工作原理
A first-order RC or RL filter is the simplest way to remove noise from a signal or to shape a frequency response. A low-pass filter passes frequencies below its cutoff and attenuates higher ones at 20 dB per decade; a high-pass filter does the opposite.
Enter any two of the three values (resistance, capacitance or inductance, cutoff frequency) and the calculator solves for the third. It then suggests the nearest standard E-series part values and shows how much the cutoff frequency moves when you use them.
The Bode plot shows the ideal magnitude response. At the cutoff frequency the gain is −3 dB, meaning the output amplitude is about 70.7% of the input. Real circuits deviate because of source and load impedance, component tolerance and parasitic elements.
公式
- RC cutoff frequency
- f_c = 1 / (2π · R · C)
- RL cutoff frequency
- f_c = R / (2π · L)
- Low-pass magnitude
- |H(f)| = 1 / √(1 + (f / f_c)²)
- High-pass magnitude
- |H(f)| = (f / f_c) / √(1 + (f / f_c)²)
计算示例
To filter PWM ripple from a 10 kΩ sense divider with a 1.6 kHz cutoff, C = 1 / (2π · 10 kΩ · 1.6 kHz) ≈ 10 nF. The nearest standard value of 10 nF gives f_c ≈ 1.59 kHz.
常见问题
What does the −3 dB point mean?
It is the frequency where the output power is half of the input power, or the amplitude is 1/√2 of the input. It is the conventional definition of a filter's cutoff frequency.
How do I get a steeper roll-off?
Cascade stages or use a second-order filter such as an RLC or Sallen-Key topology, which rolls off at 40 dB per decade.
Why does my measured cutoff differ from the calculation?
The source impedance adds to R, the load appears in parallel, and capacitors often have ±10% or worse tolerance. Account for these or buffer the filter with an op-amp.
计算结果为工程估算值，请结合数据手册、仿真和实测验证设计。