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I have a homework problem with the following circuit:

enter image description here

I have solved the transistor biasing part and then drawn the AC-circuit of it. Then I need to find the transfer function.

enter image description here

These are the calculations I did:

enter image description here

This is the drawing which I drew by hand of what I think the transfer function will be:

enter image description here

I am not sure how we ended up getting infinite for the third case. Would really appreciate some help regarding this.

Similar problems like this I want to be able to solve in just some piece of paper.

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  • \$\begingroup\$ @ jDAQ, I would appreciate your answer regarding this . Really stuck at this one and don't know if what I did is right. \$\endgroup\$
    – E199504
    Jan 30 '20 at 9:57
  • \$\begingroup\$ @jDAQ, can you please help me with this ? \$\endgroup\$
    – E199504
    Jan 30 '20 at 17:36
  • \$\begingroup\$ @jDAQ this is a picture of how the circuit actually looks like . In case this is helpful Picture \$\endgroup\$
    – E199504
    Jan 30 '20 at 18:01
  • \$\begingroup\$ Sorry, but I won't be helping you anymore. You have to be more clear on what you are asking. After all, I did explain the behavior of \$ Z_{C||L}\$ yet you are now asking for what is the transfer function \$ U_2/U_1 \$ a completely different thing. You have to include the actual calculations you did, because you mention in your "calculation" that \$ \frac{U_2}{U_1} = 1 \$ then you draw a plot that is not a constant 1, so make up your mind and include exactly what you want and all you have done so far. \$\endgroup\$
    – jDAQ
    Jan 31 '20 at 0:05
  • \$\begingroup\$ @jDAQ, I just asked bellow how did you get the three results for those three cases which was part of you your answer. To be honest I find it quite rude to say that it is a homework, because it is not If I had class I would have gone to teacher and get it explained there. Just trying to learn more \$\endgroup\$
    – E199504
    Jan 31 '20 at 9:02
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Well, I couldn't quite get what you are asking. But, looking at this circuit we can figure \$ Z_{L||C}\$,

schematic

simulate this circuit – Schematic created using CircuitLab

From the Fourier transform and circuit equations, we have that

$$ v = i Z_{L||C} = i \left( \left(j\omega L \right)^{-1}+\left(\frac{1}{j\omega C}\right)^{-1}\right)^{-1},$$

$$ Z_{L||C} = \left( \left(\frac{1}{j\omega L}\right) + \left(j\omega C \right) \right)^{-1} = \left( \frac{1- \omega^2 LC }{j\omega L} \right)^{-1} = \frac{j\omega L}{1- \omega^2 LC },$$

$$ \lim_{\omega \rightarrow \infty} Z_{L||C} = 0,$$ $$ \lim_{\omega \rightarrow \sqrt{1/LC}} Z_{L||C} = \infty,$$ $$ \lim_{\omega \rightarrow +0} Z_{L||C} = 0.$$

You could plot the values of \$ ||Z_{L||C} (jw)||\$ and get something similar to linear plot similar to <span class=\$ ||Z_{L||C} (jw)||\$ ">

Or the log-log plot

log-log plot similar to <span class=\$ ||Z_{L||C} (jw)|| \$">

So \$ ||Z_{L||C} (jw)||\$ is just as you pointed. Now, I don't get where that transfer function \$ \frac{U_1}{U_2} \$ fits in your question at all.

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  • \$\begingroup\$ how would the graph look like in this case ? \$\endgroup\$
    – E199504
    Jan 30 '20 at 21:18
  • \$\begingroup\$ Were you just looking for the impedance of \$ Z_{L||C} \$ ? \$\endgroup\$
    – jDAQ
    Jan 30 '20 at 21:34
  • \$\begingroup\$ Can you please show me how you got the results for the three cases. This is a link to a picture of the question picture \$\endgroup\$
    – E199504
    Jan 30 '20 at 23:32

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