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A two-port network has scattering parameters given by $[S] = \begin{bmatrix}s_{11} &s_{12} \\s_{21} &s_{22} \end{bmatrix}.$ If the port-2 of the two-port is short circuited, the $s_{11}$ parameter for the resultant one-port network is

  1. $\dfrac{s_{11} –  s_{11}s_{22} + s_{12}s_{21}}{1+s_{22}}$ 
  2. $\dfrac{s_{11} + s_{11}s_{22}  –  s_{12}s_{21}}{1+s_{22}}$
  3. $\dfrac{s_{11} + s_{11}s_{22}  +  s_{12}s_{21}}{1 – s_{22}}$ 
  4. $\dfrac{s_{11} –  s_{11}s_{22}   +   s_{12}s_{21}}{1 –  s_{22}}$  
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