Reply to “Comments on ‘An Analytical Design Method for a Novel Dual-Band Unequal Coupler With Four Arbitrary Terminated Resistances’”

The phase-difference performance at two desired frequencies of the generalized dual-band unequal coupler is discussed and presented in this comment as supplementary information. The condition of <inline-formula> <tex-math notation="LaTeX">${\{ \angle {S_{21}} - \angle {S_{31}}\} _{{f_1}}} + {\{ \angle {S_{21}} - \angle {S_{31}}\} _{{f_2}}} = \pi $</tex-math></inline-formula> and the analytical equations for <inline-formula> <tex-math notation="LaTeX">${\{ \angle {S_{21}} - \angle {S_{31}}\} _{{f_1} \,\text{or}\, f_{2}}}$</tex-math> </inline-formula> are provided. It can be concluded that the dual-frequency output phase differences are constant and equal to 90° when <inline-formula><tex-math notation="LaTeX">${R_2} = {R_3},$</tex-math></inline-formula> but the values of <inline-formula><tex-math notation="LaTeX">${R_1}$</tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${R_4}$</tex-math></inline-formula> can be varied. Finally, the calculated results show that the phase-difference variations about <inline-formula><tex-math notation="LaTeX">$ \pm 11\% $</tex-math> </inline-formula> in the whole useful bandwidths of these branch-line couplers are objective and acceptable in common practical applications when <inline-formula><tex-math notation="LaTeX">${R_2}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${R_3}$</tex-math></inline-formula> are in the range of 30–100 Ω <inline-formula><tex-math notation="LaTeX">$({R_2} \ne {R_3})$</tex-math></inline-formula>.