Bode plots & margins worksheet with answers

Free printable Bode plots & margins worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
vin​R = 470 ΩL = 22 mHvout​

Find the corner (−3 dB) frequency fc of the RL high-pass filter shown, with R = 470 Ω, L = 22 mH. Give it in Hz.

R = 470 ΩL = 22 mH
fc = Hz
2.Easy
|H| (dB)1101001000−80−60−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 230/((s + 30)(s + 60)) in decibels, |G(0)| in dB.

G(s) = 230/((s + 30)(s + 60))
|G(0)| = dB
3.Medium
vin​R = 2.2 kΩC = 10 nFvout​

The RC low-pass filter shown has R = 2.2 kΩ, C = 10 nF. A sinusoidal input of 22 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 2.2 kΩC = 10 nFf = 22 kHz
φ = °
4.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 45(s + 16)/(s(s + 7)) at ω = 1 rad/s, in degrees.

G(s) = 45(s + 16)/(s(s + 7))ω = 1 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​ = ?

A unity-feedback loop has the open-loop transfer function L(s) = 60/(s(s + 8)). Find the gain crossover frequency ωc, where |L(jω)| = 1.

L(s) = 60/(s(s + 8))
ωc = rad/s
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−270−180−900ω180​

A unity-feedback loop has the open-loop transfer function L(s) = K/(s(s + 2)(s + 3)). Find the gain K that gives a gain margin of 3 dB.

L(s) = K/(s(s + 2)(s + 3))GM = 3 dB
K =

Answer key

  1. 1. fc = 3400 Hz
  2. 2. |G(0)| = −17.87 dB
  3. 3. φ = −71.8 °
  4. 4. ∠G(jω) = −94.55 °
  5. 5. ωc = 6 rad/s
  6. 6. K = 21.24

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