From Pozar's Microwave Engineering (Pg. 606):

Reflection Coefficient looking into load = (Zl-Zo)/(Zl+Zo)

Where Zl is a purely real load impedance, and Zo is the
purely real characteristic impedance reference.

When you change Zo, you change the normalized center of the
Smith Chart, and therefore the Reflection Coefficient and SWR, looking
into the same load.



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