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An off - topic question to any math wiz knowledgeable about Smith chart.
There are oodles of stuff about Smith chart, but I have not be able to find
WHAT is the actual scale of the coordinates.
For example
real axis ( R +j0) goes from "zero" (left) to center of the chart - MOST of the time
designated as "one" .
Therefore - what is the scale between 0 and 1 - linear or log?
( No need to discuss log(0))
It PROBABLY makes no difference, but IMHO log scale would "loose" some visual
precision.
Please, no sermons / references about what is Smith chart , how to use it etc.
Sorry to post here , but I have limited choice.

Not a math wiz here but one of the best ways I learned about the chart back in college was to see the mathematical calculations (and thus derivations) for the actual circles. The smith chart has unique scales based on those equations which is why they are different from things you may be used to seeing. Have a look at this simplified (but well written description) of the derivation of the chart and see if that helps you visualize why the scales are so unique and why they look the way they do. I am still in awe at the genius involved almost a century ago for someone to come up with the concept. True brain power & genius.



Gedas, W8BYA EN70

Gallery at
Light travels faster than sound....
This is why some people appear bright until you hear them speak.

Hi,

The scale is neither linear nor logarithmic, and I’m not sure what it is.

Luckily it does not matter if you just want to use the smith chart.

Generally for radio work the centre is defined as 50 ohm; that is a resistance of 50 ohms would be plotted at the centre of the chart, a resistance of 100 ohms would be plotted at the 2.0 position.

The rule is divide whatever the impedance is by 50 and plot the new figure on the chart. Conversely to get a value from the chart take the reading from the chart and multiply by 50 to get the actual values.

It seems complicated but a bit of practice will make it easier.

Good luck

73
John
M0JBA

Actually, the Smith chart is "normalized" to whatever the impedance that you are working with, usually 50 but could be 75 or 450 if open wire feed line.The operation to compute is as John described, Multiply every number on the chart by the impedance you are normalized to.
Gary

Yes but the gentleman wants to know about the scaling of those curves which are defined by the uniquely derived? equations as shown in the URL I posted.

Gedas, W8BYA EN70

Gallery at
Light travels faster than sound....
This is why some people appear bright until you hear them speak.

There is no scale as such. The mathematics provides the translation from the rectangular Z coordinate system to polar and the result of that math transformation yields the curves your are referencing. We and the vna actually only deal with one of the four Chart regions. The Chart actually occupies 4 quadrants.

In 2001, I wrote a paper that constructed the chart and built it in Mathcad. The paper appeared in Applied Microwave. Each piece of the chart, the real axis and the imaginary contours were assembled as individual blocks of these mapping routines. See reference that should provide a link to the paper.



Alan

The Smith Chart coordinates are normalized to the impedance of whatever
system you are using. This is usually 50 Ohms so the 1.0 in the center of
the chart is 50 Ohms resistance, 0 Ohms reactance.

You can take any point on the Smith chart and convert to actual Ohms by
multiplying by the impedance of the system (usually the main transmission
line) you are making measurements in.

For example, the point 1.2 + j.7 is really 6 + j35 in a 50 Ohm system.

The reason for this is that you might be using different impedance
transmission lines in a design and this makes it easy to move between
different impedances.

BTW, there are Smith Charts available with 50 Ohm markings.


On Wed, Mar 25, 2020 at 11:05 AM vaclav_sal via Groups.Io <vaclav_sal=
[email protected]> wrote:

An off - topic question to any math wiz knowledgeable about Smith chart.
There are oodles of stuff about Smith chart, but I have not be able to
find
WHAT is the actual scale of the coordinates.
For example
real axis ( R +j0) goes from "zero" (left) to center of the chart - MOST
of the time
designated as "one" .
Therefore - what is the scale between 0 and 1 - linear or log?
( No need to discuss log(0))
It PROBABLY makes no difference, but IMHO log scale would "loose" some
visual
precision.
Please, no sermons / references about what is Smith chart , how to use it
etc.
Sorry to post here , but I have limited choice.

