The figure shows lossless lines $T_1,T_2$ and input reflection magnitude versus frequency. Phase velocity is $2\times10^8$ m/s in both lines. The length L of $T_2$, in metres, is ________.
The open-ended stub T2 has input impedance $-jZ_0\cot(\beta L)$. When its length is an odd quarter wavelength it looks like a short, giving reflection magnitude 1 at the junction. When it is a half wavelength it looks open, leaving the matched 50 Ω resistor and giving zero reflection.
The first maximum is 0.5 GHz, so $L=v/(4f)=2\times10^8/(4\cdot0.5\times10^9)=$ **0.10 m**. T1 changes phase but not reflection magnitude.
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