Meaning and mechanism
Low-pass filters effectively transmit low frequencies, while high-pass filters transmit high frequencies relatively well. The importance lies in determining whether to place the output at the resistor or the capacitor.
As capacitor reactance changes with frequency, the voltage-divider ratio changes too. Amplitude changes and phase shifts in time are two aspects of the same response.
Relationships and conditions
For an ideal unloaded RC filter, fc=1/(2πRC). At fc, the magnitude gain is 1/√2 of its passband value, or about −3.01 dB.
The region of blockage exhibits a gradual change, and the actual load and the input resistance of the following stage also influence the curve. We do not interpret the voltage response of this circuit, which lacks an amplifying element, as energy generation.
What to observe in the simulation
At cutoff both filters have magnitude 1/√2, approximately −3.01 dB.
The elements are ideal and output is unloaded. Noise, parasitic effects and audio playback are excluded. Experiment on screen; do not reproduce this with real power supplies, outlets or high voltage.
Key relationships and symbols
fc = 1/(2πRC) · Hlp = 1/(1+jωRC) · Hhp = jωRC/(1+jωRC)
| Symbol | Meaning | Unit |
|---|---|---|
| fc | Cutoff frequency | Hz |
| H | Complex output/input response | Dimensionless |
| dB | 20log₁₀ of the voltage magnitude ratio | dB |
Worked example
What is the magnitude gain of low-pass and high-pass filters at cutoff?
About −3.01 dB
Common misconceptions
- It is not the case that all components with frequencies higher than the cutoff frequency are immediately 0 in a low-pass filter.