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 = 47 kΩC = 2.2 nFvout​

Find the corner (−3 dB) frequency ωc of the RC low-pass filter shown, with R = 47 kΩ, C = 2.2 nF. Give it in rad/s.

R = 47 kΩC = 2.2 nF
ωc = rad/s
2.Easy
|H| (dB)1101001000−20020ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 500(s + 12)/((s + 10)(s + 90)) in decibels, |G(0)| in dB.

G(s) = 500(s + 12)/((s + 10)(s + 90))
|G(0)| = dB
3.Medium
vin​L = 100 mHC = 0.1 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 = 0.1 µF. Find the centre (resonant) frequency f0 in Hz.

R = 50 ΩL = 100 mHC = 0.1 µF
f0 = Hz
4.Medium
|H| (dB)0.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ω = 20

Find the phase ∠G(jω) of G(s) = 46(s + 13)/(s(s + 1)) at ω = 20 rad/s, in degrees.

G(s) = 46(s + 13)/(s(s + 1))ω = 20 rad/s
∠G(jω) = °
5.Hard
|H| (dB)0.10.1111010100100−100−80−60−40−20020ω (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 + 2)). Find the gain K that gives a gain margin of 12 dB.

L(s) = K/(s(s + 1)(s + 2))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) = 54/(s(s + 6)(s + 7)). Find the gain margin GM in dB.

L(s) = 54/(s(s + 6)(s + 7))
GM = dB

Answer key

  1. 1. ωc = 9671 rad/s
  2. 2. |G(0)| = 16.48 dB
  3. 3. f0 = 1592 Hz
  4. 4. ∠G(jω) = −120.2 °
  5. 5. K = 1.507
  6. 6. GM = 20.1 dB

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