Question

A 100 MHz carrier wave has a peak voltage of 5 volts. The carrier is frequency modulated (FM) by a sinusoidal modulating signal or waveform of frequency 2 KHz such that the frequency deviation ?f is 75kHZ. The modulated waveform passes through zero and is increasing at t=0. Determine the expression for the modulated carrier waveform. What are the types of Frequency Modulation? Define the Carson's Rule for FM. Write the mathematical expression for single-tone frequency modulation and define the Modulation Index of FM.

          A 100 MHz carrier wave has a peak voltage of 5 volts. The carrier is frequency modulated (FM) by a sinusoidal modulating signal or waveform of frequency 2 KHz such that the frequency deviation ?f is 75kHZ. The modulated waveform passes through zero and is increasing at t=0. Determine the expression for the modulated carrier waveform.

What are the types of Frequency Modulation?

Define the Carson's Rule for FM.

Write the mathematical expression for single-tone frequency modulation and define the Modulation Index of FM.

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A 100 MHz carrier wave has a peak voltage of 5 volts. The carrier is frequency modulated (FM) by a sinusoidal modulating signal or waveform of frequency 2 KHz such that the frequency deviation ?f is 75kHZ. The modulated waveform passes through zero and is increasing at t=0. Determine the expression for the modulated carrier waveform.

What are the types of Frequency Modulation?

Define the Carson's Rule for FM.

Write the mathematical expression for single-tone frequency modulation and define the Modulation Index of FM.

Added by Nicholas H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Adi S

04/16/2024

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A 100 MHz carrier wave has a peak voltage of 5 volts. The carrier is frequency modulated (FM) by a sinusoidal modulating signal or waveform of frequency 2 kHz such that the frequency deviation Δf is 75 kHz. The modulated waveform passes through zero and is increasing at t=0. Determine the expression for the modulated carrier waveform.

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Transcript

00:01 We can use the equation for frequency modulation.

00:04 Vmt is equal to vc into cos into ωc into t plus β into sin ωm into t.

00:14 Where vmt is instantaneous voltage of modulated waveform.

00:19 Vc is peak voltage from the carrier wave.

00:24 Ωc is equal to 2πfc.

00:27 The angular frequency of the carrier wave beta is modulation index omega m is 2 pi fm is angular frequency of the modulating signal t is time given fc is equal to 100 megahertz which is equal to 110 to per 6 hertz vc is 5 v fm is 2 into 10 to per 3 hertz delta t is 75 into 10 to per 3 hertz beta is equal to delta f by fm 75 into 10 to the 3 by 2 into 10 to the 3 which is equal to 37 .5 from the equation when we put the values we get the expression for the modulated carrier wavelength is vmt is equal to 5 into cos 2 pi into 100 into 10 to power 6 t plus 37 .5 into sine 2 pi into 2 into 10 to power 3 into t number 2 the frequency modulation fm includes narrowband frequency modulator this used in two way radio communication system wideband frequency modulator is used in high federated audio broadcasting phase modulation among many frequency modulator system implement a combination of frequency and phase modulation the formula to estimate the bandwidth of the frequency modulates signal bandwidth b is equal to 2 into beta plus fm here b is approximate bandwidth of frequency modulator signal beta is maximum frequency deviation fm is maximum frequency of modulating signal expression for single tone frequency modulation fm with a sinusoidal modulating signal is vt is equal to vc into cos 2 pi fc into t plus beta into sine 2 pi fm into t here vt is instantaneous voltage of the modulated wavelength...

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