Voltage amplifier circuit - article V0

In the article below, I tried to explain a voltage amplifier circuit to a person not knowing circuits. That explanation of mine was very bad, and I accomplished nothing in this article. Although I failed spectacularly, I still believe I can do it within a 20-minute read. Tomorrow, I will write the same article again, and I will allow myself the chance to rewrite this 2 times more before I change methods.

It is late at night, so I couldn't re-write this before posting, sorry.

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As promised, I'll talk about transistors in active circuit design today. But before that, I would like to summarize the layers of abstractions that are used in designing logic ICs. The layers, excluding analysis layers such as characterization, simulation, and metrology, are: (I can be wrong about this list)

1. Embedded Software/Firmware
2. Compiler
3. Instruction set
4. PCB Design
5. Computer Architecture
6. Logic Synthesizer
7. Circuit Layout
8. routing
9. macro cells
10. standard cells
11. semiconductor devices
12. semiconductor materials
13. semiconductor manufacturing
14. semiconductor manufacturing tools

I don't think I will elaborate on each layer in this post, and instead I will make another post with my ill-informed description of each layer. For completeness of the article and figuring out what I want to do in the future. The semiconductor industry is such ubiquitous in modern technology, and in addition to this list, I still haven't touched on topics such as photonics, wireless communications, and more. Maybe exercising my words on describing the big picture will give me a better idea on what to do.

Aside: I think active circuit design exists in both the PCB design abstraction layer and IC macro cells layer. 

Back to active circuit design. Active circuit design deals with manipulating electrical signals of voltage and current. Example functions of a circuit is to multiply a voltage by 3 (input: 20mV, output: 60mV), compare two values (input A: 40mV, input B: 20mV, output B > A: 0V), and more.

You can design the functions I listed with both opamps and transistors, where opamps are typically made from transistors. And because I need to do homework with transistors and not opamps, I will describe active circuit design with transistors today.

Important: the example below only demonstrates the concept of multiplying a voltage. The circuit analysis is INCORRECT. But this incorrectness is like a compression error. It is similar to compressing real life into pixel art, where my example below is pixel art. (if you are to learn circuits for real, the explanation below might confuse your actual learning)

First, we need to describe the relationship between the 3 terminals of a transistor, and in this case, a MOSFET. The 3 terminals are:

1. Drain
2. Gate
3. Source

The relationship between the terminals is: v_{DS} = -g_m R_D v_{GS}. We can see the transistor and the resistor as a magnifying glass. This magnifying glass is made to have a (-g_m R_D) zoom. 

Putting in some numbers. For example, g_m = 0.0001, and R_D = 1,000,000. Then, v_{DS} = -100 v_{GS}. And this circuit magnified the input voltage, v_{GS}, by a 100x. Where the output is now the voltage at v_{DS}. And this is an example of a circuit multiplying a voltage.