Hello

I will derive the **CMOS VTC** in few steps, and below is the first one. We did derive the below equations sometime back, and use the same in our derivation. The goal is to get rid of all **internal node voltages like Vgsp, Vgsn**, etc, and make the curves, a function of Vin and Vout.

Why? Because the logic gates (AND, OR, INVERTER) that are given to us for usage have (in general), 4 voltages – **Vdd, Vss, Vin and Vout.** That’s all we see from top, and there is no way, in **physical design and STA,** we look around the node voltages.

With that back ground, let’s begin

**Step 1:** Let’s start with **PMOS and convert the node voltage ‘Vgsp’ to ‘Vin’ and shift the Idsp v/s Vdsp curve to their respective quadrant.** The table on the right top explains the conversion and now, we have an **equivalent ‘Vin’ for every value of ‘Vgsp’**.

Also, since we have **2 kinds of currents ‘Idsp’ and ‘Idsn’**, let’s use only one of them, so every transistor will be a function of only one current and things will turn out to be pretty simple. **Idsp = -Idsn**

With the above **conversions and logical assumptions, below (bottom right) is the curve what we get**

Also, **Vout = Vdd + Vdsp**, so let’s **convert the Vdsp that’s present on X axis, and then the below whole curve (bottom right), becomes completely a function of Vin and Vout**

And the above curve (bottom right), does make sense, which you can figure out by calculating the current at 1 value of Vdsp and Vgsp, and comparing the same with equivalent ‘Vin’ and ‘Vout’

**For eg. -Vgsp5 of -2V is nothing but Vin = 0V, and -Vdsp of -2V is Vout = 0V**

Now the value of **current at (Vgsp, Vdsp)** of (-2V and -2V) **is the highest saturation current -Idsp** shown below, which is nothing but +Idsn with Vin = 0V and Vout = 0V

Stay with me on next post, where I will cover the Step2 and Step3 in a similar fashion, and you will realize, how easy these topics were to understand when represented in a graphical format.

* “Good graphic design solutions to communication problems can improve the flow of information in society and, therefore, substantially and positively affect education, social well-being and the daily enjoyment of life. In addition, good graphic design solutions can also have a positive economic impact.” * – Jorge Frascara

Let’s build some more graphics in my next post. Stay tuned

Kunal