Smith chart: when going from input impedance to 50Ohm, why not complex conjugate?

Hello!

When matching transistor with Zin = 1.3+1.5j to 50 Ohm, we going from Smith Chart center (50Ohm) to complex conjugate of Zin. After adding capacitors and microstrip line we get to point 1.3-1.5j, and scheme is matched.

I tried another direction, adding the same elements (capacitors and microstrip line) going from point Zin = 1.3-1.5j back to 50 Ohm. Of course, elements in reverse direction. But it gives wrong result. But if use 1.3+1.5j as starting point, then all is ok and final point is 50 Ohm.

I can't understand it theoretically, i hope somebody tell me some idea why is that?
When matching some Zin to 50 Ohm, and starting point on smith chart is center 50 Ohm, we must use complex conjugate of Zin.
But when starting from Zin, we must not use it complex conjugate! If use complex conjugate as starting point, gives very wrong result. But it is strange for me.. it kind of depends on direction where we going.

You start by placing the actual load on the chart, not the conjugant. As an example consider a simple load of 50 ohms with a series inductor of j20 so we have 50+j20. On a Zo=50 chart we plot this at 1+j.4 This is our starting point. Now we want to match this, we can see the path to Zo is on a constant R line so we know we need to add 0-j.4 to get to Zo. We know 0-j.4 is a cap. When we add it we get 1+j0 which is a perfect match. Ta Da.

Now we remove the load and look back toward the generator and what we see is the series cap of -j.4 and the 1+j0 generator for a value of 1-j.4 which is the conjugant of our load.

-H

when u use a smith chart, you have to pay attention to the little note with arrow "wavelengths toward generator"