S-Plane to Z-Plane Mapping | Bilinear Transform Interactive

Bilinear Transform s = (2/T)·(z−1)/(z+1). Maps entire jω axis to unit circle, no aliasing.

Stability Preserved Left-half s-plane maps inside the unit circle — stability is preserved.

Frequency Warping Bilinear introduces frequency warping; pre-warp critical frequencies using Ω = (2/T)·tan(ωT/2).

s-Plane to z-Plane Mapping ($z = e^{sT}$)