the circles with center on x-axis of the Smith chart represent the real part of impedance.

the circles with center on the x = 1 are the imaginary part of the impedance.

and a circle with radius 1 and centered at (0,0) represent a coaxial line with 50Ω, the (-1,0) is zero length and (1,0) is ¼ wavelength from the load.

thus, we can construct the input impedance by Smith Chart very easily.

AND i always think, the normalized input impedance should be 1 in order to give minimum reflection. However, when the source impedance is not 50Ω, it is not the case. the impedance matching for normalized source impedance is

z_{in} = z_s^*

this is come form the Maximum Power Theory.

anyway, to construct the input impedance, we just need to  remember when circuit element is in series, we use normal Smith chart, if the circuit element is in parallel, we use a 180 degree rotated Smith chart, since adding by reactance is more easy.

there is an iphone app for this: rfCalc

it is very easy to use!

the question is how do i know the source impedance!???