Understanding Smith Charts

[binhexoctdec]

Hi everyone,

I'm wondering if given a particular load impedance (Zl) and some general information such as length of the transmission line, characteristic impedance (Zo) and wavelength λ how would you be able to determine shortest distance from the load to the location on the line where the line impedance has its highest inductive reactance?

Thanks!

 

[yungman]

Plot the point, use a compass with the needle at the center, the other side on the point. Draw a circle and find the value you want on the circle! Simple!

But highest inductance don't mean a thing, because each point is a combination of L and C either in series or parallel.

Make sure you go clockwise for the length of the tx line.

 

[jsgruszynski]

Hi everyone,

I'm wondering if given a particular load impedance (Zl) and some general information such as length of the transmission line, characteristic impedance (Zo) and wavelength λ how would you be able to determine shortest distance from the load to the location on the line where the line impedance has its highest inductive reactance?

Thanks!

http://radiomagonline.com/media/2010/0910/009rad0701_Large.jpg

http://na.tm.agilent.com/pna/help/latest/smith_chart.gif

1. Find the load impedance on the Smith Chart. This is always a single point on the chart. (In other uses of a Smith Chart you can start with the point of the source Thevenin impedance).
   
2. Draw line from the center through the point to the radial perimeter - this is the phase offset of the load (or if you started with the source Thevenin, the source Thevenin phase)
   
3. Increase or decrease the angle along the radial perimeter (there is a direction labeled "toward generator" (CCW) or "away from generator" (CW)) to equivalently shortening or lengthening the transmission line attached to the load (or source)
   
4. Inductive loading is the upper half plane. Capacitive loading is the lower half plane.
   
5. As you lengthen or shorten the transmission line you rotate the angle but then you must follow the radial line back to the line of constant resistance which is what the effective load follows as you change transmission line length. If you started with a source Thevenin, and move to the load point, that phase angle between these two points is the stub length of transmission line required to match source to load.
   
6. Maximum reactive loading (inductive or capacitive) occurs at 0 degrees (of wavelength distance) which corresponds to the equivalent of a perfect open circuit load by distant such that the standing waves are maximized as if you had an open load. This is also equivalent to a parallel LC at resonance where the LC net reactive impedances goes to infinity leaving only the parallel R (which in a parallel LC is ideally infinite also). An open or short on a transmission line termination is a physically-defined electrical resonance analogous to a parallel or series LC network resonance, respectively.

A Smith Chart, btw, is a conformal map between the Lumped Model impedance and the Distributed Model transmission line and load. Conformal maps are functions that are mathematically "analytic". It turns out that solutions to Maxwell's[/PLAIN] equations are necessarily analytic so this becomes a system property.

Perhaps most oddly interesting is that if you used lumped model filters to do transmission line matching (e.g. to do an antenna loading coil to minimize its physical length but maintaining an electrical match), you must use the "dual" components of inductors and capacitors, minimally as L-networks. Because for positive, real valued inductors and capacitors, there are certain "matching solutions" that are physically impossible and give rise to so-called "forbidden regions" of solutions on the Smith Chart. These regions are "http://www.rfcafe.com/references/electrical/images/Simple%20Visio%20Smith%20Chart%20-%20Forbidden%20LowRight.png": the form of one of the most ancient "duality" symbols of humanity

Yes, the Ying and Yang of Daoism which is totally cool even beyond the core symmetry of Eulers[/PLAIN] Formula in the complex plane that gives rise to all of this by virtue of being "the general solution" to Maxwell's equations.

 

[binhexoctdec]

http://radiomagonline.com/media/2010/0910/009rad0701_Large.jpg

http://na.tm.agilent.com/pna/help/latest/smith_chart.gif

1. Find the load impedance on the Smith Chart. This is always a single point on the chart. (In other uses of a Smith Chart you can start with the point of the source Thevenin impedance).
   
2. Draw line from the center through the point to the radial perimeter - this is the phase offset of the load (or if you started with the source Thevenin, the source Thevenin phase)
   
3. Increase or decrease the angle along the radial perimeter (there is a direction labeled "toward generator" (CCW) or "away from generator" (CW)) to equivalently shortening or lengthening the transmission line attached to the load (or source)
   
4. Inductive loading is the upper half plane. Capacitive loading is the lower half plane.
   
5. As you lengthen or shorten the transmission line you rotate the angle but then you must follow the radial line back to the line of constant resistance which is what the effective load follows as you change transmission line length. If you started with a source Thevenin, and move to the load point, that phase angle between these two points is the stub length of transmission line required to match source to load.
   
6. Maximum reactive loading (inductive or capacitive) occurs at 0 degrees (of wavelength distance) which corresponds to the equivalent of a perfect open circuit load by distant such that the standing waves are maximized as if you had an open load. This is also equivalent to a parallel LC at resonance where the LC net reactive impedances goes to infinity leaving only the parallel R (which in a parallel LC is ideally infinite also). An open or short on a transmission line termination is a physically-defined electrical resonance analogous to a parallel or series LC network resonance, respectively.

A Smith Chart, btw, is a conformal map between the Lumped Model impedance and the Distributed Model transmission line and load. Conformal maps are functions that are mathematically "analytic". It turns out that solutions to Maxwell's[/PLAIN] equations are necessarily analytic so this becomes a system property.

Perhaps most oddly interesting is that if you used lumped model filters to do transmission line matching (e.g. to do an antenna loading coil to minimize its physical length but maintaining an electrical match), you must use the "dual" components of inductors and capacitors, minimally as L-networks. Because for positive, real valued inductors and capacitors, there are certain "matching solutions" that are physically impossible and give rise to so-called "forbidden regions" of solutions on the Smith Chart. These regions are "http://www.rfcafe.com/references/electrical/images/Simple%20Visio%20Smith%20Chart%20-%20Forbidden%20LowRight.png": the form of one of the most ancient "duality" symbols of humanity

Yes, the Ying and Yang of Daoism which is totally cool even beyond the core symmetry of Eulers[/PLAIN] Formula in the complex plane that gives rise to all of this by virtue of being "the general solution" to Maxwell's equations.

Thanks for your very informative response! After reading through it I think understand now how to go about solving the problem.