--
Carey Fisher
careyfisher@...

Why isn't the example = 60 + j35 ???

At 11:24 AM 3/25/2020, Carey Fisher wrote:

The Smith Chart coordinates are normalized to the impedance of whatever
system you are using. This is usually 50 Ohms so the 1.0 in the center of
the chart is 50 Ohms resistance, 0 Ohms reactance.

You can take any point on the Smith chart and convert to actual Ohms by
multiplying by the impedance of the system (usually the main transmission
line) you are making measurements in.

For example, the point 1.2 + j.7 is really 6 + j35 in a 50 Ohm system.

The reason for this is that you might be using different impedance
transmission lines in a design and this makes it easy to move between
different impedances.

BTW, there are Smith Charts available with 50 Ohm markings.

<snip>

Why isn't the example = 60 + j35 ???

Because I dropped a zero. :-)

For example, the point 1.2 + j.7 is really 60 + j35 in a 50 Ohm system.


On Wed, Mar 25, 2020 at 1:54 PM lgo51 <larryo@...> wrote:

Why isn't the example = 60 + j35 ???

At 11:24 AM 3/25/2020, Carey Fisher wrote:

The Smith Chart coordinates are normalized to the impedance of whatever
system you are using. This is usually 50 Ohms so the 1.0 in the center of
the chart is 50 Ohms resistance, 0 Ohms reactance.

You can take any point on the Smith chart and convert to actual Ohms by
multiplying by the impedance of the system (usually the main transmission
line) you are making measurements in.

For example, the point 1.2 + j.7 is really 6 + j35 in a 50 Ohm system.

The reason for this is that you might be using different impedance
transmission lines in a design and this makes it easy to move between
different impedances.

BTW, there are Smith Charts available with 50 Ohm markings.

<snip>

--
Carey Fisher
careyfisher@...

Smith Chart : In this computer era, this extremely high-effort demanding,
highly-inaccurate, old-time graphics tool became completely obsolete,
because it is a totally useless one in every other aspect except that one
of "just take-a-look demo" - or of fancy impression making to unsuspected,
innocent, inexperienced beginners, of course

Like a slide rule. Accurate enough to get useful results and visualize what's happening in a system.

You can be much more accurate by using SimSmith.

--
Art Greenberg
WA2LLN
art@...

I believe that the scale in question is linear... but it's measuring the "reflection coefficient", not "impedance". It has a value of -1 at the "zero ohms, short circuit" end, a value of 0 in the center of the chart, and a value of +1 at the "infinite ohms, open circuit" end.

The equations which go back and forth between reflection coefficient, and impedance in ohms, are neither a simple linear nor simple logarithmic relationship.

Thank you for the suggestion, from which I see now that
I have to correct what I wrote, as follows : for the newcomer,
the whole Great Idea of that very difficult to learn Smith Chart
is just of historic interest, an obsolete one, nowadays - imho,
of course.

Thanks for the reference.
Not bad first response, appreciate that very much.

Cannot say much about the rest of them.
In future I will limit my posts to
"how much is 1 and 1 " , asking to avoid sermons is futile.


Interestingly (?) on FIRST page you wrote "The chart is constructed in a rectilinear system
instead of polar..."
I am not going to dispute that...
Will try both linear and log , but I think the linear is really easier on the eye.
Many thanks.
73 AA7EJ

The Smith chart assumes that the impedances have been "normalized". Just
divide by 50 to get one in the center



Bob

On Wed, Mar 25, 2020, 8:05 AM vaclav_sal via Groups.Io <vaclav_sal=
[email protected]> wrote:

An off - topic question to any math wiz knowledgeable about Smith chart.
There are oodles of stuff about Smith chart, but I have not be able to
find
WHAT is the actual scale of the coordinates.
For example
real axis ( R +j0) goes from "zero" (left) to center of the chart - MOST
of the time
designated as "one" .
Therefore - what is the scale between 0 and 1 - linear or log?
( No need to discuss log(0))
It PROBABLY makes no difference, but IMHO log scale would "loose" some
visual
precision.
Please, no sermons / references about what is Smith chart , how to use it
etc.
Sorry to post here , but I have limited choice.

