reflection and corresponding reactance

[happsky]

A book said that:
Looking on a Smith chart a pure reactance of -45 degrees gives a corresponding
reactance of 2.375*50 ohms (at 2GHz).

how to look on the smith chart?
is there any Formula?
is there any tools calculate easily?

 

[FvM]

All you need to know is relation between s-parameter and terminating impedance and how to calculate with complex numbers. Pure reactance of -45° simply means s11 = 1 * exp(-j 45°) = 0.71 - j0.71. For some relations see https://en.wikipedia.org/wiki/Smith_chart

 

[happsky]

Thank you very much.
There is anther problem, the picture show above is a vco,and he said that reflection coefficient is -45°
while the s11 is 45°,it resonant.
but in my view,the im(Zin) should be equal to im(Zs),
and in this case,the im(Zin)=7.8, im(stoz(s11))=2.375 . it not equal. why?