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1.4. Reactance of short thin wire at high frequencies. If a thin wire 1 cm long is suspended at least a few centimeter away from any nearby conductors, it will have an equivalent inductance of about 10nH (10-9H). Using the inductive reactance formula X, =2zfL, calculate the reactance of this length of wire at (a) f =1 MHz and (b) f2 =1 GHz (GHz = gigahertz, pronounced "gig-a-hertz,"= 10°Hz). This shows how parts of a circuit you would not normally consider important, such as ', wire leads, can begin to play a significant role in the circuit at high frequencies. 2.6. Capacitance of diode at high frequencies. At high frequencies, the reverse-bias capacitance of a signal diode can limit its performance as a detector (rectifier for small signals). Suppose a signal source at a frequency f =2.4 GHz has an output impedance of Z OUT =50Q2. If you model a detector diode as a simple capacitor with junction capacitance Cj: (a) Draw the equivalent circuit of the signal source as a voltage source Vs in series with a resistance Z OUT3 and connect it to the junction capacitance C1 that returns the signal to ground. (b) Calculate the maximum value of C, that will allow 70.7% of Vs to appear across the diode capacitance. This problem shows why a high-frequency signal diode must have a small junction capacitance. 2.8. Heat loss and efficiency of power FET. Suppose you are designing a system in which a power FET is on for 50% of the time and off for the other 50% of the time, with a switching frequency between these two states of 1 kHz. When the device is off (no current flow), the applied voltage is 550V. When the device is on, it conducts a current of 45A. The R DS(ON) of the device is specified to be 50mQ. (a) What is the average power P. D(AVG) dissipated in the device? (b) If the total thermal resistance R. TH from the device junction at temperature T, to the ambient temperature T. A is 1.2°C W-1, how hot will the junction become if T. =40°C? A (c) If the total applied voltage of 550V is reduced by the voltage drop through the device while it is on, calculate the average power P. delivered to the L load. What is the system efficiency, measured as the fraction P. /P. where L IN' PIN is the total average input power? IN

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