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S-Parameter Magnitude (dB)
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Physics & Formulas
1. Transmission Line (ABCD):
$$ \begin{bmatrix} \cos(\beta l) & j Z_0 \sin(\beta l) \\ j Y_0 \sin(\beta l) & \cos(\beta l) \end{bmatrix} $$
$$ \begin{bmatrix} \cos(\beta l) & j Z_0 \sin(\beta l) \\ j Y_0 \sin(\beta l) & \cos(\beta l) \end{bmatrix} $$
2. Transformer (Ideal N):
Modeled as Coupled Inductors (k = 1).
$$Z_{in} = N^2 Z_{load}$$
Modeled as Coupled Inductors (k = 1).
$$Z_{in} = N^2 Z_{load}$$
3. Constants:
\( \beta = \frac{2\pi f \sqrt{\epsilon_{eff}}}{c} \), \( c \approx 3 \times 10^8 \text{ m/s} \)
\( \beta = \frac{2\pi f \sqrt{\epsilon_{eff}}}{c} \), \( c \approx 3 \times 10^8 \text{ m/s} \)
S11 Smith Chart