<p>An analytical model of electron transport in a planar vacuum microdiode is developed to describe transit-time instabilities arising from self-consistent space-charge feedback. The model leads to a delay-differential equation for the electron velocity that captures the coupling between the electron transit time and plasma oscillations in the gap. Analytical expressions for the small-signal impedance and the conditions for negative differential resistance are obtained. The analysis identifies discrete frequency bands where the real part of the impedance becomes negative, enabling self-sustained oscillations. The oscillation frequency is governed by the electron transit time and plasma frequency, naturally scaling into the terahertz range for micron-scale gaps. An explicit expression for the emitted power is derived by treating the modulated current as a short dipole radiator. The proposed framework provides a compact analytical description of transport-driven instabilities in vacuum micro- and nanoelectronic devices and offers guidelines for THz source design.</p>