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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

Niteesh Shanbog
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Igloo
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  • I'm currently reading his book but I would leave it C.Basso himself :) – Mike Aug 02 '18 at 18:03
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    @Verbal Kint should help you – G36 Aug 02 '18 at 18:09
  • 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. – Tony Stewart EE75 Aug 02 '18 at 19:26
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    What is EET? Avoid non-std. Acronyms – ijuneja Aug 02 '18 at 19:31
  • 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) http://cbasso.pagesperso-orange.fr/Spice.htm where I detail the procedure. – Verbal Kint Sep 22 '18 at 09:05
  • @VerbalKint Best make that an answer, I'm willing to bet others might have similar queries in the future. :-) – a concerned citizen Apr 09 '19 at 15:10
  • @a concerned citizen, sure, done, thank you for the suggestion. – Verbal Kint Apr 10 '19 at 05:26
  • ijuneja, EET is the "Extra Element Theorem". – LvW Jul 30 '19 at 13:00

1 Answers1

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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.

Verbal Kint
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