Smith Chart question

[Reg Edwards]

"> >Old timers now use it only for sentimental, recreational purposes.

As someone who's probably older than the Chart, Reg, I'm surprised to
hear you say that. I believe a lot of folks would disagree with you...

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

Well, half a dozen perhaps. And even they never use it in anger.

Face the facts!

As for me, after 60 years of experience with transmission lines, from 0.1 Hz
to 3 GHz, I have never used the chart other than out of mild curiosity to
discover what other people might do with it. ;o)
---
Reg.

 

[Tom Bruhns]

Yes, conductance. Doi. My mind was a bit of mush when I posted that,
I think. And right you are that the center of the circle is not the
line impedance, in general. Thanks for the corrections.

Cheers,
Tom

lineRick<rik_nntp@dsl.pipex.com> wrote in message news:<SKnkc.15179$k4.308370@news1.nokia.com>...

Tom Bruhns <k7itm@aol.com> wrote:
Getcherself a Smith chart program, and experiment with it. In fact,
you probably already have one in the form of RFSim99. Shunt L's and
C's result in arcs that follow a constant admittance curve. For

no - they follow a curve of constant CONDUCTANCE. No such thing as
a curve of constant admittance.

example, set up a port1 source, and a load consisting of parallel 150
ohm resistor and capacitor of, say, 0.01pF. Simulate. Set the plot
to smith x/y. Set the frequency range to 100MHz to 101MHz. Note that
the point is on the first larger admittance circle from the center of
^^^^^^^^^^^^^^^^^
conductance circle

the plot. Now "tune" the capacitor up in steps and see where the
point goes. Stop when you get to 14.8pF. Now add in a series
inductor between the source and the parallel RC. Start with it very
tiny, and adjust it up. Note that you are moving along a constant
resistance line. Note that when you get to about 112nH, you're at the
center of the chart: 50 ohms in this case. You just designed a
matching network to match from 150 ohms resistive to 50 ohms resistive
at 100MHz. Note that if you swap to a shunt inductor and series
capacitor, you can do the same thing, on the upper half of the chart.
Works for any sort of ladder network you want to put together: pi,
L-pi, T, several sections...

RFSim99's Smith chart, used this way, isn't as nice as something like
WinSmith, but it's servicable.

Try also putting in a section of transmission line: note that the
point moves in a circle centered on the line's characteristic
impedance.

Only if the line's characteristic impedance is the same as the
normalising impedance of the chart. Otherwise, the equation for
the centre of the circle is a bit of a bitch.

 

[Joel Kolstad]

Reg Edwards <g4fgq.regp@ZZZbtinternet.com> wrote:

The Smith Chart went out of date with the invention of the personal
computer.

Be sure to let the folks at Agilent and Tektronix who build the network
analyzers that let you display the results on a Smith Chart to know that...

Seriously, while you can argue that for calculation purposes a Smith Chart
doesn't get you very many digits of precision, it's still a perfectly good,
intuitive way to display data that leads to more physical insight as to how
a network is behaving that, say, plotting S parameters often does.

As an approximation it suffers from serious misleading errors at low
frequencies.

This isn't a problem with the Smitih Chart, it's a problem in that people
don't realize that those 'lossless lines' approximations to their equations
are often no longer good at lower frequencies. I guarantee you that just as
many people would incorrectly use such approximations if they were having to
perform the math themselves directly on a calculator. True, if you just
give them a computer program that uses the full equations and ends up with
the correct results, great, but where's the physical insight in that?

Old timers now use it only for sentimental, recreational purposes.

Hardly -- see above. Hopefully you'd agree that just plotting data in their
'original' domain is not always as useful as applying a mapping (as the
Smith Chart does) to that data.

---Joel Kolstad

 

[Joel Kolstad]

Paul Burridge <pb@notthisbit.osiris1.co.uk> wrote:

It's a pretty horrifying sight for anyone who hasn't seen it before.

It might be better to first present Smith Charts by just mentioning...
hmm... let's see what happens if we just plot the reflection coefficient in
polar coordinates... and then -- many pages late -- lead up to... hmmm... I
wonder what R+jX or G+jB a given point on this 'chart' refers to?

 

[Tom Bruhns]

Rick<rik_nntp@dsl.pipex.com> wrote in message news:<SKnkc.15179$k4.308370@news1.nokia.com>...

Tom Bruhns <k7itm@aol.com> wrote:

Try also putting in a section of transmission line: note that the
point moves in a circle centered on the line's characteristic
impedance.

