SOLVED PROBLEM - Frequency Modulation - by CARSON's RULE Modulation Techniques

Summary

In this example, the process of calculating the deviation ratio and bandwidth for an FM system is explained using the provided values. With a maximum deviation of 90 kHz and a maximum modulation frequency of 15 kHz, the deviation ratio is calculated as 6. Applying Carson's rule, the bandwidth is determined to be 210 kHz. The explanation outlines the formulas for both the deviation ratio and bandwidth, providing a clear understanding of these important FM system parameters.

Takeaways

• 😀 The maximum deviation in the FM system is 90 kHz.
• 😀 The maximum modulation frequency in the FM system is 15 kHz.
• 😀 The deviation ratio is calculated as the maximum deviation divided by the maximum modulation frequency.
• 😀 The formula for the deviation ratio is D = Δmax / Fmax.
• 😀 Substituting the values, the deviation ratio (D) comes out to be 6 kHz.
• 😀 The bandwidth of an FM system can be calculated using Carson's Rule.
• 😀 Carson's Rule formula for bandwidth is: Bandwidth = 2 × (Δmax + Fmax).
• 😀 The maximum deviation (Δmax) used in the bandwidth calculation is 90 kHz.
• 😀 The maximum modulation frequency (Fmax) used in the bandwidth calculation is 15 kHz.
• 😀 Substituting the values into Carson’s Rule, the bandwidth is calculated as 210 kHz.

Q & A

What is the formula for calculating the deviation ratio in an FM system?

The deviation ratio (D) is calculated using the formula: D = Δ_max / F_max, where Δ_max is the maximum frequency deviation and F_max is the maximum modulation frequency.

What is the formula for calculating the bandwidth of an FM system using Carson's rule?

The bandwidth of an FM system using Carson's rule is calculated as: Bandwidth = 2 × (Δ_max + F_max), where Δ_max is the maximum frequency deviation and F_max is the maximum modulation frequency.

What values are given for the maximum deviation and maximum modulation frequency in this example?

In this example, the maximum deviation (Δ_max) is given as 90 kHz, and the maximum modulation frequency (F_max) is given as 15 kHz.

How is the deviation ratio calculated for this example?

The deviation ratio (D) is calculated as: D = Δ_max / F_max = 90 kHz / 15 kHz = 6.

What is the deviation ratio for the given example?

The deviation ratio for the given example is 6.

What is the bandwidth of the FM system using Carson's rule in this example?

The bandwidth of the FM system is calculated as: Bandwidth = 2 × (Δ_max + F_max) = 2 × (90 kHz + 15 kHz) = 210 kHz.

How does Carson's rule help in calculating bandwidth for FM systems?

Carson's rule helps estimate the bandwidth of an FM system by taking into account both the maximum frequency deviation and the maximum modulation frequency, ensuring that the bandwidth covers the necessary range for the modulated signal.

What does the maximum deviation in an FM system represent?

The maximum deviation (Δ_max) represents the maximum shift in the frequency of the carrier signal caused by the modulation signal.

Why is the modulation frequency important in determining the bandwidth of an FM system?

The modulation frequency (F_max) determines how rapidly the carrier frequency changes and affects the required bandwidth to accurately transmit the modulated signal without distortion.

What role does the deviation ratio play in an FM system?

The deviation ratio indicates the extent of frequency deviation relative to the modulation frequency. A higher deviation ratio typically results in a wider bandwidth and better signal quality in an FM system.