Although the describing function method can produce reasonably accurate results for a wide class of systems, it can fail badly for others. For example, the method can fail if the system emphasizes higher harmonics of the nonlinearity. Such examples have been presented by Tzypkin for bang–bang systems. A fairly similar example is a closed-loop oscillator consisting of a non-inverting Schmitt trigger followed by an inverting integrator that feeds back its output to the Schmitt trigger's input. The output of the Schmitt trigger is going to be a square waveform, while that of the integrator (following it) is going to have a triangle waveform with peaks coinciding with the transitions in the square wave. Each of these two oscillator stages lags the signal exactly by 90 degrees (relative to its input). If one were to perform DF analysis on this circuit, the triangle wave at the Schmitt trigger's input would be replaced by its fundamental (sine wave), which passing through the trigger would cause a phase shift of less than 90 degrees (because the sine wave would trigger it sooner than the triangle wave does) so the system would appear not to oscillate in the same (simple) way.
