In the last 10–15 years, a significant development has been achieved in the design of Y-circulators on lumped elements based on the Y-junction of intertwined conductors placed between two magnetized ferrite disks, which are small even in the meter and decimeter wavelength ranges. Therefore, they are very attractive decoupling components for developers of electronic equipment, especially onboard. Increasing the operating frequency band of circulators of this type is an urgent task, the solution of which can expand the range of their application in promising radio-electronic equipment. Methods for solving this problem are based on the inclusion in the circulator circuit of the corresponding band-expanding matching circuits on the reactive elements. Matching circuits can be included both in each arm of the circulator, and between the common point of the intertwined conductors and the “body”. But it is important for developers of Y-circulators to know what maximum results can be achieved with the use of band-expanding circuits even before the start of development. The authors’ research, the results of which are presented in this article, is devoted to solving this problem. The studies have been carried out by a semi-empirical method based on the consideration of the eigenvalues of the impedance matrices of narrow-band and broadband Y-circulators constructed on their basis, including band-expanding circuits. Comparing the behavior of the eigenvalues of the impedance matrices in the frequency representation and in the φ-representation (φ – phase of the signal transmission coefficient from input to output) when using standard circulation conditions allowed us to obtain analytical relations for calculating the maximum possible operating frequency band and the maximum possible decoupling between the arms of the circulator, as well as to formulate a method for calculating the reactivities of matching circuits that should be included in the circulator circuit.