# Magnitude of a function with inductor and capacitor

I have a homework problem with the following circuit:

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

These are the calculations I did:

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

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.

• @ jDAQ, I would appreciate your answer regarding this . Really stuck at this one and don't know if what I did is right. Jan 30, 2020 at 9:57
• @jDAQ this is a picture of how the circuit actually looks like . In case this is helpful Picture Jan 30, 2020 at 18:01
• 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.
– jDAQ
Jan 31, 2020 at 0:05
• @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 Jan 31, 2020 at 9:02

Well, I couldn't quite get what you are asking. But, looking at this circuit we can figure $$\ Z_{L||C}\$$,

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 $||Z_{L||C} (jw)||$ ">

Or the log-log plot

$||Z_{L||C} (jw)||$">

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.

• how would the graph look like in this case ? Jan 30, 2020 at 21:18
• Were you just looking for the impedance of $Z_{L||C}$ ?
– jDAQ
Jan 30, 2020 at 21:34
• 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 Jan 30, 2020 at 23:32