Due:  Jan. 30, 2002

1.      Design compound CMOS logic gates for the following functions.  (Note that X’ = complement of X):

a.      Z = (A·B·C·D)’

b.      Z = (A + B + C + D)’

c.       Z = ((A + B)·(C + D))’

d.      Z = (((A·B) + C)·D)’

e.       Z = ((A·B) + C·(A + B))’                                                                    (10 pts)

2.  Show three different ways of implementing the XOR logic function Z = A·(B’) + (A’)·B

a. using standard CMOS logic gates (NANDs, NORs, and inverters).

b. using compound CMOS gates with an output inverter.

c. using compound CMOS gates without an output inverter.

List the number of transistors in each case, ignoring input inverters needed to generate A’ & B’.  Note that A’ is the complement of A (and similar for B’).                                             (10 pts)

3.      Design a set of CMOS gates to implement the sum function

S = ABC + (A)(B’)(C’) + (A’)(B)(C’) + (A’)(B’)(C)

(a)     using an implementation comprised only of CMOS NAND gates,

(b)     using a compound CMOS logic implementation.

In (b), try to simplify your circuit by eliminating redundant transistors.  Assume true and complement inputs are available.  Sketch out the circuit schematic at the transistor level.  (20 pts)

4.      An NMOS transistor has a threshold VT of + 0.50 volt when its source-to-substrate voltage is zero, given that the substrate is uniformly doped at 2E17 acceptor dopant atoms/cm3 and the gate oxide capacitance is 3.5 fF/um2.

(a)     Determine an expression for the threshold voltage as a function of source-to-substrate voltage.

(b)     It is desired to obtain a threshold voltage of +1.0 volt at 0 volts source potential (w/r ground).  One method suggested by the engineering team is to provide a separate bias supply for the substrate, in order to increase the source-to-substrate voltage.  What value of Vxx supply would be needed?

(c)     Rather than use a separate substrate bias generator, another group in Engineering is suggesting to use a threshold adjustment implant in the fabrication.  Assuming the implant acts as a sheet charge at the oxide-silicon interface (via the term Qfc), what dose is needed to obtain VTN = 1 volt at Vsx = 0?  Would you use acceptor (NA) or donor (ND) atoms?                                                      (20 pts)

5.  Calculate noise margins for a CMOS inverter operating at VDD = 3.3 volt with VTN = 0.75 volt, VTP = -0.75 volt, and bN = bP.    If bN = 2 bP, what are the new noise margins?          (20 pts)

6.  Design a five-stage ring oscillator built with pseudo-NMOS inverters and write out the SPICE code to represent the circuit (for numerical simulation).  Assume each stage is loaded with a 50 fF equivalent wire capacitance.  Assume all N and P devices have Leff = 0.25 um, the N-FET’s have W/L = 8/1.  Design the P-FET W/L to achieve a down level of 0.2 volt, given a full up level input condition.  Roughly estimate the device source and drain dimensions for the SPICE coding.  Transistor model names are assumed to be NMOS and PMOS.  Use the simple MOSFET equations given in the text and in class for the device currents, assuming mN = 2.5 x mP, VTN = +0.75 volt, VTP = -0.75 volt, and VDD = 3.3 volt.  You may assume Cox = 3.5 fF/um2.     (20 pts)

R. W. Knepper

Jan. 16, 2002