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​C = 22 nFR = 2.2 kΩvout​

Find the corner (−3 dB) frequency fc of the RC high-pass filter shown, with R = 2.2 kΩ, C = 22 nF. Give it in Hz.

R = 2.2 kΩC = 22 nF
fc = Hz
2.Easy
|H| (dB)0.11101001000−40−200ω (rad/s)

Find the low-frequency (DC) gain of G(s) = 31(s + 2)/((s + 40)(s + 6)) in decibels, |G(0)| in dB.

G(s) = 31(s + 2)/((s + 40)(s + 6))
|G(0)| = dB
3.Medium
|H| (dB)0.010.010.10.111101010010010001000−40−20020406080ω (rad/s)φ (°)ω (rad/s)−135−90−450ω = 0.5

Find the phase ∠G(jω) of G(s) = 19(s + 18)/(s(s + 11)) at ω = 0.5 rad/s, in degrees.

G(s) = 19(s + 18)/(s(s + 11))ω = 0.5 rad/s
∠G(jω) = °
4.Medium
vin​C = 47 nFR = 47 kΩvout​

The RC high-pass filter shown has R = 47 kΩ, C = 47 nF. A sinusoidal input of 220 Hz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 47 kΩC = 47 nFf = 220 Hz
φ = °
5.Hard
|H| (dB)0.10.1111010100100−60−40−2002040ω (rad/s)φ (°)ω (rad/s)−180−135−90−450ωc​

A unity-feedback loop has the open-loop transfer function L(s) = 64/(s(s + 8)). Find the phase margin PM in degrees.

L(s) = 64/(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 + 3)(s + 6)). Find the gain K that gives a gain margin of 4 dB.

L(s) = K/(s(s + 3)(s + 6))GM = 4 dB
K =

Answer key

  1. 1. fc = 3288 Hz
  2. 2. |G(0)| = −11.76 dB
  3. 3. ∠G(jω) = −91.01 °
  4. 4. φ = 18.13 °
  5. 5. PM = 51.83 °
  6. 6. K = 102.2

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