Only if the line's characteristic impedance is the same as the
normalising impedance of the chart. Otherwise, the equation for
the centre of the circle is a bit of a bitch.

Having not actually gone through that manipulation before, I thought
it might be worthwhile. _IF_ the line impedance is real, and of
course the Smith chart normalization impedance is real, then it's not
too bad. (In fact, properly formulated it shouldn't be bad even for
complex impedances). If r is the magnitude of the reflection
coefficient with respect to the line, whose impedance is Z1 (a real,
not complex, value) and Z0 is the chart normalization impedance, then
the circle will be centered at a Z0 reflection coefficient given by

(Z1^2-Z0^2)/[Z1^2+Z0^2+2*Z1*Z0*(1+r^2)/(1-r^2)]

In that form, it looks like it might have some nice geometric
interpretation involving triangles... Of course, you can convert that
to an impedance (which, of course, will be real-valued).

It's been a good day; I've learned something and internalized it so
I'm not likely to forget it. Thanks, Rick.

Cheers,
Tom

 

[Tim Wescott]

Paul Burridge wrote:

On Fri, 30 Apr 2004 10:50:12 -0400, Active8 <reply2group@ndbbm.net
wrote:


Yeah. Sounds like you got it. When I wrote my (unfinished) smith
chart app's GUI, I had to write the equations for the circles,
calculate the intersections, plot them, and then I said "f it" and
captured different color schemes to use for the app. The whole time
I thought the process sucked because of what the chart really is. A
distorted cartesian plane.

Think of resistance as being the y axis with all horizontal grid
lines representing const R, and the others, const X. remember the
basic triangle that desribes a phasor? the base is the R, the height
is the net X, and the hypotenuse is the Z = R + jX = sqrt(R^2 + X^2)
...

if you take the vertical lines at infinity ( 00 ) , pinch the ends
together and bend them back around to the same point ( 00 ), you get
the R circles. With the horizontal lines, you pinch one end together
and spread the other ends out. Actually, you're pinching both ends,
but bending the top and bottom back around in their respective
directions (leaving the x axis alone) to make 2 families of circles
but the 0 R cicle that bounds the chart makes it look otherwise.


It's a pretty horrifying sight for anyone who hasn't seen it before. I
imagine Mr. Smith was some sort of tortured genius who prolly shot
himself in the head shortly after devising it. Failing that, maybe
someone else should have. ;-)

Actually the Smith chart is one of the few holdovers from the 50's when
_everything_ got calculated on a nomograph of some sort. It does make
oodles of sense when all your measurements are in S parameters and most
of your available reactive components are transmission lines, though.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

 

[Paul Burridge]

On Fri, 30 Apr 2004 15:21:38 -0700, Tim Wescott
<tim@wescottnospamdesign.com> wrote:

Can anyone define "transmission line" in this context?

--

The BBC: licenced at public expense to spread lies.

 

[Rick]

Tom Bruhns <k7itm@aol.com> wrote:

Rick<rik_nntp@dsl.pipex.com> wrote in message news:<SKnkc.15179$k4.308370@news1.nokia.com>...
Tom Bruhns <k7itm@aol.com> wrote:

Try also putting in a section of transmission line: note that the
point moves in a circle centered on the line's characteristic
impedance.

Only if the line's characteristic impedance is the same as the
normalising impedance of the chart. Otherwise, the equation for
the centre of the circle is a bit of a bitch.

Having not actually gone through that manipulation before, I thought
it might be worthwhile. _IF_ the line impedance is real, and of
course the Smith chart normalization impedance is real, then it's not
too bad. (In fact, properly formulated it shouldn't be bad even for
complex impedances). If r is the magnitude of the reflection
coefficient with respect to the line, whose impedance is Z1 (a real,
not complex, value) and Z0 is the chart normalization impedance, then
the circle will be centered at a Z0 reflection coefficient given by

(Z1^2-Z0^2)/[Z1^2+Z0^2+2*Z1*Z0*(1+r^2)/(1-r^2)]

Ahh. Nice - did you derive that expression yourself? When I went
through this a few months ago I couldn't find anything in any of
my numerous books on RF/microwave...they all seem to think that
you're only interested in tlines of the same impedance as that
used to normalise your chart.
I clearly chose the most convoluted method possible to derive
my form of the same equation, in the parametric u-v coordinates:

u = (Ztl*Ztl-Z0*Z0)*(m->real)/(Ztl*Ztl+Ztl*Ztl*(m->real)+Z0*Z0*(m->real)+Z0*Z0*(m->imag)*(m->imag)+Z0*Z0*(m->real)*(m->real));
v = 0 ;

I took the impedance as one point on the circle, transformed
it through a quartwave to another impedance, converted both
of these to u-v coordindates, and that, coupled with the
observation that the circle must lie on the v=0 line is
enough to derive the equation of the circle. The equation
is now nestling somewhere in the 5,000 lines of code that
I've so far written towards my Smith Chart program.

