Low entropy transfer function, output impedance

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

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

• I'm currently reading his book but I would leave it C.Basso himself :)
– Mike
Aug 2 '18 at 18:03
• 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. Sep 22 '18 at 9:05
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.