What impedance does a 1/2-wavelength transmission line present to an RF generator when the line is shorted at the far end?
Why A transmission line repeats its terminating impedance every half wavelength, so a 1/2-wavelength line is essentially a 1:1 transformer regardless of its characteristic impedance. With a short circuit at the far end, the generator sees that same short, so the input impedance is very low (limited only by line loss). The general relation Zin = Z0(ZL + jZ0 tan(beta*L))/(Z0 + jZL tan(beta*L)) reduces to Zin = ZL when the electrical length is a half wavelength, because tan(180 degrees) = 0.
Watch out Very high impedance is what a quarter-wavelength shorted stub presents, since a quarter wave acts as an impedance inverter; a half wave does not invert, it repeats.
Half wave repeats, quarter wave inverts. Shorted half wave = still a short.