--
Rick

 

[Tim Wescott]

Paul Burridge wrote:

On Fri, 30 Apr 2004 15:21:38 -0700, Tim Wescott
tim@wescottnospamdesign.com> wrote:

Can anyone define "transmission line" in this context?

Two parallel inductors with a constant characteristic impedance (called
"instantaneous impedance in the '40s, which makes more sense to me).
Could be coax, twin-lead, stripline, microstrip, etc.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

 

[Active8]

On Sat, 01 May 2004 17:32:57 -0700, Tim Wescott wrote:

Paul Burridge wrote:

On Fri, 30 Apr 2004 15:21:38 -0700, Tim Wescott
tim@wescottnospamdesign.com> wrote:

Can anyone define "transmission line" in this context?


Two parallel inductors with a constant characteristic impedance (called
"instantaneous impedance in the '40s, which makes more sense to me).
Could be coax, twin-lead, stripline, microstrip, etc.

IIRC, you can use the scales on the perimeter of the chart and/or
the bottom scales to design your microstrip stubs *as well as* the
matching sections. Pretty cool chart, really. I wish I could find a
comprehensive online reference that covers it all as opposed to bits
and pieces.
--
Best Regards,
Mike

 

[Active8]

On 01 May 2004 15:01:40 GMT, Rick wrote:

Tom Bruhns <k7itm@aol.com> wrote:
Rick<rik_nntp@dsl.pipex.com> wrote in message news:<SKnkc.15179$k4.308370@news1.nokia.com>...
Tom Bruhns <k7itm@aol.com> wrote:

Try also putting in a section of transmission line: note that the
point moves in a circle centered on the line's characteristic
impedance.

Only if the line's characteristic impedance is the same as the
normalising impedance of the chart. Otherwise, the equation for
the centre of the circle is a bit of a bitch.

Having not actually gone through that manipulation before, I thought
it might be worthwhile. _IF_ the line impedance is real, and of
course the Smith chart normalization impedance is real, then it's not
too bad. (In fact, properly formulated it shouldn't be bad even for
complex impedances). If r is the magnitude of the reflection
coefficient with respect to the line, whose impedance is Z1 (a real,
not complex, value) and Z0 is the chart normalization impedance, then
the circle will be centered at a Z0 reflection coefficient given by

(Z1^2-Z0^2)/[Z1^2+Z0^2+2*Z1*Z0*(1+r^2)/(1-r^2)]

Ahh. Nice - did you derive that expression yourself? When I went
through this a few months ago I couldn't find anything in any of
my numerous books on RF/microwave...they all seem to think that
you're only interested in tlines of the same impedance as that
used to normalise your chart.
I clearly chose the most convoluted method possible to derive
my form of the same equation, in the parametric u-v coordinates:

u = (Ztl*Ztl-Z0*Z0)*(m->real)/(Ztl*Ztl+Ztl*Ztl*(m->real)+Z0*Z0*(m->real)+Z0*Z0*(m->imag)*(m->imag)+Z0*Z0*(m->real)*(m->real));
v = 0 ;

I took the impedance as one point on the circle, transformed
it through a quartwave to another impedance, converted both
of these to u-v coordindates, and that, coupled with the
observation that the circle must lie on the v=0 line is
enough to derive the equation of the circle. The equation
is now nestling somewhere in the 5,000 lines of code that
I've so far written towards my Smith Chart program.

LOL. That's way more lines than I've written, maybe IIRC, right
now I basically have classes to convert between Z, Y, and S params
and do the math on those complex (or polar) numbers. I think you can
multiply say a Z param with an S param. It's a bunch of function
overloading wrapped up in the param classes which derive from an
abstract base class, Param.

