The pole-zero map, invariably introduced on an ad hoc basis, gives a very good frequency domain approximation in the range 0 ≤ ωT < 1, where T is sampling period, to the unrealizable digital controller transfer functionC(z) which would result from mapping the corresponding analogue transfer functionGc(s) underz = esT,i.e., s = (1/T) Inz. A variation of the well known Tustin transformation emerges as a simple alternative.