Regarding the long-lasting, 67-years old, love affair with the Smith
Chart.

Where there's Love there's Beauty.

The beauty of a Smith Chart derives from the underlying Mathematics.
Mathematics is pure intellectual beauty.

In this case the underlying functions and their inverses are the
Complex Hyperbolic Functions like Sinh, Cosh and Tanh which Victorian
engineers were familiar with. The behaviour of the early telegraph,
telephone and power lines was exactly described by such functions. The
maths had been quietly waiting for many years for transmission lines
to
be invented.

In the absence of computers, engineers soon got fed up with designing
transmission lines, solving complex hyperbolic equations with the aid
of log tables and slide rules, and began to use graphical methods in
the form of charts.

Now, complex hyperbolic functions are 3 dimensional things. They have
two linear dimensions and angles. They cannot be represented on a flat
paper chart. They need a whole stack of charts. Such stacks of charts
were available round about the Boer War. So whilst the British Army
was setting up concentration camps in South Africa, phone engineers
were busy in their factory offices worrying about SWR on power and
long-distance telephone lines.

The Victorian multi-dimensional charts remained in use through the
days of VLF and LF radio and for 5 decades until the advent of
computers. Bear in mind the charts were just a more convenient
means of accessing data than from books of mathematica tables,
although they were of much lower precision.

See if you can find it - "A Chart Atlas of Complex Hyperbolic
Functions", A. E. Kennelly, Harvard University, 1914.

Worldwide HF radio rapidly expanded from the early 1930's. In 1938 a
certain Mr Smith noticed that at HF and higher frequencies, for rough
and ready calculations he had to use only one of the stack of charts.
This particular chart corresponded to the case of a lossless line and
when Zo was purely resistive. No real lines have zero loss or have a
purely resistive Zo. But practical lines have a sufficiently low
attenuation per wavelength and a Zo whose angle converges towards zero
with increasing frequency, for a single chart on a flat sheet of paper
to deal with sufficient accuracy calculations at frequencies down to
LF. So Mr Smith exercised his artistic talents to produce the chart we
are familiar with. Or at least which we have heard about.
----
Reg.














"Reg Edwards" wrote in message
...
Reg, you've aroused my curiosity on three points:

Why would you use 'Smith Chart' and 'anger' in the same sentence?

========================================
Just a figure of speech. "Anger" suggests setting about a job with
energy, determination and a sense of purpose. As distinct from
mere
amusement.
========================================
Why are there any frequencies where the Smith Chart is misleading
and useless?
Which frequencies are they?
========================================
Depending on the size of the errors one is prepared to tolerate and
on
the calculated parameter of interest -

Frequencies at which line attenuation per wavelength is not small.
Frequencies at which Zo is not purely real.
Frequencies at which CR is not equal to LG.
Frequencies at which the reflection coefficient is greater than 1.0

Comment : Zo is never purely real. CR is never equal to LG.
And the chart is good only to 2-digit accuracy anyway.

But Walt, you already know all this. Have you ever tried the Jones
Chart? ;o)
========================================

How can you say the Smith Chart is misleading and useless if
you've
never used
one, and never inspected one for more than a minute?

Walt, W2DU

========================================

No problem! Worked it out for myself many years ago. Some years
ago
I introduced to this newsgroup the excellent book "Transmission
Lines"
by Robert A. Chipman, 1968. It aroused some interest. Some of you
obtained a copy.

It has a whole chapter devoted to the Smith Chart and fully
describes
its limitations, imperfections, short-comings and approximations.

But the reason Chipman included the chapter was because of the great
savings in labour and time (in HIS day and age) when doing
approximate
calculations on short, low loss, HF transmission lines such as
antenna
feedlines for which it was designed. Which is all radio amateurs
ever
use it for. Hardly any amateurs ever use it in anger. It has other
applications.

I first programmed a computer for work on transmission lines around
1960. At frequencies between 0.1 Hz and 1 MHz, frequencies at which
nobody would dream of using a Smith Chart. So I never became
addicted
to it.
----
Reg.