Filters
Operation, application and uses of low-pass, high-pass, band-pass and band-stop filters.
Filters, summary notes
- 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.
- 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)
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
Filters concept map
Filters
Filters quiz
Filters, quiz
1. A low-pass filter passes:
Low frequencies and attenuates high onesHigh frequencies onlyAll frequencies equally2. At the cut-off frequency of an RC filter the output has fallen to:
70.7% of the input (-3 dB)50% of the input10% of the input3. A band-pass filter:
Passes a range of frequencies and rejects those above and below itPasses direct current only, blocking every alternating component regardless of its frequencyBlocks one narrow band of frequencies while passing everything above and below it unaffected4. At the cut-off frequency of a filter, the output voltage is:
0.707 of the input0.5 of the inputEqual to the input5. In an RC low-pass filter, the output is taken across the:
CapacitorResistorSupply6. A filter that rejects a narrow band of frequencies is called a:
Notch (band-stop) filterBand-pass filterLow-pass filter7. The cut-off frequency of an RC filter with R = 1 kΩ and C = 1 µF is approximately:
159 Hz1000 Hz6.28 Hz8. Which filter type is used to smooth the output of a rectifier?
Low-passHigh-passBand-pass9. In an RC high-pass filter, the output is taken across the:
ResistorCapacitorInductor10. The −3 dB point of a filter corresponds to:
Half the input powerHalf the input voltageZero output