. It is also a DC-balanced code. However, the price for this is a
significantly higher bandwidth relative to NRZ data. Figure 1-21 shows the
spectral densities for two short data sequences. Compared to the NRZ spectrum
(dotted line), the PRBS spectrum has significantly less spectral content at low
frequencies but more at higher frequencies. Spectral nulls are at even
harmonics. The spectrum for the constant one pattern is equal to a 1 GHz square
wave.
Figure 1-21 Power
spectral density for Manchester-coded data at 1 Gbit/s. Left: PRBS 24-1.
Right: Constant one (111111 . . .). Power density is normalized for comparison
with NRZ format (dotted line, left plot only).
1.2.2.5 Non-Return-to-Zero Inverted Code
Non-return-to-zero inverted (NRZI) code is not, as the name suggests, the
mere inversion of an NRZ-coded signal; it is an example of a differential code,
where the state of the signal depends on both the current and the previous bit.
An NRZI-coded signal changes its state when the current bit is a logic one bit
but stays constant if the current bit is a logic zero (Figure 1-22). Using
transitions rather than levels makes detection less error-prone in noise
environments, and the signal polarity is insignificant. NRZI coding is used,
for example, in USB.
Figure 1-22 NRZI
coding of a short data sequence (PRBS 24-1)
The signal properties of NRZI-coded data are similar to those of NRZ data:
The transition density can be between 0.0 (for a constant zero pattern) and 1.0
(for a constant one pattern), and the spectral content for random data is
exactly the same as for NRZ. The NRZI code is therefore not sufficient to
enable data transmission with clock recovery, or to limit the amount of ISI.
1.2.2.6 Differential Manchester Code
Differential Manchester code (DMC) is a combination of Manchester and
NRZI: It uses transitions in the middle of the bit, but the transition
direction changes with everyone in the data stream (Figure 1-23). This coding
can be generated by an XOR function of NRZI-coded data and a clock signal. DMC
is also known as conditional de-phase (CDP) code and used in token ring LANs
(IEEE 802.5).
Figure 1-23 Differential
Manchester coding of a short data sequence (PRBS 24-1)
The properties of data that is coded with DMC are very similar to those of
pure Manchester code: The signal is DC balanced, there is at least one
transition per bit, and the spectrum has low content at lower frequencies but
significantly more high-frequency content than NRZ data has.
1.2.3 Multilevel Line Codes
1.2.3.1 Bipolar Return-to-Zero Code
A variant of the RZ code is bipolar return-to-zero (BPRZ) coding, where
the signal returns to an intermediate zero level after both zero and one bits (Figure 1-24). There are
two transitions per bit, which makes synchronization of the receiver fairly
easy. The drawback is the fairly complicated circuitry and an even higher
bandwidth requirement than for RZ and R1 data. Figure 1-25 shows the
power spectral density for a BPRZ-formatted data sequence.
Figure 1-24 BPRZ
coding of a short data sequence (PRBS 24-1)
Figure 1-25 Power
spectral density for a short BPRZ-formatted data sequence (PRBS 24-1),
at 1 Gbit/s. Left: 50% duty cycle. Right: 25% duty cycle. Power density is
normalized for comparison with NRZ format (dotted line).
1.2.3.2 Pulse Amplitude Modulation
Pulse amplitude modulation (PAM) is a class of multilevel codes that
encodes several consecutive bits into one of several levels. PAM-4, for
example, encodes two bits into one out of four levels (Figure 1-26). Demodulation
is performed by detecting the signal level once per symbol period.
PAM-4-encoded data has much less high-frequency content than, for example, NRZ
data because the signal level changes only for every other bit. However, the
cost is increased transmitter and especially receiver complexity, and a lower
signal-to-noise ratio if the same levels are used. PAM-4 alone is not
sufficient for embedded clock systems, as it does not guarantee transition
density: Constant zero or one patterns are encoded as DC levels. Figure 1-27 shows the
power spectral density for a PAM-4-coded data sequence.
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Figure 1-26 PAM-4
coding of a short data sequence (PRBS 24-1)
Figure 1-27 Power
spectral density for PAM-4-coded data at 1 Gbit/s. Left: PRBS 24-1.
Right: Half-rate toggle (11001100 . . .). Power density is normalized for
comparison with NRZ format (dotted line).
1.2.4 Block Codes
1.2.4.1 mBnB Block Codes
Block codes of type mBnB take m bits of the original data and encode them
into n bits, following very specific rules. Several of the coding schemes from
the previous sections can be expressed as 1B2B codes; RZ coding, for example,
encodes every one bit as a one, followed by a zero, and every zero bit as two
zeros. Widely used in serial high-speed applications are 4B5B and in particular
8B10B coding. The dominant encoding scheme in computing applications, 8B10B
seems to hit a sweet spot with relatively low overhead (25%), ease of
implementation, coding properties such as maximum run length, and so on.
Chapter 3 describes 4B5B and 8B10B coding in greater detail.
1.2.4.2 Error Detection and Forward Error Correction
Some of the block codes from Section 1.3.4.1 enable the receiver to detect
some transmission errors, either from calculating disparity or by detecting
invalid code words. A system that is based on such coding techniques can issue
a packet resend command and transmit the packet again, this time hopefully
without an error. Ideally, however, the receiver would be able to not only
detect errors (all errors, not just a few) but also correct them.
The process of adding redundancy to the data stream and analyzing and
correcting errors in real time is called forward error correction (FEC).
Systems that use FEC can operate with less margin in transmission than non-FEC
systems. In practical applications, this means a longer range between sender
and receiver or reduced transmission power. Especially under difficult
transmission conditions, FEC systems are more effective than non-FEC systems
because fewer packets need to be retransmitted.
1.3 Summary
In this chapter, we've introduced the basic concepts of high-speed serial
transmission systems: clock architectures, line coding, and differential
electrical signaling with preemphasis or receiver equalization.
The remainder of this book describes how we can characterize such a
system, either as a whole or individually for its components. Transmitter tests
verify the electrical performance of the signal before it enters the channel,
while receiver tests verify that the worst-case realistic signals can be
understood by the receiver. Channel tests finally determine the quality of the
transmission medium.
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