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Tunable Bandpass
i want to solve this problem in communication engineering ?
A signal generator that produces +-1 V amplitude square wave in a 1(ohm) system where the fundamental frequency , f1, is tunable from 1khz to 50Mhz.. , An ideal bandpass filter with a center frequency of 175MHZ and a bandwidth of 30MHZ(+-15 MHZ).
(1) Select an f1 such that when the signal generator is cascaded with the filter that the output will be a single tone at 180 MHZ .There might be more than one correct answer.
(2) Calculate the amplitude of the resulting sinusoid.
180 is not divisible by 50, but it is by 30 MHz.
So if you set the generator at 30 MHz, the 5th harmonic, 180 MHz will pass through the filter, but the other harmonics at 150 and 210 MHz will not.
Other solutions would be the 8th harmonic of 20 MHz, but square waves don't have even harmonics.
But the 11th harmonic of 15 MHz would work.
(2)The amplitude you can determine by using fourier Analysis to get the amplitude of the 180 MHz harmonic. Square wave is a standard exercise, and it can be looked up. The 5th harmonic is:
(4/π)(1/5)sin(5πft)
and that translates to a peak amplitude of 0.255 volts, or RMS of 0.180 volts
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