In section 2.11.1 in the book Fundamentals of Applied Electromagnets by Fawwaz T. Ulaby, it says that in order for the circuit below to be matched at MM', y-in must be y-in = 1+ j0. Why is this so? How does this admittance value ensure that y-in = y0 of the feedline?
When a quantity \$q\$ is normalized a reference \$Q_0\$ must be chosen.
So then the normalised quantity $$q_{norm}=\frac{q}{Q_0}$$
In the example the characteristic admittance of the tranmission line is chosen as the reference. Since it is a complex quantity then:$$y_{norm}\angle\theta_{norm}=\frac{y\angle{\theta}}{Y_0\angle\theta_0}=\frac{y}{Y_0}\left( \theta-\theta_0\right)$$
For matching:$$y_{norm}\angle\theta_{norm}=1\angle{0^0}$$
In normalized rectangular form:$$y_{norm}\angle\theta_{norm}=1+j0$$
In the example \$Y_{in}\$ is normalized to \$Y_{0}\$.
How does this admittance value ensure that y-in = y0 of the feedline?
Be careful using notation here. Is \$Y_{in}\$ normalized or not. \$Y_{in}=1+j0\$ implies that \$Y_{in}\$ is normalized. \$Y_{in}=Y_0\angle\theta_0\$ implies that \$Y_{in}\$ is not normalized. It can't be both ways. The notation ambiguity is the source of the question.
