Numerical related to Normalization

Assume that a prototype filter is designed and a design table indicates that Rₙ = 1, Lₙ = 3.239 and Cₙ = 1.455 are the required normalized components. If the impedance level is selected as Rₛ = 1200 Ω and the frequency was normalized by ωₛ = 10.8 M rad/sec. Compute real R, L and C values.

Given:
\[
R_n = 1, \quad L_n = 3.239, \quad C_n = 1.455
\]
\[
R_s = 1200 \ \Omega, \quad \omega_s = 10.8 \times 10^{6} \ \text{rad/sec}
\]

Required:
\[
\text{Find real values of } R, L, \text{ and } C.
\]

Solution:
\[
L = \frac{R_s \cdot L_n}{\omega_s} = \frac{1200 \times 3.239}{10.8 \times 10^{6}} = 360 \ \mu H
\]

\[
R = R_s \times R_n = 1200 \times 1 = 1200 \ \Omega
\]

\[
C = \frac{C_n}{\omega_s \cdot R_s} = \frac{1.455}{10.8 \times 10^{6} \times 1200} = 112 \ pF
\]