What is a Bandpass Filter?
A bandpass filter is an electronic circuit that allows signals within a specific frequency range to pass through while attenuating frequencies outside that range. It has both a lower cutoff frequency (LCF) and an upper cutoff frequency (HCF).
Bandpass Filter Formulas
The cutoff frequencies are calculated using:
$$\text{LCF} = \frac{1}{2\pi R_{2} C_{2}}$$
$$\text{HCF} = \frac{1}{2\pi R_{1} C_{1}}$$
Where:
- Rโ and Rโ are resistances in ohms (ฮฉ)
- Cโ and Cโ are capacitances in farads (F)
- ฯ โ 3.14159
Example Calculation
Given:
- Rโ = 6 ฮฉ
- Rโ = 3 ฮฉ
- Cโ = 8 F
- Cโ = 4 F
Calculate the lower cutoff frequency:
$$\text{LCF} = \frac{1}{2\pi \times 3 \times 4} = \frac{1}{24\pi} \approx 0.0132 \text{ Hz}$$
Calculate the upper cutoff frequency:
$$\text{HCF} = \frac{1}{2\pi \times 6 \times 8} = \frac{1}{96\pi} \approx 0.00331 \text{ Hz}$$
The bandpass filter allows frequencies between approximately 0.00331 Hz and 0.0132 Hz to pass through.