Understanding Low Pass Filters

A low-pass filter allows signals with frequencies lower than a certain cutoff frequency to pass through while attenuating higher frequencies.

Formula for cutoff frequency: f_c = 1 / (2πRC)

Example:

Input:

• Resistance: 1 Omega
• Capacitance:100 nF

Steps:

1. Convert resistance to ohms: \[ 1 Omega = 1 \times 10^{6} = 1,000,000 \, \Omega\]
2. Convert capacitance to farads: \[ 100 {nF} = 100 \times 10^{-9} = 0.0000001 \, {F} \]
3. Use the formula: \[ f_c = \frac{1}{2 \pi R C} \] Substitute the values: \[ f_c = \frac{1}{2 \pi \times 1,000,000 \times 0.0000001} \]
4. Calculate: \[ f_c = \frac{1}{0.628} \approx 1.59 {Hz} \]

Output: \(f_c \approx 1.59 {Hz}\)