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An FM signal with a frequency deviation of 10 KHz and modulation frequency of 5 KHz is applied to two frequency multipliers connected in cascade. The first multiplier doubles the frequency and second multiplier triples the frequency. Determine the frequency deviation and the modulation index of the FM signal obtained at the second multiplier output. What is the frequency separation of the adiacent side frequencies of this FM signal?

Ask by Davies Gordon. in India
Jan 04,2025

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After the frequency multipliers, the FM signal has a frequency deviation of 60 kHz, a modulation index of 2, and adjacent side frequencies separated by 30 kHz.

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To determine the frequency deviation and modulation index after passing through the two frequency multipliers, we start with the initial conditions: 1. **Frequency Deviation Calculation:** The initial frequency deviation (Δf) is 10 kHz. When we double the frequency in the first multiplier, the frequency deviation also doubles. - After the first multiplier (doubling): \[ Δf' = 2 × 10 \text{ kHz} = 20 \text{ kHz} \] Then, we triple the frequency in the second multiplier, which also triples the frequency deviation: - After the second multiplier (tripling): \[ Δf'' = 3 × 20 \text{ kHz} = 60 \text{ kHz} \] 2. **Modulation Index Calculation:** The modulation index (β) is calculated as the ratio of the frequency deviation to the modulation frequency. The original modulation frequency is 5 kHz. - Calculating modulation index after both multipliers: \[ β = \frac{Δf''}{f_m} = \frac{60 \text{ kHz}}{5 \text{ kHz}} = 12 \] 3. **Adjacent Side Frequencies Separation:** The frequency separation of adjacent side frequencies in an FM signal can be determined using the formula \( f = 2Δf'' \). - Thus, frequency separation: \[ f = 2 × 60 \text{ kHz} = 120 \text{ kHz} \] So, after cascading two frequency multipliers, the output FM signal has a frequency deviation of 60 kHz, a modulation index of 12, and the frequency separation of the adjacent side frequencies is 120 kHz.

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