The mathematical expressions which occur in the treatment of non-linear devices as circuit elements are interpreted in terms of a graphical physical picture of the processes involved. This picture suggests, in turn, several useful ways of applying the equations in cases where the driving forces are so large that the ordinary power series treatment becomes prohibitively cumbersome. In particular, the application has been made in detail to the calculation of the intermediate-frequency output to be expected from a heterodyne detector having an incoming radio signal and locally generated beating oscillator voltage applied on its grid and a circuit of finite impedance to the intermediate frequency attached to its plate.