This is a study on a set of feedback amplitude modulation oscillator equations. It is based on a very simple and inexpensive algorithm which is capable of generating a complex spectrum from a sinusoidal input. We examine the original and five variations on it, discussing the details of each synthesis method. These include the addition of extra delay terms, waveshaping of the feedback signal, further heterodyning and increasing the loop delay. In complement, we provide a software implementation of these algorithms as a practical example of their application and as demonstration of their potential for synthesis instrument design.