Sunday , October 17 2021

# Different operating regions of CMOS inverter

### Different operating regions of CMOS inverter

Question: Describe the different operating regions of CMOS inverter with a neat sketch?

Solution Region A: This region occurs when 0≤Vin<Vtn in which the n-device is cut-off(Idsn=0) and the p-device is in the linear region. Since Idsn=-Idsp, the drain-to-source current Idsp for the p-device is also zero. But for  Vdsp=Vout-VDD with Vdsp=0,

The output voltage in this region is: Vout=VDD

Region B: This region occurs when Vtn≤Vin<VDD/2  in which the p-device is in the linear region and the n-device is in the saturation region. The saturation current Idsn for the n-device is obtained by setting Vgs=Vin.

This\;results\;in\;\;I_{dsn}=\frac{\beta_n}2\lbrack\;V_{in}-V_{out}\rbrack^2

In region B, Idsp is governed by voltages Vgs and Vds  described by:Vgs=(Vin-VDD) and Vds=(Vout-VDD).

The output voltage in this region is : Vout>VDD/2

Region C: This region occurs when Vin=VDD/2  in which both the p-device and the n-device are in the saturation region. The saturation currents for the two devices are obtain with Idsp=-Idsn.

\begin{array}{l}I_{dsp}=\frac{\beta_p}2\lbrack\;V_{in}-V_{DD}-V_{tp}\rbrack^2\\\\and\\\\I_{dsp}=\frac{\beta_n}2\lbrack\;V_{in}-V_{tn}\rbrack^2\\\end{array}

The output voltage VDD drops sharply

Region D: This region occurs when VDD/2 <VinVDD+Vtp in which the n-device is in the linear region and the p-device is in the saturation region. The saturation currents for the two devices obtain with Idsp=-Idsn.

\begin{array}{l}I_{dsp}=-\frac{\beta_p}2\lbrack\;V_{in}-V_{DD}-V_{tp}\rbrack^2\\\\and\\\\I_{dsp}=\beta_n\lbrack\;(V_{in}-V_{tn}{)V_{out}-\frac{V_{out}^2}2\rbrack}\\\end{array}

The output voltage in this region is : Vout<VDD/2

Region E: This region occurs when Vin≥VDD-Vtp in which the p-device is cut-off(Idsp=0) and the n-device is in the linear region.Here  Vgsp=Vin-VDD,Which is more positive than Vtp

The output voltage in this region is Vout=o

Different operating regions of CMOS inverter

Read: Switching threshold of CMOS inverter

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