The frequency-diverse array (FDA) is a promising technology because of its angle- and range-dependent beam pattern. The FDA has unique properties, such as beam scanning and focusing, which are difficult to achieve using the conventional phased antenna array theory. In this study, the relationship between range and frequency increment is analyzed, and the fundamental operation principle of FDA is thoroughly investigated. The effect of coupling among antenna elements is also discussed to analyze the FDA theory. Furthermore, a novel exponential FDA method for short-range beam focusing is presented based on the proposed FDA analysis method. The proposed method has been investigated through various case studies and applied to research efforts on FDA methods. The FDA design procedures and analysis methods are also presented in this article.