The coefficient of reflection of voltage for short circuited line is

When a transmission line is loaded with impedance it is represented as follows:

V = Incident voltage

V’= Reflected voltage

V’’= Refracted or transmitted voltage.

Transmission line impedance is surge impedance Zs.

Load impedance is ZL.

Short circuited is line is considered when ZL = 0

Coefficient of reflection is given by the expression \({V_{reflection}} = \frac{{V'}}{V}\)

\({V_{reflection}} = \frac{{{Z_L} - {Z_s}}}{{{Z_L} + {Z_S}}}\)

Calculations: 

\({{\rm{V}}_{{\rm{reflection}}}} = \frac{{0 - {Z_S}}}{{0 + {Z_S}}}\)

V reflection = -1

Therefore coefficient of reflection of voltage for a short circuited line is -1.

Additional Information

Formulas for the Coefficients of reflection and refraction are as follows

\({v_{refraction}} = \frac{{2{Z_L}}}{{{Z_L} + {Z_S}}}\)   

 \({v_{reflection}} = \frac{{{Z_L} - {Z_S}}}{{{Z_L} + {Z_S}}}\)

\({i_{refraction}} = \frac{{2{Z_S}}}{{{Z_L} + {Z_S}}}\)   

 \({i_{reflection}} = \frac{{{Z_S} - {Z_L}}}{{{Z_L} + {Z_S}}} = - {v_{reflection}}\)​