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I am trying to understand and apply the concept of low entropy transfer functions as outlined by C.Basso and equally stated by a couple of people here.

As an example, I wanted to work through an L-C 2nd order filter feeding a load

schematic

simulate this circuit – Schematic created using CircuitLab

Working through the example makes sense as the L and C are shorted or opened to quickly determine the tau of the associated elements to finally combine to produce the overall transfer function \$\frac{V_o}{V_{in}}\$

What I am trying to do is then determine the current transfer function \$\frac{I_o}{I_n}\$ as well as the input and output impedance but it's clear I haven't fully grasped this concept. Likewise, \$R_3\$ is my load and it is a constant power load so the impedance will vary. This was briefly covered in the book but only in passing.

Could someone help guide me in determining the current gain, the \$Z_{in}\$ and \$Z_{out}\$ following the EET method

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  • \$\begingroup\$ I'm currently reading his book but I would leave it C.Basso himself :) \$\endgroup\$
    – Mike
    Aug 2 '18 at 18:03
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    \$\begingroup\$ @Verbal Kint should help you \$\endgroup\$
    – G36
    Aug 2 '18 at 18:09
  • \$\begingroup\$ If you take the Norton equivalent cct of V1,rl,L then you can compute the I(R3) using Laplace if each branch if you know the initial conditions. \$\endgroup\$ Aug 2 '18 at 19:26
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    \$\begingroup\$ What is EET? Avoid non-std. Acronyms \$\endgroup\$
    – ijuneja
    Aug 2 '18 at 19:31
  • \$\begingroup\$ To get \$Z_{out}\$, simply short the input source \$V_1\$ and you end-up having three elements in parallel: \$L_1\$ and its series resistance, your load (which is a fixed value at the considered operating point) and capacitor \$C_2\$ with its ESR. Determine the time constants for the denominator \$D(s)\$ then the zeros for the numerator \$N(s)\$. The dc gain \$R_0\$ is \$R_3\$. For more details, please check my APEC 2016 seminar on FACTs (slide 90) cbasso.pagesperso-orange.fr/Spice.htm where I detail the procedure. \$\endgroup\$ Sep 22 '18 at 9:05
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To get \$Z_{out}\$, simply short the input source \$V_1\$ and you end-up having three elements in parallel: \$L_1\$ and its series resistance, your load (which is a fixed value at the considered operating point) and capacitor \$C_2\$ with its ESR. Determine the time constants for the denominator \$D(s)\$ then the zeros for the numerator \$N(s)\$. The dc gain \$R_0\$ is \$R_3||r_L\$. For more details, please check my APEC 2016 seminar on FACTs (slide 90) where I detail the procedure.

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