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Calculating peak frequency deviation and Carson's rule bandwidth

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A baseband signal has a frequency range from 50 Hz to 15.0 kHz. The signal is transmitted using frequency modulation. The FM transmitter has a modulation constant of 100 kHz per volt.

a. A 1 volt peak sine wave signal at a frequency of 5 kHz is applied to the modulation terminal of the FM transmitter. What is the peak frequency deviation of the FM carrier?

b. For the signal described in part (a) above, what is the Carson's rule bandwidth of the FM signal?

c. Is the RF signal in part (b) above a wideband FM or a narrowband FM signal?

d. What is the FM improvement factor for this signal?

e. Is AGC (automatic gain control) required in an FM broadcast receiver?

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The expert examines peak frequency deviations and Carson's rule bandwidth. The signal is described.

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Please see the attached answers. Thanks.

A baseband signal has a frequency range from 50 Hz to 15.0 kHz. The signal is transmitted using frequency modulation. The FM transmitter has a modulation constant of 100 kHz per volt.

a. A 1 volt peak sine wave signal at a frequency of 5 kHz is applied to
the modulation terminal of the FM transmitter. What is the peak
frequency deviation of the FM carrier?

Peak frequency deviation is the product of modulation constant and the peak ...

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