Why using a polar Smith chart instead of a rectilinear impedance plane?

[RoGeorge]

If you look to the page 7 of https://literature.cdn.keysight.com/litweb/pdf/5965-7707E.pdf, the first question that pops in mind is why we use a Smith Chart instead of the Rectilinear Impedance plane?

We could as well represent the complex impedance in the rectilinear plane, where the normalized impedance (let's say 50+0*i ohms) is in the middle of the horizontal axis, and the infinite in the top of the horizontal axis arrow.

- Why do we use Smith charts instead of the normal complex plane?
- Is this just because of historical reasons?
- What are the advantages of Smith charts, or else said what would be the inconveniences if we would be to switch to a rectilinear complex plane representation instead?

[OwO]

Smith chart is a polar plot of reflection coefficient, impedance is secondary to that and are what the lines in a smith chart tell you. From a smith chart you can easily tell return loss, or how well matched a load is.

[hans]

Also consider:

Orders of magnitude - a reflection coefficient of close to -1 or 1 can span many different orders of magnitude. In a linear plane, that all compresses to a single spot.

Smith charts have constant resistance/conductance circles which can be used for impedance matching to aim towards your desired impedance.

[German_EE]

For plotting results you can use either a Smith chart or a rectilinear plane, but please remember that a Smith chart can also be used for calculation. Matching networks, stubs, LC circuits, they can all be plotted until the impedance of your device hits the bullseye.

[RoGeorge]

Thank you.  I now start to believe the main reason for using polar coordinates is to make various RF calculations with the help of geometry.

Back in the days when numerical computation was done by hand, with lookup table, or with a slide ruler at most, a polar coordinates chart must have been very useful.

Just an example of such a numerical calculation made with the help of a Smith Chart (it looks like some complex magic, which indeed it is )

[TheUnnamedNewbie]

The smith chart also shows easily what is going on to the trained eye. The pattern can show how certain effects start to dominate etc.

(I'm not one of those people that can tell since I don't use them that mutch, but the PA designers can just look at a plot and go 'oh yeah this transistor output inductor is becoming capacitive there so we should do this and this and decouple that .....' just by a squigly line on that plot.

[0culus]

There's another, far more practical consideration. The Smith chart condenses an infinite complex plane into a finite diagram. Far easier to work with.

[VE2UM]

I don't know if i'm alone...

But the first time i saw a Smith chart, it remembered me immedietely a microwave reflector antenna...

If it looks, smells, sounds like RF, it is a Smith Chart !!!

73