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At the moment I'm struggling with the problem, i can calculate the transfer function of the following circuit, but not the cut-off frequency. The transfer function is in my case: $$H(s)=\frac{1}{s^3\cdot (L\cdot R1 \cdot R2 \cdot C1 \cdot C2)+s^2 \cdot (L \cdot R2 \cdot C2)+s \cdot (R1 \cdot (C1+C2))+1}$$ Thanks in advance

Circuit

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    \$\begingroup\$ Welcome to SE.EE! First of all: please note cascode =/= cascade. \$\endgroup\$
    – Huisman
    Jun 5, 2019 at 11:03
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    \$\begingroup\$ It isn't easy to solve a third order manually. Try using a mathematical tools like MatLab, Maxima, etc or simulation tools like LTspiceXVIII \$\endgroup\$
    – Huisman
    Jun 5, 2019 at 11:06
  • \$\begingroup\$ Modeling this as a (very highly dampened) PI filter, the F_resonance is about 7MHz. \$\endgroup\$ Jun 5, 2019 at 13:57

2 Answers 2

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If you want to do this 'by hand' rather than through Matlab or whatever, use the old analogue computing trick of normalising the TF with respect to the s-coefficient. This gives a more manageable set of coefficients that can be re-scaled at the end.

Assuming your TF coefficients are correct:

$$\small H(s)=\frac{1}{(1.225\times 10^{-20})s^3+(2.475\times 10^{-13})s^2+(1.584\times 10^{-7})s+1}$$

Let \$\small S=(1.584\times 10^{-7})s\$, and the TF becomes:

$$\small H(S)=\frac{1}{3.083\:S^3+9.864\:S^2+S+1}$$

Now let \$\small S=j\Omega\$ and determine the cut-off frequency, \$\small \Omega_c\$.

Finally, scale to the actual frequency via: \$ \omega_c =\frac{\Omega_c}{1.584\times 10^{-7}}\$

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You need to solve:

$$\frac{1}{\sqrt{2}}\cdot\left|\underline{\mathcal{H}}\left(\hat{\omega}\right)\right|=\left|\underline{\mathcal{H}}\left(\omega\right)\right|\space\Longleftrightarrow\space\omega=\dots\tag1$$

Using Mathematica I got (assuming that your transfer function is correct) for \$\hat{\omega}\$:

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And \$\left|\underline{\mathcal{H}}\left(\hat{\omega}\right)\right|\$ gives:

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So, solving equation \$(1)\$ gives:

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Which gives:

enter image description here

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