im trying desperately to match a 480-Ohm to 50-Ohm impedance: 
I have made the calculations and determined C=-j3.38nF and L=-j81.1uH (reactive). The inductance seems to have capacitive behavior and im certain i made a mistake. NOTE: Im not using and i don't want to use a Smith Chart for this. These are my calculations so far:$$ \begin{aligned} \text{Matching Network:} \\ 1. \quad & Q_s = \left| \frac{X_s}{Z_s} \right| \implies |X_s| = Z_s \cdot Q_s \implies Z_s = R_p, \quad X_s = \frac{wC_p}{G_p} \\ 2. \quad & Q_p = \left| \frac{B_p}{G_p} \right| \implies |B_p| = Q_p \cdot G_p, \quad B_p = G_s, \quad G_p = wL_m \\ 3. \quad & Q_d = \sqrt{\frac{R_p}{R_s} - 1} \implies Q = \approx j0.94 \\ 3 \rightarrow 1: \quad & X_s = Q_s \cdot Z_s \approx j0.94 \cdot 50\Omega \approx j47\Omega \implies C = \frac{1}{wX_s} \approx \frac{1}{2\pi \cdot 1\text{MHz} \cdot j47\Omega} \approx -j3.386 \cdot 10^{-9}F \\ 3 \rightarrow 2: \quad & X_p = Q_p \cdot R_p \approx \frac{480 \Omega}{j0.94} \approx -j510\Omega \implies L = \frac{X_p}{w} \approx \frac{-510\Omega}{2\pi \cdot 1\text{MHz}} \approx j81.4 \cdot 10^{-5}H \approx -j81.4\mu H \end{aligned} $$ What must i do to correctly define a matching-network that matches my 480-Ohm with a 50-Ohm resistor?
Im ultimately teaching myself here so i don't have someone to talk about this. Therefore, any help will be greatly appreciated!
