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)0.11101001000−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 160(s + 1)/((s + 20)(s + 4)) in decibels, |G(0)| in dB.

G(s) = 160(s + 1)/((s + 20)(s + 4))
|G(0)| = dB
2.Easy
|H| (dB)0.11101001000−60−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 1400/((s + 20)(s + 9)) in decibels, |G(0)| in dB.

G(s) = 1400/((s + 20)(s + 9))
|G(0)| = dB
3.Medium
vin​L = 100 mHC = 0.47 µFR = 50 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 50 Ω, with L = 100 mH and C = 0.47 µF. Find the quality factor Q.

R = 50 ΩL = 100 mHC = 0.47 µF
Q =
4.Medium
|H| (dB)0.10.111101010010010001000−40−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 30

Find the phase ∠G(jω) of G(s) = 36(s + 3)/(s(s + 2)) at ω = 30 rad/s, in degrees.

G(s) = 36(s + 3)/(s(s + 2))ω = 30 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 6 dB.

L(s) = K/(s(s + 2)(s + 4))GM = 6 dB
K =
6.Hard
|H| (dB)0.10.1111010100100−80−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 2.3/(s(s + 1)). Find the phase margin PM in degrees.

L(s) = 2.3/(s(s + 1))
PM = °

Answer key

  1. 1. |G(0)| = 6.021 dB
  2. 2. |G(0)| = 17.82 dB
  3. 3. Q = 9.225
  4. 4. ∠G(jω) = −91.9 °
  5. 5. K = 24.06
  6. 6. PM = 36.3 °

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