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)110100100010000−120−100−80−60−40−200?ω (rad/s)

Sketch the asymptotic Bode magnitude plot of G(s) = 50000/(s(s + 1000)(s + 50)). What is the slope n of the straight-line asymptote above 1000 rad/s, in dB/decade?

G(s) = 50000/(s(s + 1000)(s + 50))
n = dB/dec
2.Easy
vin​R = 2.2 kΩC = 100 nFvout​

Find the corner (−3 dB) frequency fc of the RC low-pass filter shown, with R = 2.2 kΩ, C = 100 nF. Give it in Hz.

R = 2.2 kΩC = 100 nF
fc = Hz
3.Medium
vin​R = 3.3 kΩC = 1 nFvout​

The RC low-pass filter shown has R = 3.3 kΩ, C = 1 nF. A sinusoidal input of 190 kHz is applied. Find the phase shift φ of vout relative to vin, in degrees.

R = 3.3 kΩC = 1 nFf = 190 kHz
φ = °
4.Medium
vin​L = 5 mHC = 10 µFR = 10 Ωvout​

In the series RLC band-pass filter shown the output is taken across R = 10 Ω, with L = 5 mH and C = 10 µF. Find the quality factor Q.

R = 10 ΩL = 5 mHC = 10 µF
Q =
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) = 210/(s(s + 3)(s + 8)). Find the phase crossover frequency ω180, where ∠L(jω) = −180°.

L(s) = 210/(s(s + 3)(s + 8))
ω180 = rad/s
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 2 dB.

L(s) = K/(s(s + 1)(s + 10))GM = 2 dB
K =

Answer key

  1. 1. n = −60 dB/dec
  2. 2. fc = 723.4 Hz
  3. 3. φ = −75.76 °
  4. 4. Q = 2.236
  5. 5. ω180 = 4.899 rad/s
  6. 6. K = 87.38

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