The observability of a system with respect to its possible outputs is usually evaluated using the rank criterion of the observability matrix or the observability indices. In addition, this paper uses the properties of the differential equations characterizing real-time electrical circuits which base their nonlinearities on the exponential function. Interplay between mathematical tools and practical considerations is done through observability coefficients, observability matrices and high order sliding mode observers for the Colpitts chaotic system, representative for such nonlinearities.