[hsdd] High-Speed Digital Design Newsletter CHIP-SCALE TRANSMISSION LINES
- From: "Dr. Howard Johnson" <howie03@xxxxxxxxxx>
- To: <hsdd@xxxxxxxxxxxxx>
- Date: Wed, 28 Jan 2004 15:33:54 -0800
CHIP-SCALE TRANSMISSION LINES
HIGH-SPEED DIGITAL DESIGN - online newsletter -
Vol. 7 Issue 01
This winter brought lots of snow and cold weather to
our region. I can't say we enjoyed the storms, but
the skiing has been terrific.
Over the holidays, I have been preparing for a busy
spring season teaching my new Advanced High-Speed
Signal Propagation course, in addition to
maintaining and re-arranging some of the material in
my original course, High-Speed Digital Design.
Thanks to all who have written with questions or
discussion about these courses (and many other
topics).
This month's letter concerns an important topic from
the advanced class: the difference between chip-
scale and pcb-scale transmission lines.
The original course deals with a broad spectrum of
high-speed phenomena. It builds a solid
understanding of ringing, crosstalk, ground bounce,
and power supply noise as they exist on printed
circuit boards. It emphasizes basic circuit
configurations where these effects may be easily
understood and learned. It treats supplementary
subjects including chip packages, oscilloscope
probes, and power systems for high-speed digital
products.
The new Advanced course, and the book that
accompanies it, is more highly specialized, delving
into issues relevant to transmission at the upper
limits of speed and distance. If you need to
transmit faster and further than ever before,
especially if you are contemplating systems above
1 GHz on printed circuit boards or long cables, this
is a terrific course for you.
! ATTENTION INTEL EMPLOYEES ! I will be in Hillsboro, OR
on February 9-10 for a private presentation of my new
Advanced Class. The seminar is open to all Intel
employees. If you're interested in attending, please
contact Jennifer at 509-997-0505 for jennifer@xxxxxxxxxxx
I'll be at DesignCon in the Bay Area next week, and will
be taking part in a panel discussion on "Establishing
Pass-Fail Criteria for High-Speed Digital Interfaces" on
Tuesday, Feb. 3rd at 4:00 PM. Stop by if you're in the area.
______________________________________________________
CHIP-SCALE TRANSMISSION LINES
The key differences between chip-scale transmission
lines and pcb-scale transmission lines can be
gleaned from examination of the propagation function
H.
Signals propagating along any transmission
structure, whether on-chip or off-chip, experience a
certain degree of attenuation H as they pass through
each unit length section of the structure. The value
of H varies dramatically between different types of
transmission structures and also as a function of
frequency, but, within any particular structure, at
any one particular frequency, you may assume the
attenuation H remains the same in each section of
that line.
Suppose you inject a sine wave into a long
transmission line having an attenuation factor (at
your sine wave frequency) of H per meter. As your
signal passes through many meters of transmission
line, each with a predefined attenuation of H, the
overall amplitude of your propagating signal clearly
decreases exponentially with distance. The value of
H determines how rapidly the signal decays as it
moves along the line.
The value of H is a complex number. The magnitude of
H specifies the gain of each unit length of the
line, while the phase of H specifies the phase
shift. A long transmission line acts like a cascade
of filters H, with each filter contributing to the
overall attenuation and phase shift of your signal.
Let's look next at two particular examples of H.
First, consider an RC line model, shown in Figure 1.
The circuit shown represents the behavior of one
short section of an RC transmission line.
Figure 1-A sine wave voltage source drives an RC
line model. The line model comprises five stages,
each having twenty ohms in series with the signal
followed by 0.5 pF shunting the signal to ground.
The voltage x(t) is measured at the source; y(t)
is measured after the fifth stage. The full
figure is included in the web version of this
article: http://www.sigcon.com/Pubs/news/7_01.htm
If you don't remember anything else from this
discussion, remember this: when the RC filter delays
an input signal, making y(t) substantially different
from x(t), there must at that time exist a
substantial voltage drop across the chain of
resistors. The voltage drop thus developed causes
each resistor to dissipate a significant amount of
power. This loss of power translates ultimately into
attenuation of the input signal amplitude.
