Joseph A. Elias, PhD. 1. Class 10: CMOS Gate Design. Topics: 1. Exclusive OR
Implementation. 2. Exclusive OR Carry Circuit. 3. PMOS Carry Circuit Equivalent.
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
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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
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Class 10: CMOS Gate Design Exclusive OR Carry Circuit (Martin c4.5)
NMOS realization •A in parallel with B •A||B in series with C •AB in parallel with (A||B)C Vout =
PMOS equivalent •A in series with B •AB in parallel with C •A||B in series with (AB)||C
Joseph A. Elias, PhD
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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
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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
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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
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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
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Class 10: CMOS Gate Design Logic Negation (Martin c4.5)
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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
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Class 10: CMOS Gate Design Equivalent Circuits (Martin c4.5)
Joseph A. Elias, PhD
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Class 10: CMOS Gate Design Fan-In and Fan-Out (Weste p264-267)
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Class 10: CMOS Gate Design Rise Delay Time (Weste p264-267)
Rise time delay where
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Class 10: CMOS Gate Design Rise Delay Time (Weste p264-267)
Re-writing
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Class 10: CMOS Gate Design Rise Delay Time (Weste p264-267)
Has the form:
where
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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
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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
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