Analytical Mode Distributions and Resonant Frequencies in Ladder Networks Used in Power Combining Oscillator Arrays

An analysis of resonant modes in ladder networks is performed using difference equations. linear and loop configurations are studied and analytical relations are derived for the mode distributions and resonant frequencies of these networks, having arbitrary elements. furthermore, it is shown that a) modes with an exponential distribution along network nodes may exist in some cases and b) the mode distributions in loop networks are independent of network elements. finally, a simple criterion is obtained for a loop structure to control the spacing between resonant frequencies.