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 renormalised. 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, moreorless, 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] <ukmicrowaves@...> wrote:


Barry Chambers
Brian Yes, I would second your suggestion about renormalisation. 73 Barry, G8AGN


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
From: mailto:ukmicrowaves@...
Sent: Saturday, July 09, 2016 12:54 PM
To: ukmicrowaves@...
Subject: [ukmicrowaves] Re: Smith Chart Hi Andy, Barry and Mark, No virus found in this
message.


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 straightforward 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. The impedance circle will also pass through the load impedance Zload. I find the free Smith chart software from Fritz Dellsperger useful to illustrate this process. It will allow you to add different components (up to five, R, L, C, lines, series and shunt, which is sufficient for most matching purposes). Try a line length of 0.499 lambda for drawing the circle because using 0.5 lambda is the same as zero lambda. I hope this helps. Marcus G0IJZ

