Parallel RLC circuit complex impedance graphing

[lys04]

Homework Statement

How can I graph the impedance against the frequency using a logarithmic scale for the frequency axis?

Relevant Equations

$$ Z = \frac{iwL-w^{2}RLC}{1-w^{2}LC+iwRC} $$

^^ as mentioned in the homework statement, the relevant equation is my worked out impedance for the circuit. I have attached a diagram of the circuit below.

 

[BvU]

https://en.wikipedia.org/wiki/Bode_plot

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[lys04]

https://en.wikipedia.org/wiki/Bode_plot

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Can you explain? I looked at it but I'm still confused

 

[BvU]

$Z$ is complex. You want to write it as $|Z| e^{j\phi}$. Do you know how to do that ?

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[lys04]

$Z$ is complex. You want to write it as $|Z| e^{j\phi}$. Do you know how to do that ?

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Is it like this? for the branch with resistor and capacitor,

And then for the branch with just the inductor in it its just wLe^90j?

And then I need to add them together which is 1/Z = 1/Z_l + 1/Z_c?

 

[BvU]

No. You already did the work to get the correct complex $Z$.

To write it as $|Z| e^{j\phi}$ you want to use $|Z|^2=ZZ^*$ with $Z^*$ the complex conjugate.
And $\tan\phi = \Im Z/\Re Z$ (imaginary part / real part).

If $Z= (a+jb)/(c+jd)$ you get the real and imaginary part by multiplying with $(c-jd)/(c-jd)$ (because then the denominator $c^2-d^2$ is real).

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