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ps1_2011

# ps1_2011 - ECE 2c problem set(Fourier Series and Fourier...

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1 ECE 2c problem set (Fourier Series and Fourier Transforms) Problem 1: Practical application of Fourier series. The drawing shows the concept of a switched-mode radio- frequency transmitter. These use switches to generate a square wave signal which is then filtered to produce the desired sine-wave. The 2 switches are in opposite phase and produce a 1 GHz square wave at their junction point. The LC filter passes only the 1 GHz fundamental compent to the load. (a) Find the AC voltage at the load and (b) if the load is 100 Ohms, find the power. (c) if we change the filter so that it passes only *5GHz*, again find the AC voltage at the load and the load power. Problem 2: Plot the following functions over one cycle , where f =1 GHz. Plot at least 28 points/waveform. To keep it from getting tedious, please use excel, Matlab, or some other computer program to calculate and plot. ) 2 cos( 1 ) ( 1 ft V t V ) 2 * 3 cos( 1 ) 3 / 1 ( ) ( ) ( 1 3 ft V t V t V ) 2 * 5 cos( 1 ) 5 / 1 ( ) ( ) ( 3 5 ft V t V t V ) ( ) ( 5 7 t V t V ) 2 * 7 cos( 1 ) 7 / 1 ( ft V Problem 3: Now do the same for these functions.

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