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 = 1 kΩC = 100 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 1 kΩ, C = 100 nF. Give it in Hz.

R = 1 kΩC = 100 nF
fc = Hz
2.Easy
vin​L = 100 mHR = 100 Ωvout​

Find the corner (−3 dB) frequency ωc of the RL low-pass filter shown, with R = 100 Ω, L = 100 mH. Give it in rad/s.

R = 100 ΩL = 100 mH
ωc = rad/s
3.Medium
|H| (dB)1101001000−60−40−2002040ω (rad/s)ω = 30

Find the exact magnitude |G(jω)| of G(s) = 3520/((s + 16)(s + 20)) at ω = 30 rad/s, in dB.

G(s) = 3520/((s + 16)(s + 20))ω = 30 rad/s
|G(jω)| = dB
4.Medium
|H| (dB)0.10.1111010100100−2002040ω (rad/s)φ (°)ω (rad/s)−90−450ω = 1

Find the phase ∠G(jω) of G(s) = 11(s + 2)/(s(s + 7)) at ω = 1 rad/s, in degrees.

G(s) = 11(s + 2)/(s(s + 7))ω = 1 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.111101010010010001000−60−40−200204060ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 560/(s(s + 8)). Find the phase margin PM in degrees.

L(s) = 560/(s(s + 8))
PM = °
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 + 5)(s + 10)). Find the gain K that gives a gain margin of 5 dB.

L(s) = K/(s(s + 5)(s + 10))GM = 5 dB
K =

Answer key

  1. 1. fc = 1592 Hz
  2. 2. ωc = 1000 rad/s
  3. 3. |G(jω)| = 9.162 dB
  4. 4. ∠G(jω) = −71.57 °
  5. 5. PM = 19.18 °
  6. 6. K = 421.8

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