Class 10: CMOS Gate Design

Topics: 1. Exclusive OR Implementation 2. Exclusive OR Carry Circuit 3. PMOS Carry Circuit Equivalent 4. CMOS Full-Adder 5. NAND, NOR Gate Considerations 6. Logic Example 7. Logic Negation 8. Mapping Logic ‘0’ 9. Equivalent Circuits 10. Fan-In and Fan-Out 11. Rise Delay Time 12. Rise Delay Time 13. Rise Delay Time 14. Fall Delay Time 15. Equal Delays

Joseph A. Elias, PhD 1 Class 10: CMOS Gate Design Exclusive OR Design (Martin c4.5) 3-input XOR Truth Table

Similar to how one derives a 2-input XOR (Martin, p.183) using (a’+b’)=(ab)’ (a’b’)=(a+b)’ a XOR b = a’b + ab’ = a’a + a’b + ab’ + bb’ = a’(a+b) + b’(a+b) = (a’+b’)(a+b) = (ab)’(a+b) = (ab + (a’b’) )’ = (ab + (a + b)’ )’

Joseph A. Elias, PhD 2 Class 10: CMOS Gate Design Exclusive OR Carry Circuit (Martin c4.5)

NMOS realization PMOS equivalent •A in parallel with B •A in series with B •A||B in series with C •AB in parallel with C •AB in parallel with (A||B)C •A||B in series with (AB)||C Vout =

Joseph A. Elias, PhD 3 Class 10: CMOS Gate Design PMOS Carry Circuit Equivalent (Martin c4.5)

•Martin indicates equivalency between these circuits •Is this true? (AB+C)(A+B) = (A+B)C + (AB) ABA + ABB + AC + BC = AC +BC +AB AB + AB + AC + BC = AC + BC + AB AB + AC + BC = AB + AC + BC equivalent

Joseph A. Elias, PhD 4 Class 10: CMOS Gate Design CMOS Full-Adder (Martin c4.5)

Sum: (A+B+C) Carry + ABC

Carry: (A+B)C + AB

Joseph A. Elias, PhD 5 Class 10: CMOS Gate Design NAND, NOR Gate Considerations (Martin c4.5)

•NAND is preferable to NOR - why? •What makes p-ch undesirable? •How does one compensate for it?

Joseph A. Elias, PhD 6 Class 10: CMOS Gate Design Logic Example (Martin c4.5) Desired Truth Table Corresponding Karnaugh Map

Grouping of 1’ (meaning what gates?):

Joseph A. Elias, PhD 7 Class 10: CMOS Gate Design Logic Negation (Martin c4.5)

Joseph A. Elias, PhD 8 Class 10: CMOS Gate Design Mapping Logic ‘0’ (Martin c4.5)

Using (a’b’)=(a+b)’

•Choice of which map to use depends on whether inputs are negated

Joseph A. Elias, PhD 9 Class 10: CMOS Gate Design Equivalent Circuits (Martin c4.5)

Joseph A. Elias, PhD 10 Class 10: CMOS Gate Design Fan-In and Fan-Out (Weste p264-267)

Joseph A. Elias, PhD 11 Class 10: CMOS Gate Design Rise Delay Time (Weste p264-267)

Rise time delay where

Joseph A. Elias, PhD 12 Class 10: CMOS Gate Design Rise Delay Time (Weste p264-267)

Re-writing

Joseph A. Elias, PhD 13 Class 10: CMOS Gate Design Rise Delay Time (Weste p264-267)

Has the form: where

Joseph A. Elias, PhD 14 Class 10: CMOS Gate Design Fall Delay Time (Weste p264-267)

Similar to rise time delay, the fall time delay as a function of fan-in and fan-out:

Assuming equal-sized gates (n/p size fixed) is the case (as in standard cells and gate arrays)

Joseph A. Elias, PhD 15 Class 10: CMOS Gate Design Equal Delays (Weste p264-267)

Assuming equal delays gives

Where the beta ratios are

So p-ch would be made (βn/ m βp) times wider for equal rise and fall delay

Joseph A. Elias, PhD 16