The frequency synthesizer performs a simple function of generating a desired frequency by manipulating a reference frequency signal, but stable and precise frequency generation is essential for reliable operation in mechanical equipment such as communication, control, surveillance, medical, and commercial fields. Frequency synthesis, which is commonly used in various contexts, has been used in analog and digital methods or hybrid methods. Especially in the field of communication, a precise frequency synthesizer is required for each frequency band, from very low-frequency AF (audio frequency) to high-frequency microwaves. The purpose of this paper is to design and implement a highly reliable frequency synthesizer for application to a railway track circuit systems using AF frequency only with the logic circuit of an FPGA (field programmable gate array) without using a microprocessor. Therefore, the development trend of analog, digital, and hybrid frequency synthesizers is examined, and a method for precise frequency synthesizer generation on the basis of the digital method is suggested. In this paper, the generated frequency generated by applying the digital frequency synthesizer using the ultra-precision algorithm completed by many trials and errors shows the performance of generating the target frequency with an accuracy of more than 99.999% and a resolution of mHz, which is much higher than the resolution of 5 Hz in the previous study. This highly precise AF-class frequency synthesizer contributes greatly to the safe operation and operation of braking and signaling systems when used in transportation equipment such as railways and subways.