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Using the parameters given below, calculate the current through two nMOS transistors in series (see Figure P3.11), when the drain of the top transistor is tied to VDD, the source of the bottom transistor is tied to VSS = 0 and their gates are tied to VDD. The substrate is also tied to VSS = 0 V. Assume that W/L = 10 for both transistors. k’ = 25 µA/V2 VT0 = 1.0 V γ = 0.39 V1/2 |2ΦF| = 0.6 V Hint: The solution requires several iterations, and the body effect on threshold voltage has to be taken into account. Start with the KCL equation

Using the parameters given below, calculate the current through two nMOS transistors in series (see Figure P3.11), when the drain of the top transistor is tied to VDD, the source of the bottom transistor is tied to VSS = 0 and their gates are tied to VDD. The substrate is also tied to VSS = 0 V. Assume that W/L = 10 for both transistors. k’ = 25 µA/V2 VT0 = 1.0 V γ = 0.39 V1/2 |2ΦF| = 0.6 V Hint: The solution requires several iterations, and the body effect on threshold voltage has to be taken into account. Start with the KCL equation

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Using the parameters given below, calculate the current through two nMOS transistors in series (see Figure P3.11), when the drain of the top transistor is tied to VDD, the source of the bottom transistor is tied to VSS = 0 and their gates are tied to VDD. The substrate is also tied to VSS = 0 V. Assume that W/L = 10 for both transistors. k’ = 25 µA/V2 VT0 = 1.0 V γ = 0.39 V1/2 |2ΦF| = 0.6 V Hint: The solution requires several iterations, and the body effect on threshold voltage has to be taken into account. Start with the KCL equation

Explanation & Steps

In the given circuit, two NMOS transistors are in series having same parameters. The only difference is the consideration of body bias effect for both transistors. For driver NMOS transistor VSB = 0, thus there will be no change in threshold voltage for this transistor. While VSB is not equal to zero for load NMOS transistor, thus threshold voltage will be altered by body bias effect of load NMOS transistor. Use following steps to determine drain current of the given circuit.

Step (1): Determine mode of operation of driver and load NMOS transistors.

Step (2): Apply KCL at midpoint to get a relation between Vx and threshold voltage of load NMOS transistor (VTL) and solve it iteratively to calculate final value of Vx and VTL.

Step (3): Use drain current of either driver or load NMOS to determine drain current in the circuit.

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