(i) Show that the input impedance of a short-circuited loss-less line of length L is Zi = i Z0 tan2π L λ , where Z0 = L0/C0. Hence or otherwise, determine the lengths of the line when it is capacitive...

(i) Show that the input impedance of a short-circuited loss-less line of length L is Zi = i Z0 tan2π L λ , where Z0 = L0/C0. Hence or otherwise, determine the lengths of the line when it is capacitive and when it is inductive. (ii) A line of characteristic impedance Z0 is matched to a load ZL by a loss-free quarter wavelength line. Show that the characteristic impedance of the matching section is Zm =  Z0ZL . Hence or otherwise show that a loss-free line of characteristic impedance Z0 and length nλ/2 may be employed to couple two high-frequency circuits without affecting other impedances.