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
|H| (dB)0.1110100−60−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 100/((s + 3)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 100/((s + 3)(s + 9))
|G(0)| = dB
2.Easy
vin​R = 4.7 kΩC = 10 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 4.7 kΩ, C = 10 nF. Give it in Hz.

R = 4.7 kΩC = 10 nF
fc = Hz
3.Medium
vin​L = 1 mHC = 2.2 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 1 mH and C = 2.2 µF. Find the −3 dB bandwidth BW in Hz.

R = 5 ΩL = 1 mHC = 2.2 µF
BW = Hz
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 32(s + 1)/(s(s + 3)) at ω = 1 rad/s, in degrees.

G(s) = 32(s + 1)/(s(s + 3))ω = 1 rad/s
∠G(jω) = °
5.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 + 4)). Find the gain K that gives a gain margin of 2 dB.

L(s) = K/(s(s + 2)(s + 4))GM = 2 dB
K =
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) = 210/(s(s + 7)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 210/(s(s + 7)(s + 8))
ω180 = rad/s

Answer key

  1. 1. |G(0)| = 11.37 dB
  2. 2. fc = 3386 Hz
  3. 3. BW = 795.8 Hz
  4. 4. ∠G(jω) = −63.43 °
  5. 5. K = 38.13
  6. 6. ω180 = 7.483 rad/s

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