On natural frequencies of a terminated transmission line with feedback

This correspondence describes three results concerning the natural frequencies of transmission lines. It is shown that 1) a transmission line can be terminated in an admittance whose real part is negative in the entire right half of the
s
plane-yet no natural frequency is in the right half of the
s
plane; 2) for capacitive termination and simple gain feedback less than unity, all natural frequencies are purely imaginary; 3) for capacitive termination and simple feedback gain greater than unity, exactly two of the natural frequencies are real, one being positive, the other negative. The utility of these results in stability analysis is shown.