HW10_Soln - ECE 200 Fall 2007 Homework 10 Solution...

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Unformatted text preview: ECE 200 Fall 2007 Homework 10 Solution Transmission and Reception of Radio Signals [12 pts total] 1. An analog multiplier chip generates an output waveform proportional to the timedomain product of two or more input signals. If the two input signals applied to the multiplier are given by v1 (t ) = (10V ) cos (2 1000 t ) and 2! v 2 (t ) = (3V ) cos (2 100 t ) + (2 V ) cos (2 200 t ) + (1V ) cos ( 2! 300 t ) , 2! 2! 2 then the output will be v12 (t ) = v1 (t ) v 2 (t ). (a) Calculate and sketch the power spectrum of the input signals. (b) Calculate and sketch the power spectrum of the signal at the output. Remember that Power = Vrms2/(1Ohm) = which for sinusoids = V2amplitude/2 Input 1 Power (v1) in Watts Power (v2) in Watts 50W Input 2 Power (v12) in Watts 4.5W Output 112.5W 112.5W 2W 0.5W f (Hz) 100 200 300 50W 12.5W 700 800 900 50W 12.5W f (Hz) 1100 1200 1300 f (Hz) 1000 [12 pts total] 2. An AM signal is generated using the signals of the previous problem (i.e., v1 (t ) = vc (t ) ! carrier signal , and v m (t ) = v 2 (t ) ! mod ulating signal ) and by applying a DC offset voltage of V DC = 5V to the modulating signal. (a) Roughly sketch the magnitude spectrum of the AM signal. (b) Calculate the signal power in Watts and dBW at each frequency and show the results on a frequency spectrum plot (i.e. power spectra in both units). (c) Determine the fraction (in Watts) of the total signal power needed to broadcast just the carrier frequency. Note that this is the power "wasted" since it does not contain any broadcast information (the carrier is the same regardless of vm(t)). [16 pts total] (will also accept answers that indicate Ac*Vdc = 4V) [10 pts total] [21 pts total] [11 pts total] ...
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