#### Smith Chart

Andy G4JNT

Can anyone remember :

On a smith chart normalised to Zo, is it possible to move along a transmission line with a different characteristic impedance using a single (paper / pen / dividers compass) action?

And if so, what's the procedure?   I very vaguely recall someone doing it, but not too sure when / who / why / how

Or does the Smith chart have to be renormalised to the new Zo with the impedance recalculated and replotted?

Andy  G4JNT

Brian Flynn GM8BJF

Hi Andy,

I get involved in this a bit. I have always read off the impedance/admittance and re-normalised. I have never come across the procedure you suggest. I do this fairly regularly to design quarter wave matching sections when the the impedances are not real.

73s

Brian, GM8BJF.
--

Andy G4JNT

The  reply below from Mark was sent direct  :

Which is, more-or-less, what I can now recall being shown all those years ago.   It works for quarter wave transformers
Honour is satisfied and it appears that route was only ever a quick approximation for an impedance that had a mostly real component.

So there isn't an exact way of doing it - I felt all along it wasn't possible as a 'correct' Smith chart procedure!  At least without renormalising.
Much prefer calculation and software for microwave design than the manual Smith chart of old.

Andy  G4JNT

>Andy
>sorry I cant reply to the list, I am away from home and don't have the correct email account set up
>In answer to the question, a slightly reserved yes
> simply place the rotation point  on the real axis   at the 50 ohm normalised value ( eg. rotate round 1.5 for 75 ohm >system on a 50 ohm chart)
> for  rotations that don't result in a large reactive transformed impedance this is really quite accurate (ie.1/4 wave >rotations and multiples of this)
>
>there is an increased error in both the displayed real and imaginary components with rotations further from the >centre and with those that result in points away from the real axis.
> there is a mathematical correction that can be applied, but that last time i looked at that was 35 years ago
> look up shifting the iconocentre
>
>hope that helps
>Mark

On 8 July 2016 at 11:52, 'brian.flynn@...' brian.flynn@... [ukmicrowaves] wrote:

Hi Andy,

I get involved in this a bit. I have always read off the
impedance/admittance and re-normalised. I have never come across the
procedure you suggest. I do this fairly regularly to design quarter wave
matching sections when the the impedances are not real.

73s

Brian, GM8BJF.
--

Barry Chambers

Brian

```73

Barry, G8AGN```
On 08/07/2016 11:52, 'brian.flynn@...' brian.flynn@... [ukmicrowaves] wrote:

Hi Andy,

I get involved in this a bit. I have always read off the
impedance/admittance and re-normalised. I have never come across the
procedure you suggest. I do this fairly regularly to design quarter wave
matching sections when the the impedances are not real.

73s

Brian, GM8BJF.
--

Brian Flynn GM8BJF

Hi Andy, Barry and Mark,

I can see Mark's suggestion will be good enough for most practical cases, but as I teach
this stuff I have to show the students how to do it "properly", ;-) . By the time the correction
is done it sounds simpler to normalise!

73s
Brian GM8BJF.

Mark GM4ISM

I agree Brian,
the graphical rotating around real impedances away from the normalised value works well only for a limited  range of transformations.  It is particularly useful for determining the intermediate impedance for a single or double quaterwave transformer.

This was taught  on BBC Shortwave stations as a quick and easy way of matching  antennas  in the days before computers and vector network analysers became  everyday objects.  Even then the graphical method was frowned upon when it came to formal training on Smith Charts at the BBC.

The technique of shifting the iconocentre, if I recall came into its own when the iconocentre about which it was necessary to rotate was complex itself.  This makes normalising ‘difficult’ and the mathematics of correcting for  a rotation about a complex impedance became less difficult, relatively.
I don’t remember much about it  but the case that always came up in the exam ( this was taught at University) was for a coax to waveguide transition.
It made my brain hurt then and it has never been needed in anger in my 30+ years as a professional antenna engineer, which is why I have all but forgotten it.

Regards
Mark GM4ISM

Sent: Saturday, July 09, 2016 12:54 PM
Subject: [ukmicrowaves] Re: Smith Chart

Hi Andy, Barry and Mark,

I can see Mark's suggestion will be good enough for most practical
cases, but as I teach
this stuff I have to show the students how to do it "properly", ;-) . By
the time the correction
is done it sounds simpler to normalise!

73s
Brian GM8BJF.

No virus found in this message.
Checked by AVG - www.avg.com
Version: 2016.0.7640 / Virus Database: 4613/12584 - Release Date: 07/09/16

marcuswalden@...

Andy, All

I don't know how to calculate the centre of the circle but if you know the VSWR on the transmission line then you know the resistances that the impedance circle must pass through. These values give you the diameter of the circle and then it's a straight-forward step to work out the centre (which will be close to the line characteristic impedance) and draw the circle on paper.

For example, a complex load Zload gives a VSWR V (you'll need to calculate this) on our transmission line Zline (which is different to the normalising impedance Z0).

The impedance circle must pass through a low resistance given by Zline / V and a high resistance given by Zline x V.