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)0.1110100100010000−120−100−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 400/((s + 200)(s + 2)). What is the slope n of the straight-line asymptote between 2 and 200 rad/s, in dB/decade?

G(s) = 400/((s + 200)(s + 2))
n = dB/dec
2.Easy
|H| (dB)0.11101001000−40−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 90(s + 11)/((s + 7)(s + 90)) in decibels, |G(0)| in dB.

G(s) = 90(s + 11)/((s + 7)(s + 90))
|G(0)| = dB
3.Medium
vin​L = 10 mHC = 1 µFR = 5 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 10 mH and C = 1 µF. Find the −3 dB bandwidth BW in Hz.

R = 5 ΩL = 10 mHC = 1 µF
BW = Hz
4.Medium
|H| (dB)0.10.1111010100100−200204060ω (rad/s)φ (°)ω (rad/s)−90−450ω = 5

Find the phase ∠G(jω) of G(s) = 15(s + 7)/(s(s + 10)) at ω = 5 rad/s, in degrees.

G(s) = 15(s + 7)/(s(s + 10))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) = K/(s(s + 4)(s + 5)). Find the gain K that gives a gain margin of 12 dB.

L(s) = K/(s(s + 4)(s + 5))GM = 12 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) = K/(s(s + 5)(s + 6)). Find the gain K that gives a gain margin of 6 dB.

L(s) = K/(s(s + 5)(s + 6))GM = 6 dB
K =

Answer key

  1. 1. n = −20 dB/dec
  2. 2. |G(0)| = 3.926 dB
  3. 3. BW = 79.58 Hz
  4. 4. ∠G(jω) = −81.03 °
  5. 5. K = 45.21
  6. 6. K = 165.4

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