Lecture 5
Static CMOS Gates
Jack Ou, Ph.D.
2-Input NOR Gate
F can only be pulled up
if A=B=0 V
F can be pulled down by
either A=1 or B=1. (Or Both)
2-Input NAND Gate
F can only be pulled
down if both A=B=1.
F will be pulled up if
either A or B is 0 V.
NAND Gates
NOR Gates
2-Input AND Gate
NAND
2-Input OR Gate
NOR
Alternative Implementation for High
Fanin Gates
Steps for Generating Non-Trivial Static
CMOS Logic Circuits
1. Implement the pull-down (NMOS)circuit
using 𝐹
– Useful technique: DeMorgan’s
Theorem
2. Synthesize the dual of the
pull-down circuits using PMOS
DeMorgan’s Theorem
• The complement of a function can be obtained by
– Replacing each variable with its complement
– Exchange the AND and OR functions
• Example
– 𝐴 + 𝐵 𝐶 = 𝐴 + 𝐵 + 𝐶 = 𝐴𝐵+𝐶
Dual
• The dual of any logic function can be obtained
by exchanging the AND and OR operations.
– ab ↔a+b
– (a+b)c ↔ab+c
A fictional AND Circuit
The current flows only when
both A and B are closed.
Fictional OR Circuit
The current flows when
either A or B is closed.
Implementation
• Use transistors in series to implement a logical
AND function
• Use transistors in parallel to implement a
logical OR function
OAI Circuit ( 𝐴 + 𝐵 𝐶)
XOR/XNOR
Mux
Determine a Boolean Expression a
Schematic
1. Determine 𝐹 implemented by a NMOS pulldown network.
2. Complement 𝐹 to obtain F.
2-Input XOR
𝐴0𝐴1(A0+A1
XNOR
𝐴0𝐴1(A0+A1)
𝐴0
𝐴1
𝐴0 + 𝐴1
𝐴0𝐴1
CMOS Gate Sizing
Device Sizing
• Obtain the same delay as the inverter for the
rise/fall cases.
– ReffN=12.5 Kohm/SQ, ReffP=30 Kohm/SQ
– Reff=Reff(L/W)
– ReffP/ReffN=2.4
– To achieve the same delay, (assume LP=LN,
WP=2.4WN, WP/WN is approximately 2.
Size Devices for the Worst Case
• Series transistors: Increase W to reduce Reff.
• Parallel transistors: assume the worst case, i.e.
only one of the parallel transistor is ON.
Transistor Sizing Without Velocity
Saturation
Figure 5.2
Assumption: Equal rise delay and fall delay
Consideration: Effective Resistance
Inverter
Inverter tPHL
tPHL=64.045 pS
NAND2 Test Circuit
NAND2 tPHL
tPHL=66.01 pS
Effective Width
• Transistors in Series
– W1||W2||W3
• Transistors in Parallel
– W+W2+W3
Trade-Off
Increase W to reduce the effective
Resistance for the pull down network.
The area is increased.
FO4
Fanout ratio: total capacitance driven by a gate dividing
by its input capacitance
VTC of Gates
Adjust VS
• Knob:
– χ as defined in EQ. 4.15
– Increase WNLP/LNWP to decreased VS.
– Decrease WNLP/LNWP to increased VS.
Switching Voltage of a NAND Gate
Both inputs tied together: effective WN=W, WP=4W, VS shifts to the right.
Both input A=high, sweep VB: effective WN=2W, WP=2W, VS shifts to the left.
Switching Voltage of a NOR Gate
Both inputs tied together: effective WN=2W, WP=2W, VS shifts to the left.
Both input A=ground, sweep VB: effective WN=W, WP=4W, VS shifts to the right.