Here, we will obtain the relationship of jΩ axis in s-plane to the unit circle in the z-plane (r = 1)

$Ω=\frac{2}{T_s} ×\frac{(2r sin⁡ω)}{(r^2+2r cos⁡ω+1 )}$ ………………(1)

For the unit circle,r=1. Thus putting r=1in the equation 1, we get

$Ω=\frac{2}{T_s} ×\frac{(2 sin⁡ω)}{(1+2 cos⁡ω+1 )}$

$∴Ω=\frac{2}{T_s} ×\frac{(2 sin⁡ω)}{(2+2 cos⁡ω )}$

$∴Ω=\frac{2}{T_s} …