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Filters
Operation, application and uses of low-pass, high-pass, band-pass and band-stop filters.
Filters — summary notes
FreeMain ideas
- A filter passes some frequencies and attenuates others, using the frequency dependence of X_L and X_C.
- Low-pass passes low frequencies and blocks high. High-pass does the reverse.
- Band-pass passes a band of frequencies; band-stop (notch) rejects a band.
- The cut-off frequency f_c is where output falls to 0.707 of input — the −3 dB point, where half the power is passed.
- In an RC low-pass filter the output is taken across the capacitor; in an RC high-pass the output is taken across the resistor.
- ⚠ Exam trap: an RC low-pass and high-pass use the same two components — check which element the output is taken across.
Key formulas
- RC cut-off frequency
- f_c = 1 / (2πRC)
- LR cut-off frequency
- f_c = R / (2πL)
- Cut-off definition
- V_out = 0.707 × V_in (−3 dB)
Solved examples
Find the cut-off frequency of an RC filter with R = 1 kΩ and C = 1 µF.
f_c = 1 / (2πRC) = 1 / (2π × 1000 × 1 × 10⁻⁶) = 159 Hz.
In a smoothing circuit after a rectifier, which type of filter is used and why?
A low-pass filter. It passes the DC (zero frequency) component while attenuating the ripple, which is at supply frequency or twice it.
RC filter — low & high pass
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