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)0.1110100−2002040ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 2700/((s + 4)(s + 7)) in decibels, |G(0)| in dB.

G(s) = 2700/((s + 4)(s + 7))
|G(0)| = dB
2.Easy
|H| (dB)10100100010000−100−80−60−40−20020?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 10000/(s(s + 200)). What is the slope n of the straight-line asymptote above 200 rad/s, in dB/decade?

G(s) = 10000/(s(s + 200))
n = dB/dec
3.Medium
vin​L = 2 mHC = 0.22 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 2 mH and C = 0.22 µF. Find the −3 dB bandwidth BW in Hz.

R = 5 ΩL = 2 mHC = 0.22 µF
BW = Hz
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 5

Find the phase ∠G(jω) of G(s) = 15(s + 10)/(s(s + 5)) at ω = 5 rad/s, in degrees.

G(s) = 15(s + 10)/(s(s + 5))ω = 5 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) = 140/(s(s + 4)(s + 10)). Find the gain margin GM in dB.

L(s) = 140/(s(s + 4)(s + 10))
GM = dB
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 + 1)(s + 10)). Find the gain K that gives a gain margin of 8 dB.

L(s) = K/(s(s + 1)(s + 10))GM = 8 dB
K =

Answer key

  1. 1. |G(0)| = 39.68 dB
  2. 2. n = −40 dB/dec
  3. 3. BW = 397.9 Hz
  4. 4. ∠G(jω) = −108.4 °
  5. 5. GM = 12.04 dB
  6. 6. K = 43.79

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