LC Butterworth – Component Sensitivity

Monte-Carlo Simulation

Each of the discrete filter components is assumed to be normally distributed with \(\sigma = 0.02 \mu \).

\begin{align*}
R_S &\sim \mathcal{N}\left( 1, (0.02)^2 \right) \\
R_L &\sim \mathcal{N}\left( 1, (0.02)^2 \right) \\
L_1 &\sim \mathcal{N}\left( 1.6180, (1.6180 \cdot 0.02)^2 \right) \\
L_2 &\sim \mathcal{N}\left( 1.6180, (1.6180 \cdot 0.02)^2 \right) \\
C_1 &\sim \mathcal{N}\left( 0.6180, (0.6180 \cdot 0.02)^2 \right) \\
C_2 &\sim \mathcal{N}\left( 2, (2 \cdot 0.02)^2 \right) \\
C_3 &\sim \mathcal{N}\left( 0.6180, (0.6180 \cdot 0.02)^2 \right) \\
\end{align*}

Magnitude response of various 5th order Butterworth filters with ladder components having an uncertainty of 2% - 1 sigma.

Pole-Zero map of a 5th order Butterworth filter with ladder components having an uncertainty of 2% - 1 sigma.
Probability distribution of pole locations of a 5th order Butterworth filter with ladder components having an uncertainty of 2% - 1 sigma.

 

The bandwidth of the Butterworth filter:

Probability distribution of 3dB bandwidth of a 5th order Butterworth filter with ladder components having an uncertainty of 2% - 1 sigma.

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