Analyze the VTC of the CMOS inverter and derive the expressions for the following regions:1 Input low voltage2 Input high voltage3 Inverter midpoint voltage

To analyze the VTC (Voltage Transfer Characteristic) of the CMOS inverter and derive the expressions for the different regions, follow these steps:

1. Input low voltage (VIL):

   • Start by considering the NMOS transistor in the CMOS inverter.
   • When the input voltage (Vin) is lower than the threshold voltage (Vtn) of the NMOS transistor, it is in the cutoff region.
   • In this region, the NMOS transistor is off, and the output voltage (Vout) is pulled up to the supply voltage (VDD) through the PMOS transistor.
   • Therefore, the expression for VIL is VIL = Vtn.

2. Input high voltage (VIH):

   • Now, consider the PMOS transistor in the CMOS inverter.
   • When the input voltage (Vin) is higher than the threshold voltage (Vtp) of the PMOS transistor, it is in the cutoff region.
   • In this region, the PMOS transistor is off, and the output voltage (Vout) is pulled down to the ground (GND) through the NMOS transistor.
   • Therefore, the expression for VIH is VIH = VDD - Vtp.

3. Inverter midpoint voltage (VM):

   • The midpoint voltage (VM) is the voltage at which the output voltage (Vout) is equal to the input voltage (Vin).
   • At this voltage, both the NMOS and PMOS transistors are partially on, and the CMOS inverter operates in the linear region.
   • To derive the expression for VM, we equate the current flowing through the NMOS and PMOS transistors.
   • The current flowing through the NMOS transistor is given by:
     • IDN = (1/2) * Kn * (Vin - Vtn)^2, where Kn is the NMOS transistor's transconductance parameter.
   • The current flowing through the PMOS transistor is given by:
     • IDP = (1/2) * Kp * (VDD - Vin - Vtp)^2, where Kp is the PMOS transistor's transconductance parameter.
   • Equating IDN and IDP, we can solve for VM.

By following these steps, you can analyze the VTC of the CMOS inverter and derive the expressions for the input low voltage (VIL), input high voltage (VIH), and inverter midpoint voltage (VM).