The Sooch current mirror of Fig. 4.60b utilizes the blocks of Fig. P4.73 to provide the proper voltage drives for the output FETs M2 and M4. (a) The function of M3 is to synthesize the vGS drive...

The Sooch current mirror of Fig. 4.60b utilizes the blocks of Fig. P4.73 to provide the proper voltage drives for the output FETs M2 and M4. (a) The function of M3 is to synthesize the vGS drive needed to sink iI at vDS 5 vOV. This requires vD3 5 vG3 2 Vt , a task performed by M6. Assuming vOV # Vt , fi nd vG6 so that vDS6 5 Vt . (b) For a diode-connected FET, the voltage at any point of its channel will lie somewhere between vS and vS 1 Vt 1 vOV. In particular, there must be a point at which this voltage is vS 1 vOV. In order to access it, we split the FET into two FETs M1 and M5 in series, as shown in Fig 4.73b (recall that two FETs in series still act as a single FET!) Prove that in order to drop vDS5 5 vOV, M5 must operate in the triode region (while M1 is saturated) and must have k5 5 k1y3 (a condition that is achieved by fabricating M5 with a WyL ratio 1y3 that of M1). What is the resulting voltage vD1? (c) Verify that once the circuit of (b) is stacked on top of that of (a) as per the Sooch circuit of Fig. 4.60b, M6’s drain will provide the required drive for M4’s gate, and M1’s drain will provide the required drives for M2’s gate as well as M6’s gate. Find vI . (d) Suppose a certain application requires the creation of the voltage 2vOV (instead of 1vOV) using the topology of Fig. P4.73b. What is the required relationship between k5 and k1 in this case?