Question

A λ/4 line, shorted at one end presents impedance at the other end equal to
1. Z₀
2. √ 2 Z₀
3. ∞ 
4. 0

Answer 1

Correct Answer - Option 3 : ∞ 

Concept:

• The load impedance, ZL at the end of the transmission line must match its characteristic impedance, Z0 Otherwise there will be reflections from the transmission line’s end.
• A quarter-wave transformer is a component that can be inserted between the transmission line and the load to match the load impedance ZL to the transmission line’s characteristic impedance Z0.
• The input impedance of a quarter-wave transformer is given as:

           \({{\rm{Z}}_{{\rm{in}}}} = \frac{{{\rm{Z}}_0^2}}{{{{\rm{Z}}_{\rm{L}}}}}\;\)

Analysis:

For a λ/4 line:

Input impedance = \({{\rm{Z}}_{{\rm{in}}}} = \frac{{{\rm{Z}}_0^2}}{{{{\rm{Z}}_{\rm{L}}}}}\;\)

Where Z₀ is the characteristic impedance. 

Now, if the line is shorted i.e Z_L = 0

Z_in = ∞