## 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.