## Chapter 16

## Q. 16.1

Objective: Determine the transition point, minimum output voltage, maximum drain current, and maximum power dissipation of an NMOS inverter with resistor load.

Specifications: Consider the circuit in Figure 16.3(a) with parameters V_{DD} = 2.5 V and R_{D} = 20 kΩ. The transistor parameters are V_{T N} = 0.5 \ V \text{ and } K_n = 0.3 \ mA/V^{2}

## Step-by-Step

## Verified Solution

The input voltage at the transition point is found from Equation (16.9). We have

(0.3)(25)(V_{I t} − 0.5)^{2} + (V_{I t} − 0.5) − 2.5 = 0

which yields

V_{I t} − 0.5 = 0.515 V or V_{I t} = 1.015 V

The output voltage at the transition point is

V_{O t} = V_{I t} − V_{T N} = 1.015 − 0.5 = 0.515 V

When v_{I} is high at v_{I} = 2.5 V, the output voltage is found from Equation (16.11). We find

v_{O} = V_{DD} − K_{n} R_{D} [2(v_{I} − V_{T N})v_{O} − v^{2}_{O} ] (16.11)

v_{O} = 2.5 − (0.3(25)[2(2.5 − 0.5)v_{O} − v^{2}_{O}]

which yields the output low level as

v_{O} = V_{O L} = 82.3 mV

The maximum drain current in the inverter occurs when v_{O} = V_{O L} and is found to be

i_{D,max} = \frac{2.5 − 0.0823}{25} ⇒ 96.7 µA

The maximum power dissipated in the inverter is

P_{D,max} = i_{D,max} \cdot V_{DD} = (0.0967)(2.5) = 0.242 mW

Comment: The level of V_{O L} is less than the threshold voltage V_{T N} ; therefore, if the output of this inverter is used to drive a similar inverter, the driver transistor of the load inverter would be cut off and its output would be high, which is the desired condition. We will compare the maximum drain currents and maximum power dissipations of the three basic NMOS inverters