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I have a simple transfer function, given by:

$$\frac{140,000}{s(s+100)}$$

I'm attempting to calculate the magnitude at $\omega$ = 100 rad/s.

So I plug in, I get $\frac{140,000}{20,000}$ = 7

Then I do $20log_{10}(7)$ = 16.9

Yet when I go through MATLAB, entering my transfer function and doing bode(sys), and then examining the point at w = 100, it tells me the magnitude there is 19.9.

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I must be missing something stupid here...

krb686
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  • I can confirm, that the result with the bode command is somewhat around 19.9. But since I'm not familiar with this topic, I don't know how you derive $20\log_{10}(7)$. Maybe you could explain a little bit about what you're doing. – Thomas Dec 04 '14 at 07:15

1 Answers1

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Hint:

When calculation the magnitude, you can't just plug in the angular frequency into the transfer function. You first need to replace $s$ by $j\omega$ and then take the absolute value of the resulting expression.

$$\left|F(j\omega)\right|=\left|\frac{1400000}{j\omega(j\omega+100)}\right|=\frac{140000}{\omega |j\omega+100|}$$

Can you take it from here?

Daniel R
  • 3,199