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RL Circuit

Have a look at this circuit. I am to find the transfer function which is defined as \$V_L(s)/V(s)\$.

Now I don't understand the solution. First of all, it defines \$V_L(s)\$ at the bottom as \$sI_2(s)\$. Shouldn't it be \$2sI_2(s)\$?

Also, shouldn't the transfer function be \$1/[s + 3 + (1/s)]\$?

Here's how I came to that conclusion. The last part of the solution I agree with is this step:

\$(2s + 2)(s + 2)I_2 - 2I_2 = V(s)\$

Then I get \$(2s^2 + 6s + 4)I_2 - 2I_2 = V(s)\$

Distributing out...

\$2sI_2[(s + 3 + 2/s) - 1/s] = V(s)\$

Now I want \$V(s)/2I_2(s)\$

so...

\$s + 3 + 1/s\$ is equal to that. Now invert that and you get the transfer function I got. What did I do wrong?

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What you did wrong was to assume that the given answer doesn't have mistakes... :-) Looks to me like there's an error. On the line after the "or", \$(2s^2 + 4s + 2)\$ is supposed to be \$(2s^2 + 6s + 2)\$. So your result is correct.

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You are right. As you derived yourself, there's a wrong passage in the text to get to the second-last line. It's an erratum.

You'd be surprised how many errata there are in books and exercise materials.

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