Seven transformations with increasing an input signal frequency, which use the first harmonics of the signal and the second and third harmonics of the heterodyne for forming an intermediate frequency, and three classical transformations with increasing the input frequency, for which an intermediate frequency is formed as a difference or a sum of the first harmonics of the heterodyne and the signal, are considered. Comparison of frequency transformations is realized in the frequency range, maximally allowable for the use, where harmonic and combination components of given and lower orders, presented in the form | nFs mFh|, do not present in the passband of the intermediate frequency amplifier. The goal of our investigations is the search for such transformations which allows working in more wide input frequency ranges in comparison with classical transformations. Transformations which use signal and heterodyne harmonics can be applied for constructing frequency synthesizers and at signal reception. Possibilities of microelectronics allow obtaining mixer elements with given characteristics, which provide increasing the conversion factor at similar frequency transformations. Consideration of frequency transforms is performed with using the analytical computations which give the possibility of their investigation at varying signal frequencies and at tunable or constant heterodyne frequencies for two types of mixers. The physical essence of the method is shown and its basis and mathematical foundation are presented. Results of transformations are grouped in the tables for their convenient evaluation and estimation. It is shown that in addition to classical frequency transforms other transforms exist whose parameters are close enough to parameters of classical transforms.