I managed to get a "Series C" button working that starts with the
last plotted point and restricts the cursor movement to the constant
R circle as you move the mouse. Get to where you're going and click
to plot the point and draw the arc. The status bar shows the cursor
position in 3 parameters and I think it's close enough to show the
net impedamce change and component value if a frequency is
specified, which must be done to get 2 port calculations done from
an s-param (or whatever) file. It calculates MAG, plots the params,
and does constant gain circles and conjugate match.

--
Best Regards,
Mike

 

[Terry Given]

"Active8" <reply2group@ndbbm.net> wrote in message
news:reug1oiknjuz.dlg@news.individual.net...

On Sat, 01 May 2004 17:32:57 -0700, Tim Wescott wrote:

Paul Burridge wrote:

On Fri, 30 Apr 2004 15:21:38 -0700, Tim Wescott
tim@wescottnospamdesign.com> wrote:

Can anyone define "transmission line" in this context?


Two parallel inductors with a constant characteristic impedance (called
"instantaneous impedance in the '40s, which makes more sense to me).
Could be coax, twin-lead, stripline, microstrip, etc.

IIRC, you can use the scales on the perimeter of the chart and/or
the bottom scales to design your microstrip stubs *as well as* the
matching sections. Pretty cool chart, really. I wish I could find a
comprehensive online reference that covers it all as opposed to bits
and pieces.
--
Best Regards,
Mike

didn't Smith write a book ?

 

[Active8]

On Sun, 2 May 2004 15:16:07 -0700, Terry Given wrote:

"Active8" <reply2group@ndbbm.net> wrote in message
news:reug1oiknjuz.dlg@news.individual.net...
On Sat, 01 May 2004 17:32:57 -0700, Tim Wescott wrote:

Paul Burridge wrote:

On Fri, 30 Apr 2004 15:21:38 -0700, Tim Wescott
tim@wescottnospamdesign.com> wrote:

Can anyone define "transmission line" in this context?


Two parallel inductors with a constant characteristic impedance (called
"instantaneous impedance in the '40s, which makes more sense to me).
Could be coax, twin-lead, stripline, microstrip, etc.

IIRC, you can use the scales on the perimeter of the chart and/or
the bottom scales to design your microstrip stubs *as well as* the
matching sections. Pretty cool chart, really. I wish I could find a
comprehensive online reference that covers it all as opposed to bits
and pieces.
--
Best Regards,
Mike

didn't Smith write a book ?

yeah. ? ...
--
Best Regards,
Mike

 

[Rick]

Paul Burridge <pb@notthisbit.osiris1.co.uk> wrote:

On Fri, 30 Apr 2004 15:21:38 -0700, Tim Wescott
tim@wescottnospamdesign.com> wrote:

Can anyone define "transmission line" in this context?

Series and parallel combinations of transmission lines can be used as
matching components (and also used to create filters, couplers and much
more besides).

Adding an a transmission line in series with any given impedance will
spin you round the smith chart - the longer the line, the further round
you go until you get back to where you started. This fact alone means
that a series combination of a resistor and the right length of line will
get you anywhere on the chart, so you can perhaps see that transmission
lines are as useful in impedance-matching as lumped-elements.

--
Rick

 

[Terry Given]

"Active8" <reply2group@ndbbm.net> wrote in message
news:nj32havs742m$.dlg@news.individual.net...

On Sun, 2 May 2004 15:16:07 -0700, Terry Given wrote:

didn't Smith write a book ?

yeah. ? ...
--
Best Regards,
Mike

well said.

Is it any good?

Cheers
Terry

 

[Paul Burridge]

On Sun, 2 May 2004 15:16:07 -0700, "Terry Given"
<the_domes@xtra.co.nz> wrote:

"Active8" <reply2group@ndbbm.net> wrote in message
news:reug1oiknjuz.dlg@news.individual.net...
On Sat, 01 May 2004 17:32:57 -0700, Tim Wescott wrote:

Paul Burridge wrote:

On Fri, 30 Apr 2004 15:21:38 -0700, Tim Wescott
tim@wescottnospamdesign.com> wrote:

Can anyone define "transmission line" in this context?


Two parallel inductors with a constant characteristic impedance (called
"instantaneous impedance in the '40s, which makes more sense to me).
Could be coax, twin-lead, stripline, microstrip, etc.

IIRC, you can use the scales on the perimeter of the chart and/or
the bottom scales to design your microstrip stubs *as well as* the
matching sections. Pretty cool chart, really. I wish I could find a
comprehensive online reference that covers it all as opposed to bits
and pieces.
--
Best Regards,
Mike

didn't Smith write a book ?

