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Bode plot with example

Short answer

A Bode plot graphs magnitude (dB) and phase (deg) vs log frequency. For H(jω)=10/(1+jω/10), magnitude is 20 dB up to ω=10 rad/s, then falls at -20 dB/dec; phase goes from 0° to -90°, with -45° at ω=10.

Describe bode plot with example.

A Bode plot is a pair of graphs of a system's frequency response H(jω)H(j\omega) against log⁡10ω\log_{10}\omega:

  • Magnitude plot: 20log⁡10∣H(jω)∣20\log_{10}|H(j\omega)| in dB,
  • Phase plot: ∠H(jω)\angle H(j\omega) in degrees.

Because a product of factors becomes a sum of dB values, the plot is drawn by adding simple straight-line (asymptotic) approximations of each factor.

Basic factors

FactorMagnitude (asymptote)Phase
Constant KK20log⁡K20\log K flat0∘0^\circ
Zero at origin jωj\omega+20+20 dB/dec, 0 dB at ω=1\omega=1+90∘+90^\circ
Pole at origin 1/jω1/j\omega−20-20 dB/dec−90∘-90^\circ
Simple pole 11+jω/a\frac{1}{1 + j\omega/a}0 dB up to aa, then −20-20 dB/dec0∘→−90∘0^\circ \to -90^\circ, −45∘-45^\circ at aa
Simple zero 1+jω/a1 + j\omega/a0 dB up to aa, then +20+20 dB/dec0∘→+90∘0^\circ \to +90^\circ

The frequency aa is the corner (break) frequency; the true curve is 3 dB from the asymptote there.

Example

H(jω)=101+jω/10H(j\omega) = \frac{10}{1 + j\omega/10}
  • K=10⇒20log⁡10=20K = 10 \Rightarrow 20\log 10 = 20 dB.
  • Pole at ω=10\omega = 10 rad/s.

Magnitude: 20 dB flat up to 10 rad/s, then falls at −20-20 dB/dec: 0 dB at 100 rad/s, −20-20 dB at 1000 rad/s. Actual value at ω=10\omega = 10: 20−3=1720 - 3 = 17 dB.

Phase: −tan⁡−1(ω/10)-\tan^{-1}(\omega/10): about 0∘0^\circ at 1, −45∘-45^\circ at 10, about −90∘-90^\circ at 100 rad/s.

dB
 20 |--------.
    |         \   -20 dB/dec
  0 +----------\--------------> w (log)
    1     10   100   1000
deg
  0 |----.
-45 |     `--.
-90 |         `-------------> w (log)
    1     10   100

Uses

  • Shows bandwidth, cutoff frequency and filter type at a glance.
  • Gives gain margin and phase margin for stability of feedback systems.
  • Quick to sketch by hand, covering a wide frequency range.

✓ Answer checked by Claude Opus 5.5 (high effort)

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