Frequency is only used to display the wavelength λ = c/f. It does not affect Gamma in this lossless terminal-reflection model.
Red = constant-resistance circles (r=0.2,0.5,1,2,5) / Blue = constant-reactance circles (x=±0.2,±0.5,±1,±2,±5) / Dashed green = |Γ| circle / Yellow = current Γ
The Smith chart maps the normalized impedance z = Z/Z_0 = r + j x to the reflection coefficient Γ = u + j v via a bilinear transform, displayed inside the unit circle of the Γ plane.
Reflection coefficient at the load:
$$\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0} = \frac{z - 1}{z + 1}$$Voltage standing wave ratio (VSWR):
$$\text{VSWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|}$$Constant-resistance circle (center and radius):
$$\text{center} = \left(\frac{r}{1+r},\,0\right), \qquad \text{radius} = \frac{1}{1+r}$$Constant-reactance circle (center and radius):
$$\text{center} = \left(1,\,\frac{1}{x}\right), \qquad \text{radius} = \frac{1}{|x|}$$The center, Γ = 0 (i.e. z = 1), is the matched point with zero reflection and VSWR = 1. Larger |Γ| means a worse match; the unit circle itself is total reflection.