The scattering parameters of a two-port network are given as follows:
$$
S_{11}=0.687 \angle 107^{\circ}, S_{21}=1.72 \angle-59^{\circ}, S_{12}=0.114 \angle-81^{\circ}, S_{22}=0.381 \angle 153^{\circ}
$$
A source of $3 \mathrm{mV}$ with internal resistance of $50 \Omega$ is connected at port-1. Assuming the characteristic impedance at its ports as $50 \Omega$, determine the scattering variable $a_1, b_1, a_2$, and $b_2$ for the following load conditions:
(a) $50 \Omega$
(b) $100 \Omega$