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Chapter 16

Q. 16.7

Objective: Determine the critical voltages on the voltage transfer curve of a CMOS inverter.

Consider a CMOS inverter biased at V_{DD} = 5  V with transistor parameters K_{n} = K_{p} and V_{T N} = −V_{T P} = 0.8  V. Then consider another CMOS inverter biased at V_{DD} = 3  V with transistor parameters K_{n} = K_{p} and V_{T N} = – V_{T P} = 0.6  V

Step-by-Step

Verified Solution

(V_{DD} = 5  V): The input voltage at the transition points is, from Equation (16.41),

v_{I} = v_{I t} = \frac{V_{DD}  +  V_{T P}  +  \sqrt{\frac{K_{n}}{K_{p}}} V_{T N}}{1  +  \sqrt{\frac{K_{n}}{K_{p}}}}                (16.41)

V_{I t} = \frac{5  +  (−0.8)  +  \sqrt{1}(0.8)}{1  +  \sqrt{1}} = 2.5  V
The output voltage at the transition point for the PMOS is, from Equation (16.37(b)),
V_{O Pt} = V_{I t}  −  V_{T P} = 2.5  −  (−0.8) = 3.2  V
and the output voltage at the transition point or the NMOS is, from Equation (16.38(b)),
V_{O Nt} = V_{I t}  −  V_{T N} = 2.5  −  0.8 = 1.7  V

(V_{DD} = 3  V): The critical voltages are
V_{I t} = 1.5  V                 V_{O Pt} = 2.1  V              V_{O Nt} = 0.9  V

Comment: The two voltage transfer curves are shown in Figure 16.27. These figures depict another advantage of CMOS technology, that is CMOS circuits can be biased over a relatively wide range of voltages.

16.27