# Connecting two-port network theory to microelectronic design (Sedra and Smith)

I am trying to connect what I'm learning in Sedra and Smith (I am currently in Chapter 7 of the 7th edition which talks about basic transistor amplifier configurations, eg. CS) to what I have learned in the past about two-port networks. In particular, I want to understand how what's going on in Sedra and Smith can be recapitulated in the language of two-port networks.

Now with the small-signal transistor models (let's stick with the MOSFET), we have only the transconductance gain $$\g_m\$$ and the output resistance (due to CLM) $$\r_0\$$. Now the general program shown by Sedra and Smith here is, for every amplifier configuration, to compute an open circuit output voltage $$\A_{vo}\$$, an input resistance $$\R_{in}\$$, and an output resistance $$\R_{o}\$$ defined by the equivalent circuit given in the attached picture.

That is, we see that we have the definitions $$A_{vo} = \left. \dfrac{v_{out}}{v_{in}} \right|_{i_o=0}$$ $$R_{in} = \dfrac{v_{in}}{i_{in}}$$ $$R_{out} = \left. \dfrac{v_{out}}{-i_{o}} \right|_{v_{in}=0}$$

Now from this general structure I'm trying to connect this to a "set of two-port parameters". My inclination is to write a system of equations as below (given that $$\v_{out}\$$ is twice in a numerator, but $$\v_{in}\$$ is in a numerator and in a denominator): $$V_{out} = -i_oR_o+A_{vo}v_{in}$$ $$i_{in} = \dfrac{1}{R_{in}}v_{in} +0i_o$$

That is, we assume no internal feedback in this basic model. The above seems to point to the so-called "g-model" being used (inverse hybrid). Is this an accurate reflection of what's going on?

Bonus points, for those who have Sedra and Smith...sometimes they distinguish between $$\R_{o}\$$ and $$\R_{out}\$$ and I have no clue what is meant by the difference. Any help would be greatly appreciated. Also, if anyone has any book recommendations for books like Sedra and Smith but which DO emphasize the important connection to two-port networks, please let me know.

Now with the small-signal transistor models (let's stick with the MOSFET), we have only the transconductance gain $$\g_m\$$ and the output resistance (due to CLM) $$\r_0\$$.

If you use this model for the transistor, you are assuming a Norton output circuit rather than Thevenin:

simulate this circuit – Schematic created using CircuitLab

As you know, you can easily convert between the Norton and Thevenin equivalent circuits to see the equivalence between your "2-port" model and your "Sedra and Smith" model (which are actually both 2-port models, just with different forms)

Bonus points, for those who have Sedra and Smith...sometimes they distinguish between $$\R_{o}\$$ and $$\R_{out}\$$ and I have no clue what is meant by the difference.

It's been a while, but I vaguely remember that $$\R_o\$$ was the output resistance of an individual transistor while $$\R_{out}\$$ was the output resistance of an entire amplifier circuit...but if that isn't consistent with what you see in your book then I'm just mis-remembering the notation.

• Thanks for the response. To be sure, I think you mean $g_mv_{in}$ right?
– EE18
Apr 3 at 15:43
• @1729_SR, yes, you're right. I'll correct it. Apr 3 at 15:48
• I see. Then the equivalent that you've drawn above is effectively that for the y-parameters, right? With $y_{12}=y_{in,out}=0$?
– EE18
Apr 3 at 15:51
• Yes, except we ignore the $y_{12}$ term since it's very small, and for the y-parameters should properly label the "resistors" as conductors instead: $g_{11}$ instead of $r_{in}$ and $g_{22}$ instead of $r_{out}$. Apr 3 at 15:55
• Gotcha. The point then that I want to confirm to myself is that two-port network theory tells us that any two-port circuit can be capitulated in the form you gave, or the one that Sedra and Smith gave (assuming it's unilateral). I was just looking for motivation for why the general program they go through is always the same. I wish they mentioned two-port theory but alas. Thank you again!
– EE18
Apr 3 at 15:58