Show that a short-circuited losalesa transmission line looks at its input end as an inductor or a capacitor. This property is used in integrated microwave circuits to simulate a capacitor or an traductor.

A section of a lossless transmission line short circuited acts a circuit reactive element ( i.e. inductor or capacitor ) and to achieve the desired reactance, the length of the transmission line has to be properly chosen.

attached below is the related diagram

Explanation:

Input impedance of a short-circuited lossless transmission line can be expressed as :

attached below is the reaming part of the solution

A section of a lossless transmission line short circuited acts a circuit reactive element ( i.e. inductor or capacitor ) and to achieve the desired reactance, the length of the transmission line has to be properly chosen. which is used in stub matching.