For people actually designing RF equipment, the Smith Chart is a valuable
tool.

--
Carey Fisher
careyfisher@...

Oooh, si tacuisses !


You try to make believe to be way above it, but:

Is that "innocent, unexperienced beginner" perhaps your own point of view?

This computer era definitely did not come into existence without many thousands of people that used the Smith Chart.

Some people don't have the desire to know more about RF applications than just to watch TV or play games etc.
(where others used the Smith Chart for them so they can do that). If that describes you: That's fine: It is your own choice.
Just click away.

But if you earnestly want to advance in RF design, read on:

Obviously you don't know SimSmith:

It combines highest design value with comparatively little learning effort,
is extremely accurate: both numerically (more accurate digits than you will ever need), graphically highly zoomable,
it has a huge number of possible and most useful applications,
and is so very flexible, that you even can use it for innovative challenges that perhaps nobody ever did before.

It's not perfect, but it is probably the best any Smith Chart user can get.

Hans, DJ7BA



-----Ursprüngliche Nachricht-----
Von: [email protected] <[email protected]> Im Auftrag von Carey Fisher
Gesendet: Donnerstag, 26. M?rz 2020 04:09
An: [email protected]
Betreff: Re: [nanovna-users] Another off-topic about Smith chart

For people actually designing RF equipment, the Smith Chart is a valuable tool.

On Wed, Mar 25, 2020 at 3:10 PM pez@arg <petrosez7@...> wrote:

Smith Chart : In this computer era, this extremely high-effort
demanding, highly-inaccurate, old-time graphics tool became completely
obsolete, because it is a totally useless one in every other aspect
except that one of "just take-a-look demo" - or of fancy impression
making to unsuspected, innocent, inexperienced beginners, of course

--
Carey Fisher
careyfisher@...




--
Diese E-Mail wurde von Avast Antivirus-Software auf Viren geprüft.

"Smith Chart : In this computer era, this extremely high-effort demanding,
highly-inaccurate, old-time graphics tool became completely obsolete,
because it is a totally useless one in every other aspect except that one
of "just take-a-look demo" - or of fancy impression making to unsuspected,
innocent, inexperienced beginners, of course"

Don't know where this idea comes from but it's bollocks. Looking at a smith chart I can instantly get a "feel" of the characteristics of a circuit. There is a reason that when asked to troubleshoot measurements I'll always request to see the smith chart first rather than the logmag plot. I can easily tell apart under-coupled vs over-coupled magnetic loop antennas looking at a smith chart, but they look identical on a logmag plot. Logmag + phase has all the information in theory, but it would take me some minutes of thinking to tell if the magloop is under-coupled or over-coupled. Of course, if I want to know the 10dB bandwidth of the antenna I'll look at logmag instead, there is a time and place for everything.

btw the impedance scale of the middle line on a smith chart is (1+x)/(1-x). It compresses [0, infinity) into [-1, 1]. If you think in terms of reflection coefficient rather than impedance, then the scale of the smith chart is linear and it's nothing more than a polar plot.

It's just 1/x but flipped and shifted ;)

On Wed, Mar 25, 2020 at 03:10 PM, pez@arg wrote:

Smith Chart : In this computer era, this extremely high-effort demanding,
highly-inaccurate, old-time graphics tool became completely obsolete,
because it is a totally useless one in every other aspect except that one
of "just take-a-look demo" - or of fancy impression making to unsuspected,
innocent, inexperienced beginners, of course

And like the current and maybe past few generations who grew up doing math on calculators, they can't even add and subtract without them. When the power goes poof, their tools are gone and they're helpless. Use the fancy programs once you learn the basics behind them. And then maybe you can develop a fancy program, too.

BruceN / K4TQL

--
*"To invent, you need a good imagination and a pile of junk"* -- Thomas Alva Edison (1847-1931)