A quadrature model for a travelling-wave-tube-type (t.w.t.) amplifier is developed. The model consists of two envelope nonlinearities, one in the inphase and the other in the quadrature path. Modified Bessel functions of 1st and 2nd order are used to approximate to these nonlinearities. This model is simpler than existing models and is found to yield an excellent agreement to the actual tube characteristics, so that analytic prediction of tube performance is readily accomplished.