Finite impedance section of a transmission line (source code)

= Finite impedance section of a transmission line
{title2=$\mathcal T=[1+(\alpha^2-1)^2\sin^2(\omega\ell/v)/(4\alpha^2)]^{-1}$}

A <length> $\ell$ with impedance ratio $\alpha$ between identical matched lossless lines has multiple internal reflections. Summing their amplitudes gives the displayed <power> transmission when the propagation <speed> is the same in all sections. It is unity at half-wave resonances even though either individual interface reflects. Matched remote terminations remove external echoes but not this <frequency> dependence.