3) At 5 MHz a lossy material is characterized by ɛε=3.6ε, μ=2.1μ and σ = 0.08(S/m)¸ |f Ē =â₂6e¯* (V/m), compute: a) The propagation constant, b) The wavelength and the phase velocity up.

(b) The circuit in Figure Q2 (b) below shows a rectifier circuit where Vin is a 10kHz sine wave with an amplitude of 2Vpp and RL is 10k. (i) (iii) The componet between A and B is a PN diode, sketch and label its silicon structure and explain its characteristics. Sketch the waveforms you would see at A and B and explain or sketch how you would connect your scope probes to measure them. Label your sketches clearly showing values and axis details. Comment on any similarities or differences between the waveforms at A and B.

+12V D7 D8 R3 Vo = ? 2.2k2 Determine: a. State of D7 if D7 is Si diode b. State of D8 if D8 is Ge diode c. Output voltage Vo +

Dopant density (cm-³) 1021 1020 1019 1018 1017 1016 10¹5 1014 1013 10¹2, 10-4 10-3 10-¹ 10⁰ 10¹ 10² 10³ 104 Resistivity (ohm-cm) FIGURE 2-8 Conversion between resistivity and dopant density of silicon at room temperature. (After [3].) N type 10-2 P type EXAMPLE 2-3 Temperature Dependence of Resistance a. What is the resistivity, p, of silicon doped with 10¹7cm-3 of arsenic? b. What is the resistance, R, of a piece of this silicon material 1 um long and 0.1 μm² in cross-sectional area? c. By what factor will R increase (or decrease) from T = 300 K to T = 400 K? d. What As concentration should one choose if she wishes to minimize the change in (c)?

Calculate the equivalent resistances Rin of the following circuits. (The resistance value of the diodes in the conduction will be 0, the resistance value of the diodes in the insulation will be taken as infinity. R1=10ohm