MOS Inverters: Static Characteristics

The inverter is the most fundamental logic gate and it can be directly applied to more complex logic circuits, such as NAND and NOR gates. Thus, the inverter designing is also crucial for digital circuit design. 

In above figure, an inverter is shown which inverts the input voltage A and gives the inverted output as B. In MOS inverter circuit design, using positive logic convention logic 1 is represented as high voltage or VDD and logic 0 is represented as low voltage. The DC voltage transfer characteristic (VTC) is also shown in above figure. The voltage Vth is called the inverter threshold voltage. 

For any input voltage between 0 and Vth = VDD/2, the output voltage is equal to VDD i.e. logic '1'. The output switches from VDD to 0 when the input is equal to Vth. 

For any input voltage between Vth and VDD, the output voltage assumes a value of 0 i.e. logic '0'. Thus, an input voltage 0 < Vin < Vth is interpreted by this ideal inverter as a logic "0," while an input voltage Vth <Vin < VDD is interpreted as a logic " 1." 

The general circuit structure of an NMOS inverter is shown in the above figure.

For very low input voltage levels which are below the threshold voltage Vth, the driver nMOS transistor is in cut-off, hence, it does not conduct any current. Therefore, the voltage drop across the load device is very small and the output voltage (Vout) is high (VOH).

When the input voltage Vin increases and crosses the Vth, the driver nMOS transistor starts conducting and certain drain current flows, and the output voltage starts decreasing. This drop in the output voltage level does not occur abruptly but rather gradually and with a finite slope. 

VTC of the nMOS inverter, shown below, indicates the operating mode of driver transistor and voltage points.

VOH: Maximum output voltage when the output level is logic " 1" 

VOL Minimum output voltage when the output level is logic "0" 

VIL: Maximum input voltage which can be interpreted as logic "0" 

VIH: Minimum input voltage which can be interpreted as logic " 1"

For any inverter circuit, estimation of the five critical voltage points i.e. VOL, VOH, VIL, VIH and Vth for different inverter designs is an important task.