Does area inside a constant circle on smith chart represent constant refection ?

[electronic_guy]

Hi,

Why does the area inside a constant circle on a smith chart represents loads with constant reflection coefficient of value equal to the circle's radius, no matter where they are inside that circle ? I just don't understand how. I mean if I take the reflection coefficient 1 circle and the area covered by it, wouldn't it make all the loads inside other constant reflection coefficient circles to have the same reflection coefficient of 1. 

Please look at the picture.

Let's say we take the constant gamma circle of -20 dB. Then if all the load points inside the area covered by that circle give same reflection coefficient which is -20dB, If I consider the constant reflection coefficient circle of 0 dB and take a load inside the -20 dB circle, then it's confusing as to which reflection coefficient to choose. Is it 0 dB or -20 dB ? I'm sure there must be something I'm missing here. I'm very new to this, please explain with little bit of maths and physical meaning of this. 

Thank you.

[RoV]

The magnitude of the reflection is the same for the points belonging to the circle (that must be centered on the chart), not for points inside it.
Remember that the chart plots the reflection coefficient in cartesian coordinates, with superimposed curves for readout of impedance and/or admittance. A circle of radius r centered on the point with ro = 0+j0 (the center) is exactly the locus of constant magnitude abs(ro)=r.

[pdenisowski]

The magnitude of the reflection is the same for the points belonging to the circle (that must be centered on the chart), not for points inside it.

Another way of saying this is that all points lying along a circle centered around the origin* have the same VSWR (voltage standing wave ratio).

The radius of the circle is the VSWR, so you can read off VSWR by looking at the point at which the circle crosses the resistive (real) axis on the right side of the axis.  In the attached image, all points on the blue circle have a VSWR of 2 and all points on the red circle have a VSWR of 5.

*or "prime center"

[radiolistener]

exactly the same reflection coefficient can be for different combination of active and reactive component of impedance. This is why you can draw circle for the same reflection coefficient.

But note that area inside or outside circle is not the same reflection. The same reflection lays exactly on circle line.