Question:medium
A modulating signal 2sin (6.28 × 106) t is added to the carrier signal 4sin(12.56 × 109) t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be ______MHz.
A modulating signal 2sin (6.28 × 106) t is added to the carrier signal 4sin(12.56 × 109) t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be ______MHz.
Updated On: Mar 13, 2026
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Correct Answer: 2
Solution and Explanation
To find the bandwidth of the output signal after passing through a band pass filter, we first need to identify the key components of the amplitude modulation process:
- Modulating Signal: m(t) = 2sin(6.28 × 106t). The frequency of the modulating signal, fm, is 1 MHz since f = \(\frac{frequency\ in\ radians}{2\pi}\).
- Carrier Signal: c(t) = 4sin(12.56 × 109t). The frequency of the carrier signal, fc, is 2 GHz using the same formula.
In amplitude modulation, the resulting signal after modulation consists of the carrier frequency and two sidebands:
- Upper Sideband (USB): fc + fm = 2 GHz + 1 MHz = 2001 MHz
- Lower Sideband (LSB): fc - fm = 2 GHz - 1 MHz = 1999 MHz
The bandwidth of the amplitude-modulated signal is twice the frequency of the modulating signal: BW = 2 × fm = 2 MHz.
Given the problem requires the bandwidth of the output signal, and the calculated bandwidth of 2 MHz matches the expected range, the solution is confirmed.
Thus, the bandwidth of the output signal of the band pass filter is 2 MHz.
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