# AND gate transistor sizing

Discussion in 'Homework Help' started by vead, May 16, 2014.

Nov 24, 2011
621
8
AND gate with cmos transistor
we can create cmos AND gate with 3 nmos and 3 pmos transistor

Equation X=AB

AND gate cmos circuit= <-NAND--Inverter->

I want to size the transistor so that the output resistance is same as that of inverter with nmos W/L=3/2 and pmos W/L=6/2

inverter with nmos W/L=3/2 and pmos W/L=6/2

parallel pmos (L will double with same W)

pmos 1 W/L=6/4 and pmos 2 W/L = 6/4

nmos series ( W will double with same L)

nmos 1 W/L= 3/4 and nmos 2 W/L=3/4
transistor size for AND gate cmos

nmos 1 W/L=6/4
nmos 2 W/L=6/4
nmos 3 W/L=3/2

pmos 1 W/L=3/4
pmos 2 W/L=3/4
pmos 3 W/L=3/2

IS this correct sizing for AND gate

Last edited: May 16, 2014
2. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Isn't the output resistance of an AND gate due entirely to the inverter that follows the NAND gate?

Nov 24, 2011
621
8
look at this Image

given, Q5 nmos W/L=3/2
Q6 pmos 3 W/L=3/1

I want to determine size Q1,Q2,Q3 ,Q4a

Q1 nmos W/L=6/4
Q2 nmos W/L=6/4
Q3 pmos 1 W/L=3/4
Q4 pmos 2 W/L=3/4

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4. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
What is "Q6 pmos 3"? Or Q4a? Or "Q3 pmos 1"?

Nov 24, 2011
621
8
how to size transistors for AND gate

look at Image that I have uploaded

AND gate create with NAND gate INVERTER
there are six transistor used to create AND gate
two nmos connected in series before the Inverter
two pmos connected in parallel in NAND gate (before inverter)

sizing ratio for nmos W/L=3/2 and pmos W/L =6/2 in inverter circuit

how to size for all transistor ?

• ###### 04146.png
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Nov 24, 2011
621
8
look at this sizing
Nmos W/L=3/2 and Pmos W/L=6/4( transistor in inverter circuit)

caseI - when to mosfet in series this is similar to one transistor with double length and same width
Example two series nmos with W=1 and L=1
resultant W/L=1/2

case II when to mosfet in parallel W will be double with same L
Example- two pmos in parallel with w=1 and L=1
resultant W/L=2/1

So I made following sizing for AND gate circuit
nmos W/L=3/2 and pmos W/L=6/4 (inverter circuit)
nmos W/L=3/1 and pmos W/L=3/4 (for nand gate circuit)

7. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
You stated in the original post: "I want to size the transistor so that the output resistance is same as that of inverter with nmos W/L=3/2 and pmos W/L=6/2"

Will: "nmos W/L=3/2 and pmos W/L=6/4 (inverter circuit)" accomplish that?