Over the years,
we've come to appreciate a good mathematical
spreadsheet. With a mathematical spreadsheet
tool, you can compose pictures, include
explanatory text, and insert "live"
equations in a single document. For
high-speed design problems, where you need
to document calculations pertaining to
physical circuit dimensions, the benefits
are obvious. Compared to regular
spreadsheets, the mathematical spreadsheets
have the advantage of showing your
work. You can see the equations. So
can your co-workers.
The mathematical spreadsheet concept is not
unique. Math spreadsheet applications are
available from several vendors. Popular
versions include
MathCad,
Mathematica, and MatLab. We happen to be
MathCad users
(although any will accomplish the basic
purpose of recording graphics, text and
equations). As a result, our collection of
high-speed design utilities have been
formatted for use with the MathCad
application. You will need the MathCad
application to run these spreadsheets. If
you use a different spreadsheet, it's not
hard to convert one format to another. If
you would
like to order MathCad, follow the link above
or call 1-800-628-4223. At the current
prices, it's a steal.
Click to view an
HTML version of the indicated file. Look
here for help on
how to add MathCad file types to your
system. You can download
the Mathcad files from .zips below.
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The
following MathCad scripts are
taken from
High-Speed Digital Design: A Handbook
of Black Magic". |
Constants |
Listing of various constants (electric
permittivity of free space, magnetic
permeability, speed of light, etc.
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General Relations Among Transmission
Line Parameters |
Relations of impedance and delay to
inductance and capacitance per unit
length. Reflection formula.
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Inductance of Circular Loop |
Includes effect of wire diameter.
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Mutual Inductance of Two Transmission
Lines |
Can be used to calculate crosstalk in
cases where the risetime exceeds the
round-trip delay (i.e., where there is
a lumped-element system).
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Microstrip Transmission Lines |
Inductance, capacitance, impedance,
and delay per inch for microstrips
(PCB trace on outer layer).
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Transmission Line Made from Round Wire
(Wire-Wrap) |
Inductance, capacitance, impedance,
and delay per inch for round-wire
transmission lines (wire-wrap or
multi-wire).
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Transmission Line made From Twisted Pair
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Inductance, capacitance, impedance,
and delay per inch for twisted-pair
transmission line.
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DC Resistance of Copper Wires and Traces
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Includes conversion of wire gauge (AWG)
to wire diameter, and PCB plating
weight to copper thickness.
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Capacitance of Two Parallel Plates
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The simplest formula, with no
fringe-field effects.
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Coaxial Transmission Line
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Inductance, capacitance, impedance,
and delay per inch for coax.
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Mutual Inductance of Two Loops
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Estimates mutual coupling for adjacent
loop structures, like those in a
connector.
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Inductance of Rectangular Loop
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Includes effect of wire diameter.
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Stripline Transmission Line |
Inductance, capacitance, impedance,
and delay per inch for strip lines
(PCB trace between two GND/PWR plane
layers).
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Transmission Line Simulator (Newly
Created Model) |
Includes effects of source impedance,
load impedance, transmission line
delay and characteristic impedance,
and risetime of driving waveform. Does
not incorporate skin-effect loss.
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MathCad Downloads:
These discussions of the derivation
of particular equations in the book may
interest you:
-
Skin Effect Calculations: Special
discussion on derivation of Skin
Effect Calculations in
High-Speed
Digital Design: A Handbook of Black
Magic
- Resistance: Concerning the
derivation on page 414 of the equation
for calculating the DC resistance of
power planes based on the diameters of
two contact points space at X amount
of distance. (newsletter v1-11)
- Ground-bounce calculations: On
page 62 of the High-Speed Digital
Design Text… where does the factor of
1.52 come from? (newsletter v1-12)
- Equiv. Circuit Source Impedance:
What is the true source impedance of
the equivalent circuit at figure 1.6
(page 13)? (newsletter v2-09)
- Via
Capacitance: On page 257, formula
[7.6] for the capacitance of a via is
a crude approximation--I've now got
some better material. (newsletter
v5-09)
- Via
Inductance: On page 259, formula
[7.9] glosses over the location of the
signal return current associated with
the via. A full discussion of the
issue is now available. (newsletter
v6-04)
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