In this work, the Paschen curves and current-voltage characteristics of three large-area short glow discharge structures with grid and solid plate electrodes are studied. The study of the Paschen's curves reveals that Paschen's law is broken for all three investigated electrode structures. It is shown that the experimentally measured Paschen curves are well approximated with a modified Paschen's law. A comparison of the current-voltage characteristics of the short glow discharge in the three types of electrode structures reveals that the use of grid electrodes allows for the increase in the discharge current. The effects of the electrode gap, which were varied from 1 mm to 7 mm, on the Paschen curves and current-voltage characteristics of short glow discharges are also investigated.