Reference no: EM13336186
Q- The PMOS transistor in the figure below has VTP = -0.5V. As the gate voltage vG is varied from +2.5 V to 0 V, the transistor moves through all of its three possible modes of operation. Specify the value of vG at which the device changes modes of operation.
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)
Q- All the transistors in the circuits shown in the figure below have the same values of |VT|, k', W/L, and A. Moreover, A is negligibly small. All operate in saturation at ID = 1 and |VGS| = |VDS| = 3 V.
(a) Find the voltages V1, V2, V3, and V4.
(b) If |VT| = 1 V and 1 = 2 mA, how large a resistor can be inserted in series with each drain connection while maintaining saturation?
(c) If the current source 1 requires at least 2 V between its terminal to operate properly, what is the largest resistor that can be placed in series with each MOSFET source while ensuring saturated-mode operation of each transistor at ID = 1? In this limiting situation, what do VI, V2, V3, and V4 become?
![619_transistor characteristics6.png](https://secure.expertsmind.com/CMSImages/619_transistor%20characteristics6.png)