In the example of Figure 1, at a sine wave frequency
of 1 GHz the circuit produces a phase delay of 47
degrees with a 2-dB loss of signal amplitude. The
moral of this story is that you can't build much
phase delay using an RC circuit without losing a lot
of your signal amplitude.
Next let's consider a different line model: the LC
circuit (Figure 2). This circuit, like figure 1,
also forms a low-pass filter, but with one key
difference. In this circuit, you can accumulate
plenty of phase delay without loss of signal
amplitude. At a frequency of 1 GHz, this circuit
produces the same 47 degrees of phase delay but with
negligible loss of signal amplitude. Even larger
phase shifts are possible at higher frequencies.
This difference between this and the previous
circuit is that here the voltage differences from
stage to stage are sustained by inductors, not
resistors. The inductors dissipate zero net power;
therefore, all the signal power transmitted by the
source is conveyed faithfully to the load. Remember
this: an LC circuit can provide a very large phase
shift (i.e., time delay) with little or no signal
attenuation.
Figure 2-A sine wave voltage source drives an LC
line model. The line model comprises five stages,
each having 1.25 nH in series with the signal
followed by 0.5 pF shunting the signal to ground.
The last stage is followed by a 50-ohm
termination to ground. The voltage x(t) is
measured at the source; y(t) is measured across
the termination resistor. The full figure is
included in the web version of this article:
http://www.sigcon.com/Pubs/news/7_01.htm
Practical transmission circuits always combine some
amount of both resistance and inductance; they are
never purely one or the other. It is, however,
useful to consider the pure RC and LC forms because
they approximate what happens in two very important
cases.
On-chip, the interconnections are so tiny (i.e.,
have such a small cross-section) that the resistance
of the connections, at modest operating speeds,
overwhelms the effect of series inductance. Series
resistance, not inductance, mostly dominates on-chip
interconnections in a 130-nm chip architecture.
On-board, the cross-section of a pcb trace is huge
by comparison to a chip interconnect. Scaling the
cross-section makes the per-unit length resistance
of a pcb trace a whole lot smaller but doesn't
affect the per-unit length inductance that much. As
a result, the roles of resistance and inductance in
a pcb trace are swapped-in a pcb trace, the
inductance matters most. At any digital logic speed
above 10 MHz, typical pcb traces act mostly like LC
structures.
Now comes the conclusion of this article: on-chip
interconnections rarely require termination, but pcb
traces often do. This conclusion is directly related
to the properties of RC and LC transmission lines.
In an RC structure, any time you make a line long
enough to build up a substantial phase shift (or
round-trip delay), the line naturally provides a
corresponding amount of signal attenuation. In such
an environment you can't produce the round-trip
reflections necessary to cause problems with ringing
and overshoot. Long lines naturally come with their
own built-in damping.
In an LC structure, you can easily construct a low-
loss line with huge amounts of phase shift (or round-
trip delay). In this environment, a signal can
bounce many times from end to end within your
transmission structure without degrading. The only
cure for objectionable bouncing in an LC line is a
termination at one end of the line, the other, or
both.
Best Regards,
Dr. Howard Johnson
EXTRA FOR EXPERTS: Those of you already conversant
with the propagation function H may recognize that
this discussion applies only to linear, time-
invariant, TEM-mode systems with propagation
occurring in one direction.
The calculation of line resistance and inductance,
and the determination of the effective mode of
operation, is included in the new Advanced High-
Speed Signal Propagation course. The course
contemplates other modes of operation including the
skin-effect-limited mode, the dielectric-loss-
limited mode, and the waveguide mode.
______________________________________________________
The new Advanced course is available in public and
private venues around the world. The next public
classes will be in Boston during the week of March
1-5. The complete schedule of public classes is
posted at www.sigcon.com -- You can arrange private
presentations through my business office at
info@xxxxxxxxxx (U.S. tel. 509.997.0505).
Dr. Johnson is the featured signal integrity
columnist for EDN Magazine (www.ednmag.com). All his
EDN publications appear at www.sigcon.com under
"Archives".
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