An electron multiplying CMOS images sensor (emCMOS) enables electron multiplication inside the pixel by the use of high voltage (hv) phase(s) under gate(s). Different possible implementations of hv gates dedicated to impact ionization require specific multiplication patterns and therefore new excess noise formulation. This paper presents a rigorous mathematical approach to the calculation of the excess noise factor for all electron multiplying CMOS pixel structures in the framework of the branching processes and the compounding theorem of the probability generating function. Validation of the model is performed by computing the variance formula for one pixel structure and its corresponding Monte Carlo simulation of the stochastic processes. The signal over noise ratio including the readout noise, SNRro, is introduced to evaluate the possible extreme low light imaging performance as a function of the multiplication parameters.