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The transfer function \(G(s) = \frac{{10}}{{(3s + 1)}}\) has a corner frequency at:
1. 3 rad/s
2. 0.33 rad/s
3. 1 rad/s
4. 30 rad/s

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Best answer
Correct Answer - Option 2 : 0.33 rad/s

Concept:

In a bode magnitude plot, a pole adds a slope of -20 dB/decade whereas a zero adds a slope of 20 dB/decade.

The initial slope of the magnitude plot is ±20n dB/decade

+ for n zeros at origin

- for n poles at the origin

The standard transfer function of a Bode magnitude plot is:

\(TF = \frac{{K\left( {1 + \frac{s}{{{\omega _1}}}} \right)\left( {1 + \frac{s}{{{\omega _2}}}} \right) \ldots }}{{{s^n}\left( {1 + \frac{s}{{{\omega _3}}}} \right)\left( {1 + \frac{s}{{{\omega _4}}}} \right) \ldots }}\)

Here, ω1, ω2, ω3, ω4, … are the corner frequencies.

n is the number poles at the origin.

Calculation:

\(G(s) = \frac{{10}}{{(3s + 1)}}\)

Comparing with standard transfer function we get,

cross-over frequency = 1/3 = 0.33 rad/sec

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