Not sure about the author, but there is at least one whole book
devoted solely to the use of the Chart!
--

The BBC: licenced at public expense to spread lies.

 

[Paul Burridge]

On 02 May 2004 11:01:39 GMT, "Rick" <rik_nntp@dsl.pipex.com> wrote:

Paul Burridge <pb@notthisbit.osiris1.co.uk> wrote:
On Fri, 30 Apr 2004 15:21:38 -0700, Tim Wescott
tim@wescottnospamdesign.com> wrote:

Can anyone define "transmission line" in this context?

Series and parallel combinations of transmission lines can be used as
matching components (and also used to create filters, couplers and much
more besides).

Adding an a transmission line in series with any given impedance will
spin you round the smith chart - the longer the line, the further round
you go until you get back to where you started. This fact alone means
that a series combination of a resistor and the right length of line will
get you anywhere on the chart, so you can perhaps see that transmission
lines are as useful in impedance-matching as lumped-elements.

Doesn't capacitance come into these lines at all???
--

The BBC: licenced at public expense to spread lies.

 

[Active8]

On Sun, 2 May 2004 22:54:35 -0700, Terry Given wrote:

"Active8" <reply2group@ndbbm.net> wrote in message
news:nj32havs742m$.dlg@news.individual.net...
On Sun, 2 May 2004 15:16:07 -0700, Terry Given wrote:

didn't Smith write a book ?

yeah. ? ...
--
Best Regards,
Mike

well said.

Is it any good?

Cheers
Terry

I may have to buy it to find out. It's usually cited in the
references of books and web resources that scratch the surface. I
just found some Agilent ANs from

http://www.sss-mag.com/pdf1.html

that I hadn't seen before.
--
Best Regards,
Mike

 

[Active8]

On Sun, 02 May 2004 14:09:47 +0100, Paul Burridge wrote:

On 02 May 2004 11:01:39 GMT, "Rick" <rik_nntp@dsl.pipex.com> wrote:

Paul Burridge <pb@notthisbit.osiris1.co.uk> wrote:
On Fri, 30 Apr 2004 15:21:38 -0700, Tim Wescott
tim@wescottnospamdesign.com> wrote:

Can anyone define "transmission line" in this context?

Series and parallel combinations of transmission lines can be used as
matching components (and also used to create filters, couplers and much
more besides).

Adding an a transmission line in series with any given impedance will
spin you round the smith chart - the longer the line, the further round
you go until you get back to where you started. This fact alone means
that a series combination of a resistor and the right length of line will
get you anywhere on the chart, so you can perhaps see that transmission
lines are as useful in impedance-matching as lumped-elements.

Doesn't capacitance come into these lines at all???

Yeah but they have inductance too, That's why they're disttributed
low pass filters and they transform impedance.
--
Best Regards,
Mike

 

[Reg Edwards]

Not sure about the author, but there is at least one whole book
devoted solely to the use of the Chart!

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

In the absence of anything more useful or of more practical use to write
about, almost anything will make a meagre living for authors and publishers.
But provided readers obtain some reiterated, sentimental, perhaps
educational satisfaction, why not? ;o)

I take a quiet unemotional viewpoint. No doubt with objections from elderly
Smith Chart, slide-rule and log-table worshippers. But Mr Smith's chart has
served its purpose and is out of date.

Historically, the chart was a simplified version of sets of charts which
first found their use in the Victorian and Heaviside age of power lines,
telegraph and carrier-telephony lines. Which charts went out of date in the
1940's.

Smith's solitary much simplified chart, because of its convenience and
despite its errors and assumptions, extended the use of charts into the age
of HF coaxial transmission lines, radar and TV, and, of course, early
digital transmission systems.

( Note: This relatively old class of charts was originally invented to
provide solutions to very practical transmission line engineering problems
involving complex hyperbolic functions. Such functions are unavoidable where
transmission line analysis is involved.

It is almost impossible to get one's grey matter around apparently simple
mathematical functions such as Tanh(A+jB), the Hyperbolic Tangent of A + jB.
It takes a long period of eduction even to understand the intermediate
graphical 'explanations' generated by charts.

These days the personal computer can provide an immediate picture of what is
taking place on a transmission line. Provided you are sufficiently
knowledgeable to enter the correct data. And, of course, if you are one of
the exceedingly few people who need to know. )
----
Reg.