shanshan

shanshan https://tsukiyokai.github.io/ shanshan 的博客 quarto-1.11.9 Fri, 06 Nov 2026 00:00:00 GMT RC 低通滤波器的频率响应 shanshan https://tsukiyokai.github.io/posts/rc-lowpass/ 一阶 RC 低通滤波器的传递函数为

$H(j\omega) = \frac{1}{1 + j\omega RC} \tag{1}$

由式 1， $|H|$ 在截止角频率 $\omega_c = 1/RC$ 处降到 $1/\sqrt{2}$ ，即 $-3\ \mathrm{dB}$ ； $\omega \gg \omega_c$ 时，幅值以 $-20\ \mathrm{dB/dec}$ 下降，相位趋于 $-90^\circ$ [1]。图 1 取 $R = 1\ \mathrm{k\Omega}$ 、 $C = 159\ \mathrm{nF}$ ，对应 $f_c = 1/(2\pi RC) \approx 1\ \mathrm{kHz}$ 。

代码

import matplotlib.pyplot as plt
import numpy as np

R, C = 1e3, 159e-9
f = np.logspace(1, 6, 500)
H = 1 / (1 + 2j * np.pi * f * R * C)

fig, (mag, phase) = plt.subplots(2, sharex=True)
mag.semilogx(f, 20 * np.log10(abs(H)))
mag.set_ylabel("|H| (dB)")
phase.semilogx(f, np.degrees(np.angle(H)))
phase.set_ylabel("phase (deg)")
phase.set_xlabel("f (Hz)")
plt.show()

图 1: RC 低通滤波器的 Bode 图

参考文献

[1]

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. Upper Saddle River, NJ: Prentice Hall, 1997.

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