Nonlinear methods are now widespread in medical and industrial applications of ultrasound. The harmonic generation within piezoelectric transducers needs to be quantified. This is particularly the case in nonlinear NDT where the nonlinearity of the medium only has to be identified. High precision measurements are then required that would spoiled by nonlinearity coming from the transducer itself. In the present work, quadratic nonlinear equations of a piezoelectric element are derived by the perturbation theory in onedimensionnal case. It is demonstrated that the nonlinear response can be represented by controlled sources of voltage and current in equivalent electric circuits. This analysis allows the nonlinear response of a loaded piezoelectric transducer to be efficiently predicted. It is shown that the influence of these acoustic loads on the nonlinear effects such as distortion depends phenomenologically on the type of non-linearity that dominates in the piezoelectric element, i.e. mechanical or electromechanical. A generalisation of nonlinear equivalent electric circuits to cases including propagation media and passive layers is presented, opening the way to the study of the nonlinear response of complex structures.