A 512M-bit DRAM is designed to be used by a microprocessor. The DRAM requires 10ns for each refresh operation and the refresh period of the DRAM is 256µs. The microprocessor issues a refresh cycle every 50ns. Determine the maximum number of rows of the DRAM that can be used by the microprocessor without any refresh issue. (c) Determine the time (in %) spent for the refresh operation using the parameters in Question 2(b).
(a) Explain why a Bandgap voltage reference is preferred over a VBE-based voltage reference. (b) A Bandgap voltage reference is depicted in Figure 3. Derive the expression for VOUT in terms of VBE + KVT where K and VT are a constant and the thermal voltage, respectively. (c) Redesign the Bandgap voltage reference such that the current in the two transistors is not drawn from VCC. (d) The bipolar transistor Q1 and the bipolar op-amp A in the Bandgap voltage reference in Figure 3 are replaced by a PMOS transistor and a CMOS op-amp, respectively. Explain if these replacements are appropriate.