FM Wave Parameters Quiz

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Questions and Answers

What is the carrier frequency of the given FM wave represented by the equation 𝑣(𝑡) = 12 cos(6 × 10^8𝑡 + 5 sin(1250𝑡))?

The carrier frequency is 100 MHz.

Calculate the modulation index for the given FM wave.

The modulation index is 5.

Identify the modulating frequency from the voltage equation of the FM wave.

The modulating frequency is approximately 200 Hz.

Determine the maximum deviation of the FM wave.

<p>The maximum deviation is 5 kHz.</p> Signup and view all the answers

What power will this FM wave dissipate in a 10 Ohm resistor?

<p>The power dissipated is 72 Watts.</p> Signup and view all the answers

Flashcards

Carrier Frequency

The frequency of the carrier wave in an FM signal, represented by the coefficient of "t" in the cosine term of the voltage equation.

Modulation Index

The ratio of the maximum frequency deviation to the modulating frequency, reflecting the extent of frequency variation.

Modulating Frequency

The frequency of the modulating signal which modifies the carrier wave, determined by the coefficient of "t" inside the sine function.

Maximum Frequency Deviation

The maximum variation in frequency from the carrier frequency, calculated as the product of the modulation index and the modulating frequency.

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Power Dissipation

The power dissipated by the FM wave in a resistor is determined using the RMS voltage of the wave and the resistance. In this case, the RMS voltage of the FM wave is found by dividing the amplitude (12 V) by the square root of 2. Using the formula P = V^2/R, where P is power, V is voltage and R is resistance, the dissipated power is calculated as (12/√2)^2/10, which results in 7.2 Watts.

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Study Notes

FM Wave Parameters

Carrier frequency: 6 × 10⁸ Hz
Modulation index: 5
Modulating frequency: 1250 Hz
Maximum deviation: calculated from modulation index(5) and modulating frequency(1250Hz), but needs more information as a calculation is needed for the value of maximum instantaneous frequency deviation.
Power dissipation in 10Ω resistor: cannot be determined without knowing the amplitude of the carrier wave (12 in the given equation is voltage, not the amplitude of the carrier wave). A complete equation for the voltage would be needed