To address the low inertia grid inverters sources provide, the virtual synchronous machine (VSM) has been one of the main approaches to regulate the active power in continuous time domain. However, continuous time solutions do not take into consideration some of the dynamic behaviors of the system, such as measurement delays and small number of samples per period, given by the limitations of the hardware used to implement these controls. This is where careful discrete design is important, taking into consideration these hardware limits to obtain reliable results. This paper presents a discrete implementation of the VSM using the direct discrete modeling method, along with a comparison between the continuous, exact discrete and Tustin approximation. The finding highlights that the continuous and Tustin approximation show deteriorating results on the dynamic metrics shown in bode plots as the sample time increases. Only direct discrete modeling can match the ideal continuous domain design. Also, since the intended implementation space is a microcontroller using digital signals, the continuous design does not work when confronted with sampling issues and PWM-noise. The approximation methods can be a quick way to transform to a discrete domain, but those methods also show problems with sampling and noise. A correct discrete implementation that works as intended, with and not around the limitations of the design space, can only be obtained with a proper control design, such as the one shown on this paper.