Consider an impedance Z = R + jX marked with point P in an impedance Smith chart as shown in Fig. The movement from point P along a constant resistance circle in the clockwise direction by an angle $${45^ \circ }$$ is equivalent to

A short-circuited stub is shunt connected to a transmission line as shown in Fig. If $${Z_0} = 50\,\,\Omega $$, the admittance Y seen at the junction of the stub and the transmission line is

In air, a lossless transmission line of length 50 cm with $$L = 10\,\mu H/m,\,\,C = 40\,\,pF/m$$ is operated at 25 MHz. Its electrical path length is

In a twin-wire transmission line in air, the adjacent voltage maxima are at 12.5 cm and 27.5. The operating frequency is