The working principle of a band-pass filter is to allow signals within a specific frequency band (between the low-frequency cutoff frequency f1 and the high-frequency cutoff frequency f2) to pass through while suppressing signals from other frequency bands. It is usually achieved by combining a high-pass and low-pass filter or through an RLC oscillation circuit.
Core principle
The core function of a band-pass filter (BPF) is to selectively transmit signals within a certain frequency range. Its working principle is based on two main implementation methods:
1. Combination of high-pass and low-pass filters:
1) The high-pass filter removes signals below the low-frequency cutoff frequency f1.
2) The low-pass filter removes signals above the high-frequency cutoff frequency f2. When these two filters are connected in series, only the frequency band from f1 to f2 is retained.
2. RLC Oscillation Circuit:
This is a resonant circuit composed of a resistor (R), an inductor (L), and a capacitor (C). It has the maximum gain at the resonant frequency (f0), and the bandwidth is determined by the difference between f2 and f1.
Ideal and Practical Characteristics
1. Ideal characteristics: A completely flat passband, with no signal attenuation outside the passband, and a very narrow transition band.
2. Actual Limitations:
1)There is a roll-off phenomenon (the transition band has a non-infinite steep attenuation), which is usually described in terms of dB per tenfold frequency.
2)Ripples (the Gibbs phenomenon) may occur at the passband edge, affecting the smoothness.
Key parameters
1. Cutoff frequency: The low-frequency f1 and high-frequency f2 determine the passband range.
2. Bandwidth (BW): BW = f2 - f1, which reflects the selectivity of the filter.
3. Quality factor (Q): Q = f0/BW, which measures the sharpness of frequency selectivity.