Microelectronic Circuits - 1

REFERENCE BOOK

I decided to crack open my Microelectronic Circuits book (Sedra/Smith) to start running through it. The goal will be to keep at it from cover to cover or until I get bored or distracted and want to move on to the next thing.

Sedra AS, Smith KC. Microelectronic Circuits 5th Ed. Oxford University Press 2004.

ISBN 0-19-514252-7

The knowledge from this set of exercises is useful in anything for which we need a working knowledge of circuit theory like robotics, microprocessor chip design, electronics modules in automobiles/planes/spaceships, and any DIY gadgets you may want to engage with (check out this guy who has been tinkering with spectral imaging of wifi).

 

PROBLEM

To start things off, I jumped into Appendix B of Sedra/Smith for a quick refresher of 2-port linear networks. In particular, the application of 2-port networks on a small signal equivalent model of the bipolar junction transistor (BJT). Let's have a look:

<LEARNING OPPORTUNITY>

First thing to observe is how this pertains to a BJT:

r_x is the input resistance, seen by current driving to the Base -- very small
r_μ is the Base-to-Collector resistance -- very large
r_π is the Base-to-Emitter resistance -- significantly larger than r_x and significantly smaller than r_μ
g_m is the transconductance from Collector to Emitter, and it is in parallel with
r_O, the output resistance -- large, not significant smaller than r_μ


We can think of r_O as the resistance seen by any downstream node that reads the output of this transistor, thus we can model it as a 2-port network.

SOLUTION

We are to find the H parameters.

Here's how I solved this problem:

COMMENTS / NOTES

• The answer given for h₂₂ in Sedra/Smith has incorrect units. Current / Voltage should have units of inverse Ohms, or Siemens.
• I was able to find the other three H parameters easily, but h₂₁ made me struggle, ngl. In particular, I wasn't sure how to deal with a transconductance in parallel with a short circuit. 
• Remember that for a short circuit, all parallel resistors are eliminated. 
• Contrary to the popular saying, current does not always take the "path of least resistance". However, current does always take the path of no resistance.
• It turns out that you can't eliminate transconductances in parallel with short circuits. Instead, you just apply them to KCL.
• Observe how the short circuit affects the potentials in this circuit. 
• In particular, a transconductance is not a resistance and in this small signal equivalent, it is shown as connected between two nodes of 0 V. 
• That means that r_μ and r_π are in parallel, both with one node at v_π and the other at common.
• Therefore, we can think of it as there being a potential -v_π across resistor r_μ (sorry, looks like my highlight didn't show up in the image).
• Now KCL works perfectly by showing that the current flowing into the node, I₂, is balanced by the two currents flowing out, the transconductance and the potential drop across resistor r_μ (which is negative, so the current ends up flowing into the node from this IR as well).

Concept of this Project

A

s a former graduate student, I remember wondering quite a few times whether I was "approaching the problem correctly," and realizing after an hour or so of perceived progress, "...no I wasn't."

Times like these made me think of how useful it would be to have some kind of a discussion board, some forum on which I and other people could bounce ideas off each other to develop a better problem-solving strategy; rather than try to find the right path, collaborate our minds to carve one out - after all, teamwork is what allowed us to survive the Ice Age through the Pleistocene and collaboration is what allows us today to make breakthroughs in semiconductor process manufacturing as we reach the end of Moore's Law. Our survival and progress as a species has depended on us working together, n'est pas?

But that was grad school. No one had time to actually put their good ideas to use. So here we are.

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The purpose of this blog, first and foremost, is to serve as a diary of sorts in my quest for knowledge. I am using this space to help me stay connected with technical knowledge from my past and organize my thoughts to explore new and interesting things in the future. So, this is essentially me trying to practice the old sentiment, 'Learn something new everyday.'

My intended format is a periodic update (eventually, I'd like this to be daily, but at the moment I'm not sure that such ambition is wise) in which I will attempt some number of problems from some [engineering, mathematics, pure science, economics, ... ] topic, and share my work with the community. If it helps some budding STEM student in the process, so much the better.

Since I am an American who has traveled to places where speech is not a freedom but rather a rare luxury, I have gained a deep appreciation for the First Amendment. As such, anyone is free to comment on, criticize, disagree with, encourage, contribute to, question, answer, despise, or appreciate this blog. However, freedom of speech is not freedom to slander, so please don't.


I had a professor who liked to tell us that he didn't care about cheating in his class. Obviously, this was a ruse, for he always followed up with a caveat:

However, I myself never cheated because I was just too damn arrogant to believe that someone else could come up with an answer better than mine.

In the same vein, I would strongly advise against plagiarizing any work that you see here because though I am indifferent to how you use it, I make no claim that it is correct - only that it is mine and that it is open to discussion. But more importantly, do you really want to rob yourself the experience of understanding that problem, no matter how hellish it may be?


Finally, I have no idea how this blog is going to grow, if it's going to grow, or if it will even be effective for me or anyone else, but I'm definitely excited to start.

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Let's learn something new.