The Bode-Fano Integrals as an Objective Measure of Antenna Bandwidth Reflection Coefficient Product Limit

The Bode-Fano integral is proposed as an objective tool for assessing the bandwidth of antennas and special schemes for antenna bandwidth improvement. The limiting gain-bandwidth product is a measure of optimum power transfer from source to loads. For loads represented in Darlington canonical form, optimum tolerance can be calculated using the Bode-Fano theory. In this paper for the first time the Fano limit has been calculated for loads with up to four reactive elements. It was note that even though increasing the substrate height of coaxially feed microstrip patch antennas will increase the antenna bandwidth; however this is only true up to some specific heights and afterwards the antenna potential bandwidth decreases for future increase in substrate height. Also for double resonance circuits it was concluded that the maximum potential bandwidth is obtained if the two resonant frequencies are the same