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

Find the corner (−3 dB) frequency ω_c of the RL high-pass filter shown, with R = 10 Ω, L = 4.7 mH. Give it in rad/s.

R = 10 ΩL = 4.7 mH

ω_c = rad/s

2.Easy

Sketch the asymptotic Bode magnitude plot of G(s) = 10000/((s + 200)(s + 10)). What is the slope n of the straight-line asymptote between 10 and 200 rad/s, in dB/decade?

G(s) = 10000/((s + 200)(s + 10))

n = dB/dec

3.Medium

The RC low-pass filter shown has R = 2.2 kΩ, C = 47 nF. A sinusoidal input of 15 kHz is applied. Find the gain |H| = |v_out/v_in| in dB.

R = 2.2 kΩC = 47 nFf = 15 kHz

|H| = dB

4.Medium

In the series RLC band-pass filter shown the output is taken across R = 5 Ω, with L = 10 mH and C = 0.22 µF. Find the quality factor Q.

R = 5 ΩL = 10 mHC = 0.22 µF

Q =

5.Hard

A unity-feedback loop has the open-loop transfer function L(s) = K/(s(s + 7)(s + 8)). Find the gain K that gives a gain margin of 12 dB.

L(s) = K/(s(s + 7)(s + 8))GM = 12 dB

K =

6.Hard

A unity-feedback loop has the open-loop transfer function L(s) = K/(s(s + 6)(s + 9)). Find the gain K that gives a gain margin of 8 dB.

L(s) = K/(s(s + 6)(s + 9))GM = 8 dB

K =

Answer key

1. ω_c = 2128 rad/s
2. n = −20 dB/dec
3. |H| = −19.82 dB
4. Q = 42.64
5. K = 211
6. K = 322.5

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