2. (17 points) The purpose of this problem is to explore one use of the voltage-dependent depletion capacitance of a diode. Consider the schematic shown here for the front end

of a simple radio with an antenna near the top of the diagram in Figure 3-2 and connected to a tunable tank circuit.. Let R1 = 75 N and the inductor's value be L= (1000+X 31D) nH. The silicon diode has a pn junction area of 40 µm × 50 um^2, with both sides doped relatively heavily at NA-ND=1018 cm³. Assume Is = 1 pA. (a) What is the built-in voltage of the diode? (See Razavi's Eq. 2.69.) (b) What is the zero-bias depletion capacitance of the diode? (See Razavi's Eq. 2.76.) (c) What is the resonant frequency of the tank circuit if the diode is not biased? (d) If you want to tune the radio to KCSU-FM, what should be the voltage of V tune?[Note that there is a sign error (or labeling error) in Razavi’s Eq. 2.75. There is no positive reverse voltage (VR =-That equation should have read VD) that can make the capacitance approach infinity. C_{\text {depl }}=\frac{C_{0}}{\sqrt{1+\frac{V_{R}}{V_{b i}}}} See, for example, that the corrected equation is used in Example 2.15 in Eq. 2.82.]