In this paper, we develop a powerful analytical model of wireless network with Superposition Coding (SC), also referred to as Non Orthogonal Multiple Access (NOMA). This model allows to establish a closed form expression of the minimum power a base station (BS) need to transmit, for a user to achieve a given SINR (signal to interference plus noise ratio) whatever its location in the area covered by the base station. It moreover allows to establish a closed form expression of the minimum total transmit power of a base station. These closed form expressions allow to establish performance of wireless networks, by minimizing the base stations transmit powers. As an application, we show that these closed form expressions allow to quantify the energetic performance, spectral efficiency, total throughput and the coverage of a BS, in a simple and quick way.