An impedance matching power combining/dividing system and a method for combining power combiners/dividers are presented. The impedance matching power combiner comprises a cylindrical matching cavity, two or more coaxial inputs, each of the two or more coaxial inputs having an inner input conductor and an outer input conductor and having a source impedance, a coaxial output having an inner output conductor and an outer output conductor and having a load impedance and a circular matching plate suspended inside the cylindrical matching cavity, wherein the inner input conductors and the inner output conductor are electrically connected to the matching plate, the outer input conductors and the outer output conductor are electrically connected to the cylindrical matching cavity and the cylindrical matching cavity at least partially matches the source impedance with the load impedance. The system and method to combine/divide groups of power combiners/dividers to handle high power are also presented. The power combiners/dividers have a small transverse dimension that they easily fit in a phased array lattice structure and operate at high frequencies.