What impedance does a 1/8-wavelength transmission line present to an RF generator when the line is open at the far end?
Why An open-ended line shorter than a quarter wavelength behaves like a capacitor. The input impedance of a lossless open line is Zin = -jZ0 cot(βl); at 1/8 wavelength βl = 45 degrees and cot(45°) = 1, so Zin = -jZ0, a pure capacitive reactance equal in magnitude to the characteristic impedance. Only at 1/4 wavelength does the open line transform into a short, and beyond that it turns inductive.
Watch out An inductive reactance is what a 1/8-wavelength line with a shorted far end presents; infinite impedance applies only to a very short open stub or a half-wavelength open line.
Open stub starts as a capacitor, shorted stub starts as an inductor. At 1/8 wave the magnitude is exactly Z0.