# Sizing transistors for a CMOS circuit?

Say we have this cmos circuit any advice how you would size up the transistors assuming that the gate is minimum-sized. Ive done some reading and I am struggling to understand. Is there an definition to define this?? I feel like it is really simple. Thanks

For minimum sizing, we usually say that L is minimal. What we actually scale is the W.

The NMOS in a inverter of minimal size is defined as being of size "1". All other sizes are in reference to this.

Depending on the coursebook you ask, a PMOS is said to be "2 times worse" than a NMOS of the same size. So our default inverter looks like this (I used to more common transistor symbol found in most digital/VLSI design textbooks):

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What we usually want, is that when the output is pulled to 0 by a certain set of inputs, the resistance to ground (or rather, the current capability of the gate) is the same as that of a single inverter. This means, if you have 2 transistors in series to ground, you need to make them 2 times bigger to compensate.

I've redrawn the pulldown network from the gate in your question.

When we look at this, we can see that E gives us a path from the output to ground. Therefor, we can keep this minimal, and it's size will be 1.

C', D', A and B form parallel/series branches. In the worst case (worst case where we still have a output equal to 0, ofcourse), only one transistor of each parallel pair will be on. So, we will have 2 gates in series. This doubles their resistance, so we need to also double their size to compensate. In other words, these transistors will be size 2.

This method can be used as a shortcut for finding the size easily. So here for the pmos circuit the maximum worst delay that can be generated is by having three transistors in series. so that may be t1 t3 and t5 or the next possible combination would be t2 t4 and t5. we know that 2nmos = pmos size. so, we first multiply 2 and then for three transistors in series it should be multiplied again with 3. so, 6 is the size for pmos. and for nmos the worst case of delay that can be generated is by using 2 transistors in series the combinations might be t7 t9 or t8 t10. so, 2 would be the size of